YES Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z060-split.srs

Termination w.r.t. Q of the given QTRS could be proven:

0 QTRS
↳1 FlatCCProof (⇔, 0 ms)
↳2 QTRS
↳3 RootLabelingProof (⇔, 119 ms)
↳4 QTRS
↳5 QTRSRRRProof (⇔, 4227 ms)
↳6 QTRS
↳7 QTRSRRRProof (⇔, 106 ms)
↳8 QTRS
↳9 QTRSRRRProof (⇔, 64 ms)
↳10 QTRS
↳11 QTRSRRRProof (⇔, 38 ms)
↳12 QTRS
↳13 QTRSRRRProof (⇔, 60 ms)
↳14 QTRS
↳15 DependencyPairsProof (⇔, 57 ms)
↳16 QDP
↳17 DependencyGraphProof (⇔, 0 ms)
↳18 AND
    ↳19 QDP
        ↳20 UsableRulesProof (⇔, 1 ms)
        ↳21 QDP
        ↳22 QDPOrderProof (⇔, 0 ms)
        ↳23 QDP
        ↳24 QDPOrderProof (⇔, 421 ms)
        ↳25 QDP
        ↳26 PisEmptyProof (⇔, 0 ms)
        ↳27 YES
    ↳28 QDP
        ↳29 UsableRulesProof (⇔, 0 ms)
        ↳30 QDP
        ↳31 QDPOrderProof (⇔, 10 ms)
        ↳32 QDP
        ↳33 DependencyGraphProof (⇔, 0 ms)
        ↳34 QDP
        ↳35 QDPOrderProof (⇔, 922 ms)
        ↳36 QDP
        ↳37 UsableRulesProof (⇔, 0 ms)
        ↳38 QDP
        ↳39 QDPOrderProof (⇔, 0 ms)
        ↳40 QDP
        ↳41 PisEmptyProof (⇔, 0 ms)
        ↳42 YES
    ↳43 QDP
        ↳44 UsableRulesProof (⇔, 0 ms)
        ↳45 QDP
        ↳46 QDPOrderProof (⇔, 23 ms)
        ↳47 QDP
        ↳48 DependencyGraphProof (⇔, 0 ms)
        ↳49 QDP
        ↳50 QDPOrderProof (⇔, 924 ms)
        ↳51 QDP
        ↳52 UsableRulesProof (⇔, 0 ms)
        ↳53 QDP
        ↳54 QDPOrderProof (⇔, 0 ms)
        ↳55 QDP
        ↳56 PisEmptyProof (⇔, 0 ms)
        ↳57 YES
    ↳58 QDP
        ↳59 UsableRulesProof (⇔, 0 ms)
        ↳60 QDP
        ↳61 QDPOrderProof (⇔, 6 ms)
        ↳62 QDP
        ↳63 DependencyGraphProof (⇔, 0 ms)
        ↳64 QDP
        ↳65 QDPOrderProof (⇔, 944 ms)
        ↳66 QDP
        ↳67 UsableRulesProof (⇔, 0 ms)
        ↳68 QDP
        ↳69 QDPOrderProof (⇔, 0 ms)
        ↳70 QDP
        ↳71 PisEmptyProof (⇔, 0 ms)
        ↳72 YES
    ↳73 QDP
        ↳74 UsableRulesProof (⇔, 0 ms)
        ↳75 QDP
        ↳76 QDPOrderProof (⇔, 7 ms)
        ↳77 QDP
        ↳78 DependencyGraphProof (⇔, 0 ms)
        ↳79 QDP
        ↳80 QDPOrderProof (⇔, 969 ms)
        ↳81 QDP
        ↳82 UsableRulesProof (⇔, 0 ms)
        ↳83 QDP
        ↳84 QDPOrderProof (⇔, 0 ms)
        ↳85 QDP
        ↳86 PisEmptyProof (⇔, 0 ms)
        ↳87 YES
    ↳88 QDP
        ↳89 UsableRulesProof (⇔, 0 ms)
        ↳90 QDP
        ↳91 QDPOrderProof (⇔, 21 ms)
        ↳92 QDP
        ↳93 DependencyGraphProof (⇔, 0 ms)
        ↳94 QDP
        ↳95 QDPOrderProof (⇔, 900 ms)
        ↳96 QDP
        ↳97 UsableRulesProof (⇔, 0 ms)
        ↳98 QDP
        ↳99 QDPOrderProof (⇔, 0 ms)
        ↳100 QDP
        ↳101 PisEmptyProof (⇔, 0 ms)
        ↳102 YES
    ↳103 QDP
        ↳104 UsableRulesProof (⇔, 0 ms)
        ↳105 QDP
        ↳106 QDPOrderProof (⇔, 56 ms)
        ↳107 QDP
        ↳108 DependencyGraphProof (⇔, 0 ms)
        ↳109 TRUE
    ↳110 QDP
        ↳111 UsableRulesProof (⇔, 0 ms)
        ↳112 QDP
        ↳113 QDPOrderProof (⇔, 26 ms)
        ↳114 QDP
        ↳115 DependencyGraphProof (⇔, 0 ms)
        ↳116 TRUE
    ↳117 QDP
        ↳118 UsableRulesProof (⇔, 0 ms)
        ↳119 QDP
        ↳120 QDPOrderProof (⇔, 40 ms)
        ↳121 QDP
        ↳122 DependencyGraphProof (⇔, 0 ms)
        ↳123 TRUE
    ↳124 QDP
        ↳125 UsableRulesProof (⇔, 0 ms)
        ↳126 QDP
        ↳127 QDPOrderProof (⇔, 44 ms)
        ↳128 QDP
        ↳129 DependencyGraphProof (⇔, 0 ms)
        ↳130 TRUE
    ↳131 QDP
        ↳132 UsableRulesProof (⇔, 0 ms)
        ↳133 QDP
        ↳134 QDPOrderProof (⇔, 30 ms)
        ↳135 QDP
        ↳136 DependencyGraphProof (⇔, 0 ms)
        ↳137 TRUE
    ↳138 QDP
        ↳139 UsableRulesProof (⇔, 0 ms)
        ↳140 QDP
        ↳141 QDPOrderProof (⇔, 40 ms)
        ↳142 QDP
        ↳143 DependencyGraphProof (⇔, 0 ms)
        ↳144 TRUE
    ↳145 QDP
        ↳146 UsableRulesProof (⇔, 0 ms)
        ↳147 QDP
        ↳148 QDPOrderProof (⇔, 20 ms)
        ↳149 QDP
        ↳150 DependencyGraphProof (⇔, 0 ms)
        ↳151 TRUE
    ↳152 QDP
        ↳153 UsableRulesProof (⇔, 0 ms)
        ↳154 QDP
        ↳155 QDPOrderProof (⇔, 54 ms)
        ↳156 QDP
        ↳157 DependencyGraphProof (⇔, 0 ms)
        ↳158 TRUE
    ↳159 QDP
        ↳160 UsableRulesProof (⇔, 0 ms)
        ↳161 QDP
        ↳162 QDPOrderProof (⇔, 28 ms)
        ↳163 QDP
        ↳164 DependencyGraphProof (⇔, 0 ms)
        ↳165 TRUE
    ↳166 QDP
        ↳167 UsableRulesProof (⇔, 0 ms)
        ↳168 QDP
        ↳169 QDPOrderProof (⇔, 21 ms)
        ↳170 QDP
        ↳171 DependencyGraphProof (⇔, 0 ms)
        ↳172 TRUE
    ↳173 QDP
        ↳174 UsableRulesProof (⇔, 0 ms)
        ↳175 QDP
        ↳176 QDPOrderProof (⇔, 22 ms)
        ↳177 QDP
        ↳178 DependencyGraphProof (⇔, 0 ms)
        ↳179 TRUE
    ↳180 QDP
        ↳181 UsableRulesProof (⇔, 0 ms)
        ↳182 QDP
        ↳183 QDPOrderProof (⇔, 71 ms)
        ↳184 QDP
        ↳185 DependencyGraphProof (⇔, 0 ms)
        ↳186 TRUE
    ↳187 QDP
        ↳188 UsableRulesProof (⇔, 0 ms)
        ↳189 QDP
        ↳190 QDPOrderProof (⇔, 59 ms)
        ↳191 QDP
        ↳192 DependencyGraphProof (⇔, 0 ms)
        ↳193 TRUE

(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

Begin(b(a(b(b(b(x)))))) → Wait(Right1(x))
Begin(a(b(b(b(x))))) → Wait(Right2(x))
Begin(b(b(b(x)))) → Wait(Right3(x))
Begin(b(b(x))) → Wait(Right4(x))
Begin(b(x)) → Wait(Right5(x))
Right1(b(End(x))) → Left(a(b(b(b(b(b(a(End(x)))))))))
Right2(b(b(End(x)))) → Left(a(b(b(b(b(b(a(End(x)))))))))
Right3(b(b(a(End(x))))) → Left(a(b(b(b(b(b(a(End(x)))))))))
Right4(b(b(a(b(End(x)))))) → Left(a(b(b(b(b(b(a(End(x)))))))))
Right5(b(b(a(b(b(End(x))))))) → Left(a(b(b(b(b(b(a(End(x)))))))))
Right1(b(x)) → Ab(Right1(x))
Right2(b(x)) → Ab(Right2(x))
Right3(b(x)) → Ab(Right3(x))
Right4(b(x)) → Ab(Right4(x))
Right5(b(x)) → Ab(Right5(x))
Right1(a(x)) → Aa(Right1(x))
Right2(a(x)) → Aa(Right2(x))
Right3(a(x)) → Aa(Right3(x))
Right4(a(x)) → Aa(Right4(x))
Right5(a(x)) → Aa(Right5(x))
Ab(Left(x)) → Left(b(x))
Aa(Left(x)) → Left(a(x))
Wait(Left(x)) → Begin(x)
b(b(a(b(b(b(x)))))) → a(b(b(b(b(b(a(x)))))))

Q is empty.

(1) FlatCCProof (EQUIVALENT transformation)

We used flat context closure [ROOTLAB] As Q is empty the flat context closure was sound AND complete.

(2) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

Begin(Begin(b(a(b(b(b(x))))))) → Begin(Wait(Right1(x)))
b(Begin(b(a(b(b(b(x))))))) → b(Wait(Right1(x)))
a(Begin(b(a(b(b(b(x))))))) → a(Wait(Right1(x)))
Wait(Begin(b(a(b(b(b(x))))))) → Wait(Wait(Right1(x)))
Right1(Begin(b(a(b(b(b(x))))))) → Right1(Wait(Right1(x)))
Right2(Begin(b(a(b(b(b(x))))))) → Right2(Wait(Right1(x)))
Right3(Begin(b(a(b(b(b(x))))))) → Right3(Wait(Right1(x)))
Right4(Begin(b(a(b(b(b(x))))))) → Right4(Wait(Right1(x)))
Right5(Begin(b(a(b(b(b(x))))))) → Right5(Wait(Right1(x)))
End(Begin(b(a(b(b(b(x))))))) → End(Wait(Right1(x)))
Left(Begin(b(a(b(b(b(x))))))) → Left(Wait(Right1(x)))
Ab(Begin(b(a(b(b(b(x))))))) → Ab(Wait(Right1(x)))
Aa(Begin(b(a(b(b(b(x))))))) → Aa(Wait(Right1(x)))
Begin(Begin(a(b(b(b(x)))))) → Begin(Wait(Right2(x)))
b(Begin(a(b(b(b(x)))))) → b(Wait(Right2(x)))
a(Begin(a(b(b(b(x)))))) → a(Wait(Right2(x)))
Wait(Begin(a(b(b(b(x)))))) → Wait(Wait(Right2(x)))
Right1(Begin(a(b(b(b(x)))))) → Right1(Wait(Right2(x)))
Right2(Begin(a(b(b(b(x)))))) → Right2(Wait(Right2(x)))
Right3(Begin(a(b(b(b(x)))))) → Right3(Wait(Right2(x)))
Right4(Begin(a(b(b(b(x)))))) → Right4(Wait(Right2(x)))
Right5(Begin(a(b(b(b(x)))))) → Right5(Wait(Right2(x)))
End(Begin(a(b(b(b(x)))))) → End(Wait(Right2(x)))
Left(Begin(a(b(b(b(x)))))) → Left(Wait(Right2(x)))
Ab(Begin(a(b(b(b(x)))))) → Ab(Wait(Right2(x)))
Aa(Begin(a(b(b(b(x)))))) → Aa(Wait(Right2(x)))
Begin(Begin(b(b(b(x))))) → Begin(Wait(Right3(x)))
b(Begin(b(b(b(x))))) → b(Wait(Right3(x)))
a(Begin(b(b(b(x))))) → a(Wait(Right3(x)))
Wait(Begin(b(b(b(x))))) → Wait(Wait(Right3(x)))
Right1(Begin(b(b(b(x))))) → Right1(Wait(Right3(x)))
Right2(Begin(b(b(b(x))))) → Right2(Wait(Right3(x)))
Right3(Begin(b(b(b(x))))) → Right3(Wait(Right3(x)))
Right4(Begin(b(b(b(x))))) → Right4(Wait(Right3(x)))
Right5(Begin(b(b(b(x))))) → Right5(Wait(Right3(x)))
End(Begin(b(b(b(x))))) → End(Wait(Right3(x)))
Left(Begin(b(b(b(x))))) → Left(Wait(Right3(x)))
Ab(Begin(b(b(b(x))))) → Ab(Wait(Right3(x)))
Aa(Begin(b(b(b(x))))) → Aa(Wait(Right3(x)))
Begin(Begin(b(b(x)))) → Begin(Wait(Right4(x)))
b(Begin(b(b(x)))) → b(Wait(Right4(x)))
a(Begin(b(b(x)))) → a(Wait(Right4(x)))
Wait(Begin(b(b(x)))) → Wait(Wait(Right4(x)))
Right1(Begin(b(b(x)))) → Right1(Wait(Right4(x)))
Right2(Begin(b(b(x)))) → Right2(Wait(Right4(x)))
Right3(Begin(b(b(x)))) → Right3(Wait(Right4(x)))
Right4(Begin(b(b(x)))) → Right4(Wait(Right4(x)))
Right5(Begin(b(b(x)))) → Right5(Wait(Right4(x)))
End(Begin(b(b(x)))) → End(Wait(Right4(x)))
Left(Begin(b(b(x)))) → Left(Wait(Right4(x)))
Ab(Begin(b(b(x)))) → Ab(Wait(Right4(x)))
Aa(Begin(b(b(x)))) → Aa(Wait(Right4(x)))
Begin(Begin(b(x))) → Begin(Wait(Right5(x)))
b(Begin(b(x))) → b(Wait(Right5(x)))
a(Begin(b(x))) → a(Wait(Right5(x)))
Wait(Begin(b(x))) → Wait(Wait(Right5(x)))
Right1(Begin(b(x))) → Right1(Wait(Right5(x)))
Right2(Begin(b(x))) → Right2(Wait(Right5(x)))
Right3(Begin(b(x))) → Right3(Wait(Right5(x)))
Right4(Begin(b(x))) → Right4(Wait(Right5(x)))
Right5(Begin(b(x))) → Right5(Wait(Right5(x)))
End(Begin(b(x))) → End(Wait(Right5(x)))
Left(Begin(b(x))) → Left(Wait(Right5(x)))
Ab(Begin(b(x))) → Ab(Wait(Right5(x)))
Aa(Begin(b(x))) → Aa(Wait(Right5(x)))
Begin(Right1(b(End(x)))) → Begin(Left(a(b(b(b(b(b(a(End(x))))))))))
b(Right1(b(End(x)))) → b(Left(a(b(b(b(b(b(a(End(x))))))))))
a(Right1(b(End(x)))) → a(Left(a(b(b(b(b(b(a(End(x))))))))))
Wait(Right1(b(End(x)))) → Wait(Left(a(b(b(b(b(b(a(End(x))))))))))
Right1(Right1(b(End(x)))) → Right1(Left(a(b(b(b(b(b(a(End(x))))))))))
Right2(Right1(b(End(x)))) → Right2(Left(a(b(b(b(b(b(a(End(x))))))))))
Right3(Right1(b(End(x)))) → Right3(Left(a(b(b(b(b(b(a(End(x))))))))))
Right4(Right1(b(End(x)))) → Right4(Left(a(b(b(b(b(b(a(End(x))))))))))
Right5(Right1(b(End(x)))) → Right5(Left(a(b(b(b(b(b(a(End(x))))))))))
End(Right1(b(End(x)))) → End(Left(a(b(b(b(b(b(a(End(x))))))))))
Left(Right1(b(End(x)))) → Left(Left(a(b(b(b(b(b(a(End(x))))))))))
Ab(Right1(b(End(x)))) → Ab(Left(a(b(b(b(b(b(a(End(x))))))))))
Aa(Right1(b(End(x)))) → Aa(Left(a(b(b(b(b(b(a(End(x))))))))))
Begin(Right2(b(b(End(x))))) → Begin(Left(a(b(b(b(b(b(a(End(x))))))))))
b(Right2(b(b(End(x))))) → b(Left(a(b(b(b(b(b(a(End(x))))))))))
a(Right2(b(b(End(x))))) → a(Left(a(b(b(b(b(b(a(End(x))))))))))
Wait(Right2(b(b(End(x))))) → Wait(Left(a(b(b(b(b(b(a(End(x))))))))))
Right1(Right2(b(b(End(x))))) → Right1(Left(a(b(b(b(b(b(a(End(x))))))))))
Right2(Right2(b(b(End(x))))) → Right2(Left(a(b(b(b(b(b(a(End(x))))))))))
Right3(Right2(b(b(End(x))))) → Right3(Left(a(b(b(b(b(b(a(End(x))))))))))
Right4(Right2(b(b(End(x))))) → Right4(Left(a(b(b(b(b(b(a(End(x))))))))))
Right5(Right2(b(b(End(x))))) → Right5(Left(a(b(b(b(b(b(a(End(x))))))))))
End(Right2(b(b(End(x))))) → End(Left(a(b(b(b(b(b(a(End(x))))))))))
Left(Right2(b(b(End(x))))) → Left(Left(a(b(b(b(b(b(a(End(x))))))))))
Ab(Right2(b(b(End(x))))) → Ab(Left(a(b(b(b(b(b(a(End(x))))))))))
Aa(Right2(b(b(End(x))))) → Aa(Left(a(b(b(b(b(b(a(End(x))))))))))
Begin(Right3(b(b(a(End(x)))))) → Begin(Left(a(b(b(b(b(b(a(End(x))))))))))
b(Right3(b(b(a(End(x)))))) → b(Left(a(b(b(b(b(b(a(End(x))))))))))
a(Right3(b(b(a(End(x)))))) → a(Left(a(b(b(b(b(b(a(End(x))))))))))
Wait(Right3(b(b(a(End(x)))))) → Wait(Left(a(b(b(b(b(b(a(End(x))))))))))
Right1(Right3(b(b(a(End(x)))))) → Right1(Left(a(b(b(b(b(b(a(End(x))))))))))
Right2(Right3(b(b(a(End(x)))))) → Right2(Left(a(b(b(b(b(b(a(End(x))))))))))
Right3(Right3(b(b(a(End(x)))))) → Right3(Left(a(b(b(b(b(b(a(End(x))))))))))
Right4(Right3(b(b(a(End(x)))))) → Right4(Left(a(b(b(b(b(b(a(End(x))))))))))
Right5(Right3(b(b(a(End(x)))))) → Right5(Left(a(b(b(b(b(b(a(End(x))))))))))
End(Right3(b(b(a(End(x)))))) → End(Left(a(b(b(b(b(b(a(End(x))))))))))
Left(Right3(b(b(a(End(x)))))) → Left(Left(a(b(b(b(b(b(a(End(x))))))))))
Ab(Right3(b(b(a(End(x)))))) → Ab(Left(a(b(b(b(b(b(a(End(x))))))))))
Aa(Right3(b(b(a(End(x)))))) → Aa(Left(a(b(b(b(b(b(a(End(x))))))))))
Begin(Right4(b(b(a(b(End(x))))))) → Begin(Left(a(b(b(b(b(b(a(End(x))))))))))
b(Right4(b(b(a(b(End(x))))))) → b(Left(a(b(b(b(b(b(a(End(x))))))))))
a(Right4(b(b(a(b(End(x))))))) → a(Left(a(b(b(b(b(b(a(End(x))))))))))
Wait(Right4(b(b(a(b(End(x))))))) → Wait(Left(a(b(b(b(b(b(a(End(x))))))))))
Right1(Right4(b(b(a(b(End(x))))))) → Right1(Left(a(b(b(b(b(b(a(End(x))))))))))
Right2(Right4(b(b(a(b(End(x))))))) → Right2(Left(a(b(b(b(b(b(a(End(x))))))))))
Right3(Right4(b(b(a(b(End(x))))))) → Right3(Left(a(b(b(b(b(b(a(End(x))))))))))
Right4(Right4(b(b(a(b(End(x))))))) → Right4(Left(a(b(b(b(b(b(a(End(x))))))))))
Right5(Right4(b(b(a(b(End(x))))))) → Right5(Left(a(b(b(b(b(b(a(End(x))))))))))
End(Right4(b(b(a(b(End(x))))))) → End(Left(a(b(b(b(b(b(a(End(x))))))))))
Left(Right4(b(b(a(b(End(x))))))) → Left(Left(a(b(b(b(b(b(a(End(x))))))))))
Ab(Right4(b(b(a(b(End(x))))))) → Ab(Left(a(b(b(b(b(b(a(End(x))))))))))
Aa(Right4(b(b(a(b(End(x))))))) → Aa(Left(a(b(b(b(b(b(a(End(x))))))))))
Begin(Right5(b(b(a(b(b(End(x)))))))) → Begin(Left(a(b(b(b(b(b(a(End(x))))))))))
b(Right5(b(b(a(b(b(End(x)))))))) → b(Left(a(b(b(b(b(b(a(End(x))))))))))
a(Right5(b(b(a(b(b(End(x)))))))) → a(Left(a(b(b(b(b(b(a(End(x))))))))))
Wait(Right5(b(b(a(b(b(End(x)))))))) → Wait(Left(a(b(b(b(b(b(a(End(x))))))))))
Right1(Right5(b(b(a(b(b(End(x)))))))) → Right1(Left(a(b(b(b(b(b(a(End(x))))))))))
Right2(Right5(b(b(a(b(b(End(x)))))))) → Right2(Left(a(b(b(b(b(b(a(End(x))))))))))
Right3(Right5(b(b(a(b(b(End(x)))))))) → Right3(Left(a(b(b(b(b(b(a(End(x))))))))))
Right4(Right5(b(b(a(b(b(End(x)))))))) → Right4(Left(a(b(b(b(b(b(a(End(x))))))))))
Right5(Right5(b(b(a(b(b(End(x)))))))) → Right5(Left(a(b(b(b(b(b(a(End(x))))))))))
End(Right5(b(b(a(b(b(End(x)))))))) → End(Left(a(b(b(b(b(b(a(End(x))))))))))
Left(Right5(b(b(a(b(b(End(x)))))))) → Left(Left(a(b(b(b(b(b(a(End(x))))))))))
Ab(Right5(b(b(a(b(b(End(x)))))))) → Ab(Left(a(b(b(b(b(b(a(End(x))))))))))
Aa(Right5(b(b(a(b(b(End(x)))))))) → Aa(Left(a(b(b(b(b(b(a(End(x))))))))))
Begin(Right1(b(x))) → Begin(Ab(Right1(x)))
b(Right1(b(x))) → b(Ab(Right1(x)))
a(Right1(b(x))) → a(Ab(Right1(x)))
Wait(Right1(b(x))) → Wait(Ab(Right1(x)))
Right1(Right1(b(x))) → Right1(Ab(Right1(x)))
Right2(Right1(b(x))) → Right2(Ab(Right1(x)))
Right3(Right1(b(x))) → Right3(Ab(Right1(x)))
Right4(Right1(b(x))) → Right4(Ab(Right1(x)))
Right5(Right1(b(x))) → Right5(Ab(Right1(x)))
End(Right1(b(x))) → End(Ab(Right1(x)))
Left(Right1(b(x))) → Left(Ab(Right1(x)))
Ab(Right1(b(x))) → Ab(Ab(Right1(x)))
Aa(Right1(b(x))) → Aa(Ab(Right1(x)))
Begin(Right2(b(x))) → Begin(Ab(Right2(x)))
b(Right2(b(x))) → b(Ab(Right2(x)))
a(Right2(b(x))) → a(Ab(Right2(x)))
Wait(Right2(b(x))) → Wait(Ab(Right2(x)))
Right1(Right2(b(x))) → Right1(Ab(Right2(x)))
Right2(Right2(b(x))) → Right2(Ab(Right2(x)))
Right3(Right2(b(x))) → Right3(Ab(Right2(x)))
Right4(Right2(b(x))) → Right4(Ab(Right2(x)))
Right5(Right2(b(x))) → Right5(Ab(Right2(x)))
End(Right2(b(x))) → End(Ab(Right2(x)))
Left(Right2(b(x))) → Left(Ab(Right2(x)))
Ab(Right2(b(x))) → Ab(Ab(Right2(x)))
Aa(Right2(b(x))) → Aa(Ab(Right2(x)))
Begin(Right3(b(x))) → Begin(Ab(Right3(x)))
b(Right3(b(x))) → b(Ab(Right3(x)))
a(Right3(b(x))) → a(Ab(Right3(x)))
Wait(Right3(b(x))) → Wait(Ab(Right3(x)))
Right1(Right3(b(x))) → Right1(Ab(Right3(x)))
Right2(Right3(b(x))) → Right2(Ab(Right3(x)))
Right3(Right3(b(x))) → Right3(Ab(Right3(x)))
Right4(Right3(b(x))) → Right4(Ab(Right3(x)))
Right5(Right3(b(x))) → Right5(Ab(Right3(x)))
End(Right3(b(x))) → End(Ab(Right3(x)))
Left(Right3(b(x))) → Left(Ab(Right3(x)))
Ab(Right3(b(x))) → Ab(Ab(Right3(x)))
Aa(Right3(b(x))) → Aa(Ab(Right3(x)))
Begin(Right4(b(x))) → Begin(Ab(Right4(x)))
b(Right4(b(x))) → b(Ab(Right4(x)))
a(Right4(b(x))) → a(Ab(Right4(x)))
Wait(Right4(b(x))) → Wait(Ab(Right4(x)))
Right1(Right4(b(x))) → Right1(Ab(Right4(x)))
Right2(Right4(b(x))) → Right2(Ab(Right4(x)))
Right3(Right4(b(x))) → Right3(Ab(Right4(x)))
Right4(Right4(b(x))) → Right4(Ab(Right4(x)))
Right5(Right4(b(x))) → Right5(Ab(Right4(x)))
End(Right4(b(x))) → End(Ab(Right4(x)))
Left(Right4(b(x))) → Left(Ab(Right4(x)))
Ab(Right4(b(x))) → Ab(Ab(Right4(x)))
Aa(Right4(b(x))) → Aa(Ab(Right4(x)))
Begin(Right5(b(x))) → Begin(Ab(Right5(x)))
b(Right5(b(x))) → b(Ab(Right5(x)))
a(Right5(b(x))) → a(Ab(Right5(x)))
Wait(Right5(b(x))) → Wait(Ab(Right5(x)))
Right1(Right5(b(x))) → Right1(Ab(Right5(x)))
Right2(Right5(b(x))) → Right2(Ab(Right5(x)))
Right3(Right5(b(x))) → Right3(Ab(Right5(x)))
Right4(Right5(b(x))) → Right4(Ab(Right5(x)))
Right5(Right5(b(x))) → Right5(Ab(Right5(x)))
End(Right5(b(x))) → End(Ab(Right5(x)))
Left(Right5(b(x))) → Left(Ab(Right5(x)))
Ab(Right5(b(x))) → Ab(Ab(Right5(x)))
Aa(Right5(b(x))) → Aa(Ab(Right5(x)))
Begin(Right1(a(x))) → Begin(Aa(Right1(x)))
b(Right1(a(x))) → b(Aa(Right1(x)))
a(Right1(a(x))) → a(Aa(Right1(x)))
Wait(Right1(a(x))) → Wait(Aa(Right1(x)))
Right1(Right1(a(x))) → Right1(Aa(Right1(x)))
Right2(Right1(a(x))) → Right2(Aa(Right1(x)))
Right3(Right1(a(x))) → Right3(Aa(Right1(x)))
Right4(Right1(a(x))) → Right4(Aa(Right1(x)))
Right5(Right1(a(x))) → Right5(Aa(Right1(x)))
End(Right1(a(x))) → End(Aa(Right1(x)))
Left(Right1(a(x))) → Left(Aa(Right1(x)))
Ab(Right1(a(x))) → Ab(Aa(Right1(x)))
Aa(Right1(a(x))) → Aa(Aa(Right1(x)))
Begin(Right2(a(x))) → Begin(Aa(Right2(x)))
b(Right2(a(x))) → b(Aa(Right2(x)))
a(Right2(a(x))) → a(Aa(Right2(x)))
Wait(Right2(a(x))) → Wait(Aa(Right2(x)))
Right1(Right2(a(x))) → Right1(Aa(Right2(x)))
Right2(Right2(a(x))) → Right2(Aa(Right2(x)))
Right3(Right2(a(x))) → Right3(Aa(Right2(x)))
Right4(Right2(a(x))) → Right4(Aa(Right2(x)))
Right5(Right2(a(x))) → Right5(Aa(Right2(x)))
End(Right2(a(x))) → End(Aa(Right2(x)))
Left(Right2(a(x))) → Left(Aa(Right2(x)))
Ab(Right2(a(x))) → Ab(Aa(Right2(x)))
Aa(Right2(a(x))) → Aa(Aa(Right2(x)))
Begin(Right3(a(x))) → Begin(Aa(Right3(x)))
b(Right3(a(x))) → b(Aa(Right3(x)))
a(Right3(a(x))) → a(Aa(Right3(x)))
Wait(Right3(a(x))) → Wait(Aa(Right3(x)))
Right1(Right3(a(x))) → Right1(Aa(Right3(x)))
Right2(Right3(a(x))) → Right2(Aa(Right3(x)))
Right3(Right3(a(x))) → Right3(Aa(Right3(x)))
Right4(Right3(a(x))) → Right4(Aa(Right3(x)))
Right5(Right3(a(x))) → Right5(Aa(Right3(x)))
End(Right3(a(x))) → End(Aa(Right3(x)))
Left(Right3(a(x))) → Left(Aa(Right3(x)))
Ab(Right3(a(x))) → Ab(Aa(Right3(x)))
Aa(Right3(a(x))) → Aa(Aa(Right3(x)))
Begin(Right4(a(x))) → Begin(Aa(Right4(x)))
b(Right4(a(x))) → b(Aa(Right4(x)))
a(Right4(a(x))) → a(Aa(Right4(x)))
Wait(Right4(a(x))) → Wait(Aa(Right4(x)))
Right1(Right4(a(x))) → Right1(Aa(Right4(x)))
Right2(Right4(a(x))) → Right2(Aa(Right4(x)))
Right3(Right4(a(x))) → Right3(Aa(Right4(x)))
Right4(Right4(a(x))) → Right4(Aa(Right4(x)))
Right5(Right4(a(x))) → Right5(Aa(Right4(x)))
End(Right4(a(x))) → End(Aa(Right4(x)))
Left(Right4(a(x))) → Left(Aa(Right4(x)))
Ab(Right4(a(x))) → Ab(Aa(Right4(x)))
Aa(Right4(a(x))) → Aa(Aa(Right4(x)))
Begin(Right5(a(x))) → Begin(Aa(Right5(x)))
b(Right5(a(x))) → b(Aa(Right5(x)))
a(Right5(a(x))) → a(Aa(Right5(x)))
Wait(Right5(a(x))) → Wait(Aa(Right5(x)))
Right1(Right5(a(x))) → Right1(Aa(Right5(x)))
Right2(Right5(a(x))) → Right2(Aa(Right5(x)))
Right3(Right5(a(x))) → Right3(Aa(Right5(x)))
Right4(Right5(a(x))) → Right4(Aa(Right5(x)))
Right5(Right5(a(x))) → Right5(Aa(Right5(x)))
End(Right5(a(x))) → End(Aa(Right5(x)))
Left(Right5(a(x))) → Left(Aa(Right5(x)))
Ab(Right5(a(x))) → Ab(Aa(Right5(x)))
Aa(Right5(a(x))) → Aa(Aa(Right5(x)))
Begin(Ab(Left(x))) → Begin(Left(b(x)))
b(Ab(Left(x))) → b(Left(b(x)))
a(Ab(Left(x))) → a(Left(b(x)))
Wait(Ab(Left(x))) → Wait(Left(b(x)))
Right1(Ab(Left(x))) → Right1(Left(b(x)))
Right2(Ab(Left(x))) → Right2(Left(b(x)))
Right3(Ab(Left(x))) → Right3(Left(b(x)))
Right4(Ab(Left(x))) → Right4(Left(b(x)))
Right5(Ab(Left(x))) → Right5(Left(b(x)))
End(Ab(Left(x))) → End(Left(b(x)))
Left(Ab(Left(x))) → Left(Left(b(x)))
Ab(Ab(Left(x))) → Ab(Left(b(x)))
Aa(Ab(Left(x))) → Aa(Left(b(x)))
Begin(Aa(Left(x))) → Begin(Left(a(x)))
b(Aa(Left(x))) → b(Left(a(x)))
a(Aa(Left(x))) → a(Left(a(x)))
Wait(Aa(Left(x))) → Wait(Left(a(x)))
Right1(Aa(Left(x))) → Right1(Left(a(x)))
Right2(Aa(Left(x))) → Right2(Left(a(x)))
Right3(Aa(Left(x))) → Right3(Left(a(x)))
Right4(Aa(Left(x))) → Right4(Left(a(x)))
Right5(Aa(Left(x))) → Right5(Left(a(x)))
End(Aa(Left(x))) → End(Left(a(x)))
Left(Aa(Left(x))) → Left(Left(a(x)))
Ab(Aa(Left(x))) → Ab(Left(a(x)))
Aa(Aa(Left(x))) → Aa(Left(a(x)))
Begin(Wait(Left(x))) → Begin(Begin(x))
b(Wait(Left(x))) → b(Begin(x))
a(Wait(Left(x))) → a(Begin(x))
Wait(Wait(Left(x))) → Wait(Begin(x))
Right1(Wait(Left(x))) → Right1(Begin(x))
Right2(Wait(Left(x))) → Right2(Begin(x))
Right3(Wait(Left(x))) → Right3(Begin(x))
Right4(Wait(Left(x))) → Right4(Begin(x))
Right5(Wait(Left(x))) → Right5(Begin(x))
End(Wait(Left(x))) → End(Begin(x))
Left(Wait(Left(x))) → Left(Begin(x))
Ab(Wait(Left(x))) → Ab(Begin(x))
Aa(Wait(Left(x))) → Aa(Begin(x))
Begin(b(b(a(b(b(b(x))))))) → Begin(a(b(b(b(b(b(a(x))))))))
b(b(b(a(b(b(b(x))))))) → b(a(b(b(b(b(b(a(x))))))))
a(b(b(a(b(b(b(x))))))) → a(a(b(b(b(b(b(a(x))))))))
Wait(b(b(a(b(b(b(x))))))) → Wait(a(b(b(b(b(b(a(x))))))))
Right1(b(b(a(b(b(b(x))))))) → Right1(a(b(b(b(b(b(a(x))))))))
Right2(b(b(a(b(b(b(x))))))) → Right2(a(b(b(b(b(b(a(x))))))))
Right3(b(b(a(b(b(b(x))))))) → Right3(a(b(b(b(b(b(a(x))))))))
Right4(b(b(a(b(b(b(x))))))) → Right4(a(b(b(b(b(b(a(x))))))))
Right5(b(b(a(b(b(b(x))))))) → Right5(a(b(b(b(b(b(a(x))))))))
End(b(b(a(b(b(b(x))))))) → End(a(b(b(b(b(b(a(x))))))))
Left(b(b(a(b(b(b(x))))))) → Left(a(b(b(b(b(b(a(x))))))))
Ab(b(b(a(b(b(b(x))))))) → Ab(a(b(b(b(b(b(a(x))))))))
Aa(b(b(a(b(b(b(x))))))) → Aa(a(b(b(b(b(b(a(x))))))))

Q is empty.

(3) RootLabelingProof (EQUIVALENT transformation)

We used plain root labeling [ROOTLAB] with the following heuristic: LabelAll: All function symbols get labeled
As Q is empty the root labeling was sound AND complete.

(4) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → b_{Left_1}(Left_{b_1}(b_{b_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → b_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → b_{Left_1}(Left_{b_1}(b_{End_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → a_{Left_1}(Left_{b_1}(b_{b_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → a_{Left_1}(Left_{b_1}(b_{a_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → a_{Left_1}(Left_{b_1}(b_{End_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → End_{Left_1}(Left_{b_1}(b_{b_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → End_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → End_{Left_1}(Left_{b_1}(b_{End_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → b_{Left_1}(Left_{a_1}(a_{b_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → b_{Left_1}(Left_{a_1}(a_{a_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → b_{Left_1}(Left_{a_1}(a_{End_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → a_{Left_1}(Left_{a_1}(a_{b_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → a_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → a_{Left_1}(Left_{a_1}(a_{End_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → End_{Left_1}(Left_{a_1}(a_{b_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → End_{Left_1}(Left_{a_1}(a_{a_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → End_{Left_1}(Left_{a_1}(a_{End_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Begin_{Begin_1}(Begin_{Begin_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Begin_{Begin_1}(Begin_{a_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Begin_{Begin_1}(Begin_{Wait_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Begin_{Begin_1}(Begin_{Right1_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Begin_{Begin_1}(Begin_{Right2_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Begin_{Begin_1}(Begin_{Right3_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Begin_{Begin_1}(Begin_{Right4_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Begin_{Begin_1}(Begin_{Right5_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Begin_{Begin_1}(Begin_{End_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Begin_{Begin_1}(Begin_{Left_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Begin_{Begin_1}(Begin_{Ab_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Begin_{Begin_1}(Begin_{Aa_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → b_{Begin_1}(Begin_{Begin_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → b_{Begin_1}(Begin_{a_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → b_{Begin_1}(Begin_{Wait_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → b_{Begin_1}(Begin_{Right1_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → b_{Begin_1}(Begin_{Right2_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → b_{Begin_1}(Begin_{Right3_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → b_{Begin_1}(Begin_{Right4_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → b_{Begin_1}(Begin_{Right5_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → b_{Begin_1}(Begin_{End_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → b_{Begin_1}(Begin_{Left_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → b_{Begin_1}(Begin_{Ab_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → b_{Begin_1}(Begin_{Aa_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → a_{Begin_1}(Begin_{Begin_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → a_{Begin_1}(Begin_{a_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → a_{Begin_1}(Begin_{Wait_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → a_{Begin_1}(Begin_{Right1_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → a_{Begin_1}(Begin_{Right2_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → a_{Begin_1}(Begin_{Right3_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → a_{Begin_1}(Begin_{Right4_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → a_{Begin_1}(Begin_{Right5_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → a_{Begin_1}(Begin_{End_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → a_{Begin_1}(Begin_{Left_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → a_{Begin_1}(Begin_{Ab_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → a_{Begin_1}(Begin_{Aa_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Wait_{Begin_1}(Begin_{Begin_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Wait_{Begin_1}(Begin_{a_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Wait_{Begin_1}(Begin_{Wait_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Wait_{Begin_1}(Begin_{Right1_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Wait_{Begin_1}(Begin_{Right2_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Wait_{Begin_1}(Begin_{Right3_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Wait_{Begin_1}(Begin_{Right4_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Wait_{Begin_1}(Begin_{Right5_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Wait_{Begin_1}(Begin_{End_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Wait_{Begin_1}(Begin_{Left_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Wait_{Begin_1}(Begin_{Ab_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Wait_{Begin_1}(Begin_{Aa_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Right1_{Begin_1}(Begin_{Begin_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Right1_{Begin_1}(Begin_{a_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Right1_{Begin_1}(Begin_{Wait_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Right1_{Begin_1}(Begin_{Right1_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Right1_{Begin_1}(Begin_{Right2_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right1_{Begin_1}(Begin_{Right3_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Right1_{Begin_1}(Begin_{Right4_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Right1_{Begin_1}(Begin_{Right5_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right1_{Begin_1}(Begin_{End_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Right1_{Begin_1}(Begin_{Left_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Right1_{Begin_1}(Begin_{Ab_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right1_{Begin_1}(Begin_{Aa_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Right2_{Begin_1}(Begin_{Begin_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Right2_{Begin_1}(Begin_{a_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Right2_{Begin_1}(Begin_{Wait_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Right2_{Begin_1}(Begin_{Right1_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Right2_{Begin_1}(Begin_{Right2_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right2_{Begin_1}(Begin_{Right3_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Right2_{Begin_1}(Begin_{Right4_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Right2_{Begin_1}(Begin_{Right5_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right2_{Begin_1}(Begin_{End_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Right2_{Begin_1}(Begin_{Left_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Right2_{Begin_1}(Begin_{Ab_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right2_{Begin_1}(Begin_{Aa_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Right3_{Begin_1}(Begin_{Begin_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Right3_{Begin_1}(Begin_{a_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Right3_{Begin_1}(Begin_{Wait_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Right3_{Begin_1}(Begin_{Right1_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Right3_{Begin_1}(Begin_{Right2_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right3_{Begin_1}(Begin_{Right3_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Right3_{Begin_1}(Begin_{Right4_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Right3_{Begin_1}(Begin_{Right5_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right3_{Begin_1}(Begin_{End_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Right3_{Begin_1}(Begin_{Left_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Right3_{Begin_1}(Begin_{Ab_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right3_{Begin_1}(Begin_{Aa_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Right4_{Begin_1}(Begin_{Begin_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Right4_{Begin_1}(Begin_{a_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Right4_{Begin_1}(Begin_{Wait_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Right4_{Begin_1}(Begin_{Right1_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Right4_{Begin_1}(Begin_{Right2_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right4_{Begin_1}(Begin_{Right3_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Right4_{Begin_1}(Begin_{Right4_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Right4_{Begin_1}(Begin_{Right5_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right4_{Begin_1}(Begin_{End_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Right4_{Begin_1}(Begin_{Left_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Right4_{Begin_1}(Begin_{Ab_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right4_{Begin_1}(Begin_{Aa_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Right5_{Begin_1}(Begin_{Begin_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Right5_{Begin_1}(Begin_{a_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Right5_{Begin_1}(Begin_{Wait_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Right5_{Begin_1}(Begin_{Right1_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Right5_{Begin_1}(Begin_{Right2_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right5_{Begin_1}(Begin_{Right3_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Right5_{Begin_1}(Begin_{Right4_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Right5_{Begin_1}(Begin_{Right5_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right5_{Begin_1}(Begin_{End_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Right5_{Begin_1}(Begin_{Left_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Right5_{Begin_1}(Begin_{Ab_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right5_{Begin_1}(Begin_{Aa_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → End_{Begin_1}(Begin_{Begin_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → End_{Begin_1}(Begin_{a_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → End_{Begin_1}(Begin_{Wait_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → End_{Begin_1}(Begin_{Right1_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → End_{Begin_1}(Begin_{Right2_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → End_{Begin_1}(Begin_{Right3_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → End_{Begin_1}(Begin_{Right4_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → End_{Begin_1}(Begin_{Right5_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → End_{Begin_1}(Begin_{End_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → End_{Begin_1}(Begin_{Left_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → End_{Begin_1}(Begin_{Ab_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → End_{Begin_1}(Begin_{Aa_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Left_{Begin_1}(Begin_{Begin_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Left_{Begin_1}(Begin_{a_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Left_{Begin_1}(Begin_{Wait_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Left_{Begin_1}(Begin_{Right1_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Left_{Begin_1}(Begin_{Right2_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Left_{Begin_1}(Begin_{Right3_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Left_{Begin_1}(Begin_{Right4_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Left_{Begin_1}(Begin_{Right5_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Left_{Begin_1}(Begin_{End_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Left_{Begin_1}(Begin_{Left_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Left_{Begin_1}(Begin_{Ab_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Left_{Begin_1}(Begin_{Aa_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Ab_{Begin_1}(Begin_{Begin_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Ab_{Begin_1}(Begin_{a_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Ab_{Begin_1}(Begin_{Wait_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Ab_{Begin_1}(Begin_{Right1_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Ab_{Begin_1}(Begin_{Right2_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Ab_{Begin_1}(Begin_{Right3_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Ab_{Begin_1}(Begin_{Right4_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Ab_{Begin_1}(Begin_{Right5_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Ab_{Begin_1}(Begin_{End_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Ab_{Begin_1}(Begin_{Left_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Ab_{Begin_1}(Begin_{Ab_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Ab_{Begin_1}(Begin_{Aa_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Aa_{Begin_1}(Begin_{Begin_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Aa_{Begin_1}(Begin_{a_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Aa_{Begin_1}(Begin_{Wait_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Aa_{Begin_1}(Begin_{Right1_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Aa_{Begin_1}(Begin_{Right2_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Aa_{Begin_1}(Begin_{Right3_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Aa_{Begin_1}(Begin_{Right4_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Aa_{Begin_1}(Begin_{Right5_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Aa_{Begin_1}(Begin_{End_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Aa_{Begin_1}(Begin_{Left_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Aa_{Begin_1}(Begin_{Ab_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Aa_{Begin_1}(Begin_{Aa_1}(x))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))

Q is empty.

(5) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = x1   
POL(Aa_{Ab_1}(x1)) = 1 + x1   
POL(Aa_{Begin_1}(x1)) = x1   
POL(Aa_{Left_1}(x1)) = 2 + x1   
POL(Aa_{Right1_1}(x1)) = x1   
POL(Aa_{Right2_1}(x1)) = 1 + x1   
POL(Aa_{Right3_1}(x1)) = x1   
POL(Aa_{Right4_1}(x1)) = x1   
POL(Aa_{Right5_1}(x1)) = x1   
POL(Aa_{Wait_1}(x1)) = x1   
POL(Aa_{a_1}(x1)) = x1   
POL(Aa_{b_1}(x1)) = 2 + x1   
POL(Ab_{Aa_1}(x1)) = x1   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Begin_1}(x1)) = x1   
POL(Ab_{Left_1}(x1)) = 2 + x1   
POL(Ab_{Right1_1}(x1)) = x1   
POL(Ab_{Right2_1}(x1)) = 1 + x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Ab_{Right4_1}(x1)) = x1   
POL(Ab_{Right5_1}(x1)) = x1   
POL(Ab_{Wait_1}(x1)) = x1   
POL(Ab_{a_1}(x1)) = x1   
POL(Ab_{b_1}(x1)) = 1 + x1   
POL(Begin_{Aa_1}(x1)) = 6 + x1   
POL(Begin_{Ab_1}(x1)) = 5 + x1   
POL(Begin_{Begin_1}(x1)) = x1   
POL(Begin_{End_1}(x1)) = 7 + x1   
POL(Begin_{Left_1}(x1)) = x1   
POL(Begin_{Right1_1}(x1)) = 7 + x1   
POL(Begin_{Right2_1}(x1)) = 8 + x1   
POL(Begin_{Right3_1}(x1)) = 6 + x1   
POL(Begin_{Right4_1}(x1)) = 7 + x1   
POL(Begin_{Right5_1}(x1)) = 7 + x1   
POL(Begin_{Wait_1}(x1)) = x1   
POL(Begin_{a_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = 3 + x1   
POL(End_{Aa_1}(x1)) = 1 + x1   
POL(End_{Ab_1}(x1)) = 3 + x1   
POL(End_{Begin_1}(x1)) = x1   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = 2 + x1   
POL(End_{Right1_1}(x1)) = 3 + x1   
POL(End_{Right2_1}(x1)) = 4 + x1   
POL(End_{Right3_1}(x1)) = 3 + x1   
POL(End_{Right4_1}(x1)) = 3 + x1   
POL(End_{Right5_1}(x1)) = 3 + x1   
POL(End_{Wait_1}(x1)) = x1   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = 2 + x1   
POL(Left_{Aa_1}(x1)) = 4 + x1   
POL(Left_{Ab_1}(x1)) = 4 + x1   
POL(Left_{Begin_1}(x1)) = 3 + x1   
POL(Left_{End_1}(x1)) = 5 + x1   
POL(Left_{Left_1}(x1)) = 3 + x1   
POL(Left_{Right1_1}(x1)) = 6 + x1   
POL(Left_{Right2_1}(x1)) = 7 + x1   
POL(Left_{Right3_1}(x1)) = 4 + x1   
POL(Left_{Right4_1}(x1)) = 6 + x1   
POL(Left_{Right5_1}(x1)) = 6 + x1   
POL(Left_{Wait_1}(x1)) = 3 + x1   
POL(Left_{a_1}(x1)) = x1   
POL(Left_{b_1}(x1)) = 1 + x1   
POL(Right1_{Aa_1}(x1)) = x1   
POL(Right1_{Ab_1}(x1)) = x1   
POL(Right1_{Begin_1}(x1)) = 3 + x1   
POL(Right1_{End_1}(x1)) = x1   
POL(Right1_{Left_1}(x1)) = x1   
POL(Right1_{Right1_1}(x1)) = 1 + x1   
POL(Right1_{Right2_1}(x1)) = 3 + x1   
POL(Right1_{Right3_1}(x1)) = 1 + x1   
POL(Right1_{Right4_1}(x1)) = 1 + x1   
POL(Right1_{Right5_1}(x1)) = 1 + x1   
POL(Right1_{Wait_1}(x1)) = 3 + x1   
POL(Right1_{a_1}(x1)) = 3 + x1   
POL(Right1_{b_1}(x1)) = 4 + x1   
POL(Right2_{Aa_1}(x1)) = x1   
POL(Right2_{Ab_1}(x1)) = 1 + x1   
POL(Right2_{Begin_1}(x1)) = 1 + x1   
POL(Right2_{End_1}(x1)) = x1   
POL(Right2_{Left_1}(x1)) = 1 + x1   
POL(Right2_{Right1_1}(x1)) = 2 + x1   
POL(Right2_{Right2_1}(x1)) = 3 + x1   
POL(Right2_{Right3_1}(x1)) = 1 + x1   
POL(Right2_{Right4_1}(x1)) = 2 + x1   
POL(Right2_{Right5_1}(x1)) = 1 + x1   
POL(Right2_{Wait_1}(x1)) = 1 + x1   
POL(Right2_{a_1}(x1)) = 1 + x1   
POL(Right2_{b_1}(x1)) = 2 + x1   
POL(Right3_{Aa_1}(x1)) = x1   
POL(Right3_{Ab_1}(x1)) = x1   
POL(Right3_{Begin_1}(x1)) = 5 + x1   
POL(Right3_{End_1}(x1)) = 6 + x1   
POL(Right3_{Left_1}(x1)) = x1   
POL(Right3_{Right1_1}(x1)) = 1 + x1   
POL(Right3_{Right2_1}(x1)) = 2 + x1   
POL(Right3_{Right3_1}(x1)) = 6 + x1   
POL(Right3_{Right4_1}(x1)) = 1 + x1   
POL(Right3_{Right5_1}(x1)) = 1 + x1   
POL(Right3_{Wait_1}(x1)) = 5 + x1   
POL(Right3_{a_1}(x1)) = 5 + x1   
POL(Right3_{b_1}(x1)) = 6 + x1   
POL(Right4_{Aa_1}(x1)) = x1   
POL(Right4_{Ab_1}(x1)) = 1 + x1   
POL(Right4_{Begin_1}(x1)) = 1 + x1   
POL(Right4_{End_1}(x1)) = 1 + x1   
POL(Right4_{Left_1}(x1)) = x1   
POL(Right4_{Right1_1}(x1)) = 2 + x1   
POL(Right4_{Right2_1}(x1)) = 2 + x1   
POL(Right4_{Right3_1}(x1)) = 2 + x1   
POL(Right4_{Right4_1}(x1)) = 2 + x1   
POL(Right4_{Right5_1}(x1)) = 2 + x1   
POL(Right4_{Wait_1}(x1)) = 1 + x1   
POL(Right4_{a_1}(x1)) = 1 + x1   
POL(Right4_{b_1}(x1)) = 2 + x1   
POL(Right5_{Aa_1}(x1)) = x1   
POL(Right5_{Ab_1}(x1)) = x1   
POL(Right5_{Begin_1}(x1)) = x1   
POL(Right5_{End_1}(x1)) = x1   
POL(Right5_{Left_1}(x1)) = x1   
POL(Right5_{Right1_1}(x1)) = 1 + x1   
POL(Right5_{Right2_1}(x1)) = 2 + x1   
POL(Right5_{Right3_1}(x1)) = 1 + x1   
POL(Right5_{Right4_1}(x1)) = 1 + x1   
POL(Right5_{Right5_1}(x1)) = 1 + x1   
POL(Right5_{Wait_1}(x1)) = x1   
POL(Right5_{a_1}(x1)) = x1   
POL(Right5_{b_1}(x1)) = 1 + x1   
POL(Wait_{Aa_1}(x1)) = x1   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Begin_1}(x1)) = x1   
POL(Wait_{Left_1}(x1)) = 2 + x1   
POL(Wait_{Right1_1}(x1)) = 1 + x1   
POL(Wait_{Right2_1}(x1)) = 1 + x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(Wait_{Right4_1}(x1)) = 2 + x1   
POL(Wait_{Right5_1}(x1)) = 2 + x1   
POL(Wait_{Wait_1}(x1)) = x1   
POL(Wait_{a_1}(x1)) = x1   
POL(Wait_{b_1}(x1)) = 1 + x1   
POL(a_{Aa_1}(x1)) = x1   
POL(a_{Ab_1}(x1)) = 1 + x1   
POL(a_{Begin_1}(x1)) = 1 + x1   
POL(a_{End_1}(x1)) = 1 + x1   
POL(a_{Left_1}(x1)) = 1 + x1   
POL(a_{Right1_1}(x1)) = 2 + x1   
POL(a_{Right2_1}(x1)) = 3 + x1   
POL(a_{Right3_1}(x1)) = 2 + x1   
POL(a_{Right4_1}(x1)) = 2 + x1   
POL(a_{Right5_1}(x1)) = 2 + x1   
POL(a_{Wait_1}(x1)) = 1 + x1   
POL(a_{a_1}(x1)) = x1   
POL(a_{b_1}(x1)) = 1 + x1   
POL(b_{Aa_1}(x1)) = 1 + x1   
POL(b_{Ab_1}(x1)) = 3 + x1   
POL(b_{Begin_1}(x1)) = 2 + x1   
POL(b_{End_1}(x1)) = 4 + x1   
POL(b_{Left_1}(x1)) = 2 + x1   
POL(b_{Right1_1}(x1)) = 4 + x1   
POL(b_{Right2_1}(x1)) = 4 + x1   
POL(b_{Right3_1}(x1)) = 3 + x1   
POL(b_{Right4_1}(x1)) = 3 + x1   
POL(b_{Right5_1}(x1)) = 3 + x1   
POL(b_{Wait_1}(x1)) = 2 + x1   
POL(b_{a_1}(x1)) = x1   
POL(b_{b_1}(x1)) = 1 + x1   
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Begin_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → b_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → a_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Wait_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right1_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right2_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right3_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right4_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right5_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → End_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Left_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Ab_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Begin_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Wait_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Right1_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Right2_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Right3_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Right4_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Right5_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{End_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Left_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Ab_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Aa_{Wait_1}(Wait_{Right1_1}(Right1_{Aa_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Begin_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Begin_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
b_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → b_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
a_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → a_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Wait_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Wait_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Right1_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Right1_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Right2_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Right2_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Right3_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Right3_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Right4_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Right4_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Right5_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Right5_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
End_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → End_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Left_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Left_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Ab_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Ab_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Begin_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{b_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{a_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Wait_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Right1_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Right2_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Right3_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Right4_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Right5_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{End_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Left_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Ab_1}(x)))
Aa_{Begin_1}(Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x)))))) → Aa_{Wait_1}(Wait_{Right2_1}(Right2_{Aa_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Begin_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Wait_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Right1_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Right2_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Right3_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Right4_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Right5_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{End_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Left_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Ab_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{Aa_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Begin_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → b_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → a_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Wait_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Right1_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Right2_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Right3_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Right4_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Right5_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → End_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Left_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Ab_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Begin_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Begin_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{a_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Wait_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Wait_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right1_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Right1_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right2_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Right2_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right3_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Right3_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right4_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Right4_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Right5_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Right5_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{End_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{End_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Left_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Left_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Ab_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Ab_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{Aa_1}(x)))) → Aa_{Wait_1}(Wait_{Right4_1}(Right4_{Aa_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Begin_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → b_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → a_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Wait_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Right1_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Right2_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Right3_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Right4_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Right5_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → End_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Left_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Ab_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Begin_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Begin_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{a_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Wait_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Wait_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Right1_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Right1_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Right2_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Right2_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Right3_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Right3_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Right4_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Right4_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Right5_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Right5_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{End_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{End_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Left_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Left_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Ab_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Ab_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{Aa_1}(x))) → Aa_{Wait_1}(Wait_{Right5_1}(Right5_{Aa_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → b_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → a_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → End_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Begin_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Begin_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Begin_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
b_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → b_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
a_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → a_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Wait_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Wait_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Right1_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Right1_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Right2_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Right2_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Right3_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Right3_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Right4_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Right4_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Right5_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Right5_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
End_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → End_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Left_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Left_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Begin_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Begin_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Wait_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Wait_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Right1_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Right1_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Right2_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Right2_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Right3_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Right3_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Right4_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Right4_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Right5_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Right5_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{End_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Left_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Left_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Ab_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Ab_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{Aa_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{Aa_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Begin_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Begin_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
b_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → b_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
a_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → a_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Right1_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Right1_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Right2_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Right2_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Right3_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Right3_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Right4_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Right4_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Right5_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Right5_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
End_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → End_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Left_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Left_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Begin_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Begin_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Wait_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Wait_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Right1_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Right1_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Right2_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Right2_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Right3_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Right3_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Right4_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Right4_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Right5_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Right5_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{End_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{End_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Left_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Left_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Ab_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Ab_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{Aa_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{Aa_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Begin_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Begin_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
b_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → b_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
a_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → a_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Right1_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Right1_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Right2_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Right2_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Right3_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Right3_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Right4_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Right4_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Right5_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Right5_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
End_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → End_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Left_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Left_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Begin_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Begin_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Wait_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Wait_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Right1_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Right1_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Right2_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Right2_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Right3_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Right3_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Right4_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Right4_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Right5_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Right5_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{End_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{End_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Left_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Left_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Ab_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Ab_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{Aa_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{Aa_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Begin_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Begin_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
b_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → b_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
a_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → a_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Wait_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Wait_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Right1_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Right1_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Right2_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Right2_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Right3_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Right3_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Right4_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Right4_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Right5_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Right5_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
End_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → End_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Left_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Left_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Begin_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Begin_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Wait_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Wait_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Right1_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Right1_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Right2_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Right2_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Right3_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Right3_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Right4_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Right4_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Right5_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Right5_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{End_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{End_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Left_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Left_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Ab_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Ab_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{Aa_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{Aa_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Begin_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Begin_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
b_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → b_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
a_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → a_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Wait_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Wait_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Right1_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Right1_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Right2_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Right2_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Right3_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Right3_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Right4_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Right4_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Right5_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Right5_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
End_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → End_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Left_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Left_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Begin_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Begin_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Wait_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Wait_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Right1_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Right1_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Right2_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Right2_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Right3_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Right3_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Right4_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Right4_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Right5_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Right5_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{End_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{End_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Left_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Left_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Ab_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Ab_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{Aa_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{Aa_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Begin_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Begin_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
b_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → b_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
a_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → a_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Wait_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Wait_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Right1_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Right1_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Right2_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Right2_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Right3_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Right3_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Right4_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Right4_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Right5_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Right5_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
End_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → End_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Left_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Left_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Begin_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Begin_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Wait_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Wait_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Right1_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Right1_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Right2_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Right2_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Right3_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Right3_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Right4_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Right4_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Right5_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Right5_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{End_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{End_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Left_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Left_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Ab_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Ab_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{Aa_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{Aa_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Begin_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Begin_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
b_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → b_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
a_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → a_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Right1_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Right1_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Right2_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Right2_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Right3_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Right3_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Right4_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Right4_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Right5_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Right5_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
End_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → End_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Left_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Left_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Begin_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Begin_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Wait_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Wait_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Right1_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Right1_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Right2_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Right2_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Right3_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Right3_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Right4_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Right4_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Right5_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Right5_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{End_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{End_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Left_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Left_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Ab_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Ab_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{Aa_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{Aa_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
b_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → b_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
a_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → a_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Right1_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Right1_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Right2_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Right2_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Right3_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Right3_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Right4_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Right4_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Right5_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Right5_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
End_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → End_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Begin_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Begin_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Wait_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Wait_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Right1_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Right1_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Right2_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Right2_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Right3_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Right3_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Right4_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Right4_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Right5_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Right5_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Left_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Left_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Ab_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Ab_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{Aa_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{Aa_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Begin_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Begin_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
b_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → b_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
a_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → a_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Wait_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Wait_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Right1_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Right1_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Right2_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Right2_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Right3_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Right3_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Right4_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Right4_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Right5_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Right5_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
End_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → End_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Left_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Left_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Begin_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Begin_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Wait_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Wait_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Right1_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Right1_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Right2_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Right2_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Right3_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Right3_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Right4_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Right4_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Right5_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Right5_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{End_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{End_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Left_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Left_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Ab_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Ab_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{Aa_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{Aa_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Begin_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Begin_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
b_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → b_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
a_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → a_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Wait_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Wait_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Right1_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Right1_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Right2_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Right2_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Right3_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Right3_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Right4_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Right4_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Right5_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Right5_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
End_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → End_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Left_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Left_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Begin_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Begin_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Wait_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Wait_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Right1_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Right1_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Right2_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Right2_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Right3_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Right3_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Right4_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Right4_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Right5_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Right5_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{End_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{End_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Left_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Left_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Ab_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Ab_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Begin_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Begin_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → b_{Left_1}(Left_{b_1}(b_{b_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → b_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → b_{Left_1}(Left_{b_1}(b_{End_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
b_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → b_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → a_{Left_1}(Left_{b_1}(b_{b_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → a_{Left_1}(Left_{b_1}(b_{a_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → a_{Left_1}(Left_{b_1}(b_{End_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
a_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → a_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Right1_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Right1_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Right2_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Right2_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Right3_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Right3_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Right4_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Right4_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Right5_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Right5_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → End_{Left_1}(Left_{b_1}(b_{b_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → End_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → End_{Left_1}(Left_{b_1}(b_{End_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
End_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → End_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Left_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Left_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Begin_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Begin_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Wait_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Wait_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Right1_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Right1_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Right2_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Right2_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Right3_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Right3_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Right4_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Right4_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Right5_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Right5_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{End_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{End_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Left_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Left_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Ab_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Ab_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{Aa_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{Aa_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Begin_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Begin_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → b_{Left_1}(Left_{a_1}(a_{b_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → b_{Left_1}(Left_{a_1}(a_{a_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → b_{Left_1}(Left_{a_1}(a_{End_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
b_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → b_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → a_{Left_1}(Left_{a_1}(a_{b_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → a_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → a_{Left_1}(Left_{a_1}(a_{End_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
a_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → a_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Right1_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Right1_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Right2_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Right2_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Right3_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Right3_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Right4_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Right4_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Right5_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Right5_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → End_{Left_1}(Left_{a_1}(a_{b_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → End_{Left_1}(Left_{a_1}(a_{a_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → End_{Left_1}(Left_{a_1}(a_{End_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
End_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → End_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Left_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Left_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Begin_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Begin_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Wait_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Wait_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Right1_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Right1_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Right2_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Right2_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Right3_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Right3_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Right4_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Right4_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Right5_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Right5_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{End_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{End_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Left_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Left_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Ab_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Ab_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{Aa_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{Aa_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Begin_{Begin_1}(Begin_{Begin_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Begin_{Begin_1}(Begin_{a_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Begin_{Begin_1}(Begin_{Wait_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Begin_{Begin_1}(Begin_{Right1_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Begin_{Begin_1}(Begin_{Right2_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Begin_{Begin_1}(Begin_{Right4_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Begin_{Begin_1}(Begin_{Right5_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Begin_{Begin_1}(Begin_{Left_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Begin_{Begin_1}(Begin_{Ab_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → b_{Begin_1}(Begin_{Begin_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → b_{Begin_1}(Begin_{a_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → b_{Begin_1}(Begin_{Wait_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → b_{Begin_1}(Begin_{Right1_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → b_{Begin_1}(Begin_{Right2_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → b_{Begin_1}(Begin_{Right4_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → b_{Begin_1}(Begin_{Right5_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → b_{Begin_1}(Begin_{Left_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → b_{Begin_1}(Begin_{Ab_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → a_{Begin_1}(Begin_{Begin_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → a_{Begin_1}(Begin_{a_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → a_{Begin_1}(Begin_{Wait_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → a_{Begin_1}(Begin_{Right1_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → a_{Begin_1}(Begin_{Right2_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → a_{Begin_1}(Begin_{Right4_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → a_{Begin_1}(Begin_{Right5_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → a_{Begin_1}(Begin_{Left_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → a_{Begin_1}(Begin_{Ab_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Wait_{Begin_1}(Begin_{Begin_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Wait_{Begin_1}(Begin_{a_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Wait_{Begin_1}(Begin_{Wait_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Wait_{Begin_1}(Begin_{Right1_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Wait_{Begin_1}(Begin_{Right2_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Wait_{Begin_1}(Begin_{Right4_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Wait_{Begin_1}(Begin_{Right5_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Wait_{Begin_1}(Begin_{Left_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Wait_{Begin_1}(Begin_{Ab_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Right1_{Begin_1}(Begin_{Begin_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Right1_{Begin_1}(Begin_{a_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Right1_{Begin_1}(Begin_{Wait_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Right1_{Begin_1}(Begin_{Right1_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Right1_{Begin_1}(Begin_{Right2_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Right1_{Begin_1}(Begin_{Right4_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Right1_{Begin_1}(Begin_{Right5_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Right1_{Begin_1}(Begin_{Left_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Right1_{Begin_1}(Begin_{Ab_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Right2_{Begin_1}(Begin_{Begin_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Right2_{Begin_1}(Begin_{a_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Right2_{Begin_1}(Begin_{Wait_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Right2_{Begin_1}(Begin_{Right1_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Right2_{Begin_1}(Begin_{Right2_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Right2_{Begin_1}(Begin_{Right4_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Right2_{Begin_1}(Begin_{Right5_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Right2_{Begin_1}(Begin_{Left_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Right2_{Begin_1}(Begin_{Ab_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Right3_{Begin_1}(Begin_{Begin_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Right3_{Begin_1}(Begin_{a_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Right3_{Begin_1}(Begin_{Wait_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Right3_{Begin_1}(Begin_{Right1_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Right3_{Begin_1}(Begin_{Right2_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Right3_{Begin_1}(Begin_{Right4_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Right3_{Begin_1}(Begin_{Right5_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Right3_{Begin_1}(Begin_{Left_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Right3_{Begin_1}(Begin_{Ab_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Right4_{Begin_1}(Begin_{Begin_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Right4_{Begin_1}(Begin_{a_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Right4_{Begin_1}(Begin_{Wait_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Right4_{Begin_1}(Begin_{Right1_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Right4_{Begin_1}(Begin_{Right2_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Right4_{Begin_1}(Begin_{Right4_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Right4_{Begin_1}(Begin_{Right5_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Right4_{Begin_1}(Begin_{Left_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Right4_{Begin_1}(Begin_{Ab_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Right5_{Begin_1}(Begin_{Begin_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Right5_{Begin_1}(Begin_{a_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Right5_{Begin_1}(Begin_{Wait_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Right5_{Begin_1}(Begin_{Right1_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Right5_{Begin_1}(Begin_{Right2_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Right5_{Begin_1}(Begin_{Right4_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Right5_{Begin_1}(Begin_{Right5_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Right5_{Begin_1}(Begin_{Left_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Right5_{Begin_1}(Begin_{Ab_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → End_{Begin_1}(Begin_{Begin_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → End_{Begin_1}(Begin_{a_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → End_{Begin_1}(Begin_{Wait_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → End_{Begin_1}(Begin_{Right1_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → End_{Begin_1}(Begin_{Right2_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → End_{Begin_1}(Begin_{Right4_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → End_{Begin_1}(Begin_{Right5_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → End_{Begin_1}(Begin_{Left_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → End_{Begin_1}(Begin_{Ab_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Left_{Begin_1}(Begin_{Begin_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Left_{Begin_1}(Begin_{a_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Left_{Begin_1}(Begin_{Wait_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Left_{Begin_1}(Begin_{Right1_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Left_{Begin_1}(Begin_{Right2_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Left_{Begin_1}(Begin_{Right4_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Left_{Begin_1}(Begin_{Right5_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Left_{Begin_1}(Begin_{Left_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Left_{Begin_1}(Begin_{Ab_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Ab_{Begin_1}(Begin_{Begin_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Ab_{Begin_1}(Begin_{a_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Ab_{Begin_1}(Begin_{Wait_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Ab_{Begin_1}(Begin_{Right1_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Ab_{Begin_1}(Begin_{Right2_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Ab_{Begin_1}(Begin_{Right4_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Ab_{Begin_1}(Begin_{Right5_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Ab_{Begin_1}(Begin_{Left_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Ab_{Begin_1}(Begin_{Ab_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Begin_1}(x))) → Aa_{Begin_1}(Begin_{Begin_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{a_1}(x))) → Aa_{Begin_1}(Begin_{a_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Wait_1}(x))) → Aa_{Begin_1}(Begin_{Wait_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Right1_1}(x))) → Aa_{Begin_1}(Begin_{Right1_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Right2_1}(x))) → Aa_{Begin_1}(Begin_{Right2_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Right4_1}(x))) → Aa_{Begin_1}(Begin_{Right4_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Right5_1}(x))) → Aa_{Begin_1}(Begin_{Right5_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Left_1}(x))) → Aa_{Begin_1}(Begin_{Left_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Ab_1}(x))) → Aa_{Begin_1}(Begin_{Ab_1}(x))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Begin_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Begin_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
End_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → End_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Begin_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Begin_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Wait_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Wait_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right1_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right1_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right2_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right2_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right3_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right3_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right4_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right4_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Right5_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Right5_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{End_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Left_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Left_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Ab_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Ab_1}(x))))))))
Aa_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{Aa_1}(x))))))) → Aa_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{Aa_1}(x))))))))


(6) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Begin_{Begin_1}(Begin_{Right3_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Begin_{Begin_1}(Begin_{End_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Begin_{Begin_1}(Begin_{Aa_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → b_{Begin_1}(Begin_{Right3_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → b_{Begin_1}(Begin_{End_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → b_{Begin_1}(Begin_{Aa_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → a_{Begin_1}(Begin_{Right3_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → a_{Begin_1}(Begin_{End_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → a_{Begin_1}(Begin_{Aa_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Wait_{Begin_1}(Begin_{Right3_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Wait_{Begin_1}(Begin_{End_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Wait_{Begin_1}(Begin_{Aa_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right1_{Begin_1}(Begin_{Right3_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right1_{Begin_1}(Begin_{End_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right1_{Begin_1}(Begin_{Aa_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right2_{Begin_1}(Begin_{Right3_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right2_{Begin_1}(Begin_{End_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right2_{Begin_1}(Begin_{Aa_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right3_{Begin_1}(Begin_{Right3_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right3_{Begin_1}(Begin_{End_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right3_{Begin_1}(Begin_{Aa_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right4_{Begin_1}(Begin_{Right3_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right4_{Begin_1}(Begin_{End_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right4_{Begin_1}(Begin_{Aa_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right5_{Begin_1}(Begin_{Right3_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right5_{Begin_1}(Begin_{End_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right5_{Begin_1}(Begin_{Aa_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → End_{Begin_1}(Begin_{Right3_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → End_{Begin_1}(Begin_{End_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → End_{Begin_1}(Begin_{Aa_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Left_{Begin_1}(Begin_{Right3_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Left_{Begin_1}(Begin_{End_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Left_{Begin_1}(Begin_{Aa_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Ab_{Begin_1}(Begin_{Right3_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Ab_{Begin_1}(Begin_{End_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Ab_{Begin_1}(Begin_{Aa_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Aa_{Begin_1}(Begin_{Right3_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Aa_{Begin_1}(Begin_{End_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Aa_{Begin_1}(Begin_{Aa_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.

(7) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = x1   
POL(Aa_{Ab_1}(x1)) = x1   
POL(Aa_{Begin_1}(x1)) = x1   
POL(Aa_{Left_1}(x1)) = x1   
POL(Aa_{Right1_1}(x1)) = 2 + x1   
POL(Aa_{Right2_1}(x1)) = 1 + x1   
POL(Aa_{Right3_1}(x1)) = x1   
POL(Aa_{Right4_1}(x1)) = 1 + x1   
POL(Aa_{Right5_1}(x1)) = 1 + x1   
POL(Aa_{Wait_1}(x1)) = x1   
POL(Ab_{Aa_1}(x1)) = x1   
POL(Ab_{Ab_1}(x1)) = x1   
POL(Ab_{Begin_1}(x1)) = x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right1_1}(x1)) = 2 + x1   
POL(Ab_{Right2_1}(x1)) = 1 + x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Ab_{Right4_1}(x1)) = 1 + x1   
POL(Ab_{Right5_1}(x1)) = 1 + x1   
POL(Ab_{Wait_1}(x1)) = x1   
POL(Ab_{a_1}(x1)) = x1   
POL(Ab_{b_1}(x1)) = 1 + x1   
POL(Begin_{Aa_1}(x1)) = x1   
POL(Begin_{Begin_1}(x1)) = x1   
POL(Begin_{End_1}(x1)) = x1   
POL(Begin_{Right3_1}(x1)) = 1 + x1   
POL(Begin_{Wait_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = x1   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = x1   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{Aa_1}(x1)) = 1 + x1   
POL(Left_{Begin_1}(x1)) = x1   
POL(Left_{End_1}(x1)) = 1 + x1   
POL(Left_{Right3_1}(x1)) = 2 + x1   
POL(Left_{Wait_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = x1   
POL(Left_{b_1}(x1)) = x1   
POL(Right1_{Begin_1}(x1)) = x1   
POL(Right1_{Wait_1}(x1)) = x1   
POL(Right1_{a_1}(x1)) = x1   
POL(Right1_{b_1}(x1)) = x1   
POL(Right2_{Begin_1}(x1)) = x1   
POL(Right2_{Wait_1}(x1)) = x1   
POL(Right2_{a_1}(x1)) = x1   
POL(Right2_{b_1}(x1)) = x1   
POL(Right3_{Begin_1}(x1)) = x1   
POL(Right3_{End_1}(x1)) = x1   
POL(Right3_{Wait_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = x1   
POL(Right3_{b_1}(x1)) = x1   
POL(Right4_{Begin_1}(x1)) = x1   
POL(Right4_{Wait_1}(x1)) = x1   
POL(Right4_{a_1}(x1)) = x1   
POL(Right4_{b_1}(x1)) = x1   
POL(Right5_{Aa_1}(x1)) = x1   
POL(Right5_{Begin_1}(x1)) = x1   
POL(Right5_{Wait_1}(x1)) = x1   
POL(Right5_{a_1}(x1)) = x1   
POL(Right5_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = x1   
POL(Wait_{Ab_1}(x1)) = x1   
POL(Wait_{Begin_1}(x1)) = x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right2_1}(x1)) = 2 + x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(Wait_{Wait_1}(x1)) = x1   
POL(Wait_{a_1}(x1)) = x1   
POL(Wait_{b_1}(x1)) = 1 + x1   
POL(a_{Aa_1}(x1)) = 1 + x1   
POL(a_{Begin_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 1 + x1   
POL(a_{Wait_1}(x1)) = x1   
POL(a_{a_1}(x1)) = x1   
POL(a_{b_1}(x1)) = x1   
POL(b_{Begin_1}(x1)) = x1   
POL(b_{End_1}(x1)) = x1   
POL(b_{Wait_1}(x1)) = x1   
POL(b_{a_1}(x1)) = x1   
POL(b_{b_1}(x1)) = x1   
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Begin_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{b_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{a_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Wait_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right1_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right2_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right3_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right4_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Right5_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{End_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Left_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Ab_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right1_1}(Right1_{b_1}(b_{End_1}(End_{Aa_1}(x)))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Wait_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Wait_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Begin_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Begin_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Left_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Left_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{End_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{End_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{Aa_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{Aa_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Begin_{Begin_1}(Begin_{Right3_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Begin_{Begin_1}(Begin_{End_1}(x))
Begin_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Begin_{Begin_1}(Begin_{Aa_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → b_{Begin_1}(Begin_{Right3_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → b_{Begin_1}(Begin_{End_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → b_{Begin_1}(Begin_{Aa_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → a_{Begin_1}(Begin_{Right3_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → a_{Begin_1}(Begin_{End_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → a_{Begin_1}(Begin_{Aa_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Wait_{Begin_1}(Begin_{Right3_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Wait_{Begin_1}(Begin_{End_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Wait_{Begin_1}(Begin_{Aa_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right1_{Begin_1}(Begin_{Right3_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right1_{Begin_1}(Begin_{End_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right1_{Begin_1}(Begin_{Aa_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right2_{Begin_1}(Begin_{Right3_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right2_{Begin_1}(Begin_{End_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right2_{Begin_1}(Begin_{Aa_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right3_{Begin_1}(Begin_{Right3_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right3_{Begin_1}(Begin_{End_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right3_{Begin_1}(Begin_{Aa_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right4_{Begin_1}(Begin_{Right3_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right4_{Begin_1}(Begin_{End_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right4_{Begin_1}(Begin_{Aa_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Right5_{Begin_1}(Begin_{Right3_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Right5_{Begin_1}(Begin_{End_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Right5_{Begin_1}(Begin_{Aa_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → End_{Begin_1}(Begin_{Right3_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → End_{Begin_1}(Begin_{End_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → End_{Begin_1}(Begin_{Aa_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Left_{Begin_1}(Begin_{Right3_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Left_{Begin_1}(Begin_{End_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Left_{Begin_1}(Begin_{Aa_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Ab_{Begin_1}(Begin_{Right3_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Ab_{Begin_1}(Begin_{End_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Ab_{Begin_1}(Begin_{Aa_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Right3_1}(x))) → Aa_{Begin_1}(Begin_{Right3_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{End_1}(x))) → Aa_{Begin_1}(Begin_{End_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{Aa_1}(x))) → Aa_{Begin_1}(Begin_{Aa_1}(x))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Wait_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Wait_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Ab_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Ab_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))


(8) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.

(9) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = x1   
POL(Aa_{Ab_1}(x1)) = x1   
POL(Aa_{Begin_1}(x1)) = x1   
POL(Aa_{Left_1}(x1)) = x1   
POL(Aa_{Right1_1}(x1)) = x1   
POL(Aa_{Right2_1}(x1)) = 1 + x1   
POL(Aa_{Right3_1}(x1)) = x1   
POL(Aa_{Right4_1}(x1)) = x1   
POL(Aa_{Right5_1}(x1)) = x1   
POL(Aa_{Wait_1}(x1)) = x1   
POL(Ab_{Aa_1}(x1)) = x1   
POL(Ab_{Ab_1}(x1)) = x1   
POL(Ab_{Begin_1}(x1)) = x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right1_1}(x1)) = x1   
POL(Ab_{Right2_1}(x1)) = 1 + x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Ab_{Right4_1}(x1)) = x1   
POL(Ab_{Right5_1}(x1)) = x1   
POL(Ab_{Wait_1}(x1)) = x1   
POL(Begin_{Begin_1}(x1)) = x1   
POL(Begin_{Wait_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = x1   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = x1   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{Begin_1}(x1)) = x1   
POL(Left_{Wait_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = x1   
POL(Left_{b_1}(x1)) = x1   
POL(Right1_{Begin_1}(x1)) = x1   
POL(Right1_{Wait_1}(x1)) = x1   
POL(Right1_{a_1}(x1)) = x1   
POL(Right1_{b_1}(x1)) = x1   
POL(Right2_{Begin_1}(x1)) = x1   
POL(Right2_{Wait_1}(x1)) = x1   
POL(Right2_{a_1}(x1)) = x1   
POL(Right2_{b_1}(x1)) = x1   
POL(Right3_{Begin_1}(x1)) = x1   
POL(Right3_{Wait_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = x1   
POL(Right3_{b_1}(x1)) = x1   
POL(Right4_{Begin_1}(x1)) = x1   
POL(Right4_{Wait_1}(x1)) = x1   
POL(Right4_{a_1}(x1)) = x1   
POL(Right4_{b_1}(x1)) = x1   
POL(Right5_{Begin_1}(x1)) = x1   
POL(Right5_{Wait_1}(x1)) = x1   
POL(Right5_{a_1}(x1)) = x1   
POL(Right5_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = x1   
POL(Wait_{Ab_1}(x1)) = x1   
POL(Wait_{Begin_1}(x1)) = x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(Wait_{Wait_1}(x1)) = x1   
POL(a_{Begin_1}(x1)) = x1   
POL(a_{End_1}(x1)) = x1   
POL(a_{Wait_1}(x1)) = x1   
POL(a_{a_1}(x1)) = x1   
POL(a_{b_1}(x1)) = x1   
POL(b_{Begin_1}(x1)) = x1   
POL(b_{End_1}(x1)) = x1   
POL(b_{Wait_1}(x1)) = x1   
POL(b_{a_1}(x1)) = x1   
POL(b_{b_1}(x1)) = x1   
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))


(10) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.

(11) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = x1   
POL(Aa_{Ab_1}(x1)) = x1   
POL(Aa_{Begin_1}(x1)) = x1   
POL(Aa_{Left_1}(x1)) = x1   
POL(Aa_{Right1_1}(x1)) = x1   
POL(Aa_{Right2_1}(x1)) = x1   
POL(Aa_{Right3_1}(x1)) = x1   
POL(Aa_{Right4_1}(x1)) = x1   
POL(Aa_{Right5_1}(x1)) = 1 + x1   
POL(Aa_{Wait_1}(x1)) = x1   
POL(Ab_{Aa_1}(x1)) = x1   
POL(Ab_{Ab_1}(x1)) = x1   
POL(Ab_{Begin_1}(x1)) = x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right1_1}(x1)) = x1   
POL(Ab_{Right2_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Ab_{Right4_1}(x1)) = x1   
POL(Ab_{Right5_1}(x1)) = 1 + x1   
POL(Ab_{Wait_1}(x1)) = x1   
POL(Begin_{Begin_1}(x1)) = x1   
POL(Begin_{Wait_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = x1   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = x1   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{Begin_1}(x1)) = x1   
POL(Left_{Wait_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = x1   
POL(Left_{b_1}(x1)) = x1   
POL(Right1_{Begin_1}(x1)) = x1   
POL(Right1_{Wait_1}(x1)) = x1   
POL(Right1_{a_1}(x1)) = x1   
POL(Right1_{b_1}(x1)) = x1   
POL(Right2_{Begin_1}(x1)) = x1   
POL(Right2_{Wait_1}(x1)) = x1   
POL(Right2_{a_1}(x1)) = x1   
POL(Right2_{b_1}(x1)) = x1   
POL(Right3_{Begin_1}(x1)) = x1   
POL(Right3_{Wait_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = x1   
POL(Right3_{b_1}(x1)) = x1   
POL(Right4_{Begin_1}(x1)) = x1   
POL(Right4_{Wait_1}(x1)) = x1   
POL(Right4_{a_1}(x1)) = x1   
POL(Right4_{b_1}(x1)) = x1   
POL(Right5_{Begin_1}(x1)) = x1   
POL(Right5_{Wait_1}(x1)) = x1   
POL(Right5_{a_1}(x1)) = x1   
POL(Right5_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = x1   
POL(Wait_{Ab_1}(x1)) = x1   
POL(Wait_{Begin_1}(x1)) = x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(Wait_{Wait_1}(x1)) = x1   
POL(a_{Begin_1}(x1)) = x1   
POL(a_{End_1}(x1)) = x1   
POL(a_{Wait_1}(x1)) = x1   
POL(a_{a_1}(x1)) = x1   
POL(a_{b_1}(x1)) = x1   
POL(b_{Begin_1}(x1)) = x1   
POL(b_{End_1}(x1)) = x1   
POL(b_{Wait_1}(x1)) = x1   
POL(b_{a_1}(x1)) = x1   
POL(b_{b_1}(x1)) = x1   
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Begin_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{b_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{a_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Wait_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right1_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right2_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right3_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right4_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Right5_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{End_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Left_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Ab_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{End_1}(End_{Aa_1}(x)))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))


(12) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.

(13) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = x1   
POL(Aa_{Ab_1}(x1)) = x1   
POL(Aa_{Begin_1}(x1)) = x1   
POL(Aa_{Left_1}(x1)) = x1   
POL(Aa_{Right1_1}(x1)) = x1   
POL(Aa_{Right2_1}(x1)) = x1   
POL(Aa_{Right3_1}(x1)) = x1   
POL(Aa_{Right4_1}(x1)) = x1   
POL(Aa_{Right5_1}(x1)) = x1   
POL(Aa_{Wait_1}(x1)) = x1   
POL(Ab_{Aa_1}(x1)) = x1   
POL(Ab_{Ab_1}(x1)) = x1   
POL(Ab_{Begin_1}(x1)) = x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right1_1}(x1)) = x1   
POL(Ab_{Right2_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Ab_{Right4_1}(x1)) = x1   
POL(Ab_{Right5_1}(x1)) = x1   
POL(Ab_{Wait_1}(x1)) = x1   
POL(Begin_{Begin_1}(x1)) = x1   
POL(Begin_{Wait_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = x1   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = x1   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{Begin_1}(x1)) = x1   
POL(Left_{Wait_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = x1   
POL(Left_{b_1}(x1)) = x1   
POL(Right1_{Begin_1}(x1)) = x1   
POL(Right1_{Wait_1}(x1)) = x1   
POL(Right1_{a_1}(x1)) = x1   
POL(Right1_{b_1}(x1)) = x1   
POL(Right2_{Begin_1}(x1)) = x1   
POL(Right2_{Wait_1}(x1)) = x1   
POL(Right2_{a_1}(x1)) = x1   
POL(Right2_{b_1}(x1)) = x1   
POL(Right3_{Begin_1}(x1)) = x1   
POL(Right3_{Wait_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = x1   
POL(Right3_{b_1}(x1)) = x1   
POL(Right4_{Begin_1}(x1)) = x1   
POL(Right4_{Wait_1}(x1)) = x1   
POL(Right4_{a_1}(x1)) = x1   
POL(Right4_{b_1}(x1)) = x1   
POL(Right5_{Begin_1}(x1)) = x1   
POL(Right5_{Wait_1}(x1)) = x1   
POL(Right5_{a_1}(x1)) = x1   
POL(Right5_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = x1   
POL(Wait_{Ab_1}(x1)) = x1   
POL(Wait_{Begin_1}(x1)) = x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(Wait_{Wait_1}(x1)) = x1   
POL(a_{Begin_1}(x1)) = x1   
POL(a_{End_1}(x1)) = x1   
POL(a_{Wait_1}(x1)) = x1   
POL(a_{a_1}(x1)) = x1   
POL(a_{b_1}(x1)) = x1   
POL(b_{Begin_1}(x1)) = x1   
POL(b_{End_1}(x1)) = 1 + x1   
POL(b_{Wait_1}(x1)) = x1   
POL(b_{a_1}(x1)) = x1   
POL(b_{b_1}(x1)) = x1   
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Begin_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{b_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{a_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Wait_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right1_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right2_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right3_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right4_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Right5_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{End_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Left_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Ab_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{End_1}(End_{Aa_1}(x))))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))


(14) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.

(15) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.

(16) Obligation:

Q DP problem:
The TRS P consists of the following rules:

BEGIN_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → BEGIN_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
BEGIN_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{b_1}(x))
BEGIN_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{B_1}(x)
BEGIN_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → BEGIN_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
BEGIN_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{a_1}(x))
B_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → B_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
B_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{b_1}(x))
B_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{B_1}(x)
B_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → B_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
B_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{a_1}(x))
A_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → A_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
A_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{b_1}(x))
A_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{B_1}(x)
A_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → A_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
A_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{a_1}(x))
WAIT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
WAIT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{b_1}(x))
WAIT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{B_1}(x)
WAIT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
WAIT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{a_1}(x))
RIGHT1_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT1_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT1_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{b_1}(x))
RIGHT1_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{B_1}(x)
RIGHT1_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT1_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
RIGHT1_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{a_1}(x))
RIGHT2_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT2_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT2_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{b_1}(x))
RIGHT2_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{B_1}(x)
RIGHT2_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT2_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
RIGHT2_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{a_1}(x))
RIGHT3_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT3_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{b_1}(x))
RIGHT3_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{B_1}(x)
RIGHT3_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT3_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
RIGHT3_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{a_1}(x))
RIGHT4_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT4_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT4_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{b_1}(x))
RIGHT4_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{B_1}(x)
RIGHT4_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT4_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
RIGHT4_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{a_1}(x))
RIGHT5_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT5_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT5_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{b_1}(x))
RIGHT5_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{B_1}(x)
RIGHT5_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT5_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
RIGHT5_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{a_1}(x))
END_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → END_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
END_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{b_1}(x))
END_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{B_1}(x)
END_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → END_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
END_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{a_1}(x))
LEFT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → LEFT_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
LEFT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{b_1}(x))
LEFT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{B_1}(x)
LEFT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → LEFT_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
LEFT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{a_1}(x))
AB_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → AB_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
AB_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{b_1}(x))
AB_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{B_1}(x)
AB_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → AB_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
AB_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{a_1}(x))
AA_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → AA_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
AA_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{b_1}(x))
AA_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{B_1}(x)
AA_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → AA_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
AA_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{RIGHT3_1}(Right3_{a_1}(x))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))
AB_{RIGHT1_1}(Right1_{b_1}(b_{b_1}(x))) → AB_{AB_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
AB_{RIGHT1_1}(Right1_{b_1}(b_{b_1}(x))) → AB_{RIGHT1_1}(Right1_{b_1}(x))
AB_{RIGHT1_1}(Right1_{b_1}(b_{b_1}(x))) → RIGHT1_{B_1}(x)
AB_{RIGHT1_1}(Right1_{b_1}(b_{a_1}(x))) → AB_{AB_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
AB_{RIGHT1_1}(Right1_{b_1}(b_{a_1}(x))) → AB_{RIGHT1_1}(Right1_{a_1}(x))
AA_{RIGHT1_1}(Right1_{b_1}(b_{b_1}(x))) → AA_{AB_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
AA_{RIGHT1_1}(Right1_{b_1}(b_{b_1}(x))) → AB_{RIGHT1_1}(Right1_{b_1}(x))
AA_{RIGHT1_1}(Right1_{b_1}(b_{b_1}(x))) → RIGHT1_{B_1}(x)
AA_{RIGHT1_1}(Right1_{b_1}(b_{a_1}(x))) → AA_{AB_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
AA_{RIGHT1_1}(Right1_{b_1}(b_{a_1}(x))) → AB_{RIGHT1_1}(Right1_{a_1}(x))
AB_{RIGHT2_1}(Right2_{b_1}(b_{b_1}(x))) → AB_{AB_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
AB_{RIGHT2_1}(Right2_{b_1}(b_{b_1}(x))) → AB_{RIGHT2_1}(Right2_{b_1}(x))
AB_{RIGHT2_1}(Right2_{b_1}(b_{b_1}(x))) → RIGHT2_{B_1}(x)
AB_{RIGHT2_1}(Right2_{b_1}(b_{a_1}(x))) → AB_{AB_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
AB_{RIGHT2_1}(Right2_{b_1}(b_{a_1}(x))) → AB_{RIGHT2_1}(Right2_{a_1}(x))
AA_{RIGHT2_1}(Right2_{b_1}(b_{b_1}(x))) → AA_{AB_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
AA_{RIGHT2_1}(Right2_{b_1}(b_{b_1}(x))) → AB_{RIGHT2_1}(Right2_{b_1}(x))
AA_{RIGHT2_1}(Right2_{b_1}(b_{b_1}(x))) → RIGHT2_{B_1}(x)
AA_{RIGHT2_1}(Right2_{b_1}(b_{a_1}(x))) → AA_{AB_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
AA_{RIGHT2_1}(Right2_{b_1}(b_{a_1}(x))) → AB_{RIGHT2_1}(Right2_{a_1}(x))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → WAIT_{AB_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → AB_{RIGHT3_1}(Right3_{b_1}(x))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → RIGHT3_{B_1}(x)
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{a_1}(x))) → WAIT_{AB_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
WAIT_{RIGHT3_1}(Right3_{b_1}(b_{a_1}(x))) → AB_{RIGHT3_1}(Right3_{a_1}(x))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → AB_{AB_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → AB_{RIGHT3_1}(Right3_{b_1}(x))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → RIGHT3_{B_1}(x)
AB_{RIGHT3_1}(Right3_{b_1}(b_{a_1}(x))) → AB_{AB_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
AB_{RIGHT3_1}(Right3_{b_1}(b_{a_1}(x))) → AB_{RIGHT3_1}(Right3_{a_1}(x))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → AA_{AB_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → AB_{RIGHT3_1}(Right3_{b_1}(x))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → RIGHT3_{B_1}(x)
AA_{RIGHT3_1}(Right3_{b_1}(b_{a_1}(x))) → AA_{AB_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
AA_{RIGHT3_1}(Right3_{b_1}(b_{a_1}(x))) → AB_{RIGHT3_1}(Right3_{a_1}(x))
AB_{RIGHT4_1}(Right4_{b_1}(b_{b_1}(x))) → AB_{AB_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
AB_{RIGHT4_1}(Right4_{b_1}(b_{b_1}(x))) → AB_{RIGHT4_1}(Right4_{b_1}(x))
AB_{RIGHT4_1}(Right4_{b_1}(b_{b_1}(x))) → RIGHT4_{B_1}(x)
AB_{RIGHT4_1}(Right4_{b_1}(b_{a_1}(x))) → AB_{AB_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
AB_{RIGHT4_1}(Right4_{b_1}(b_{a_1}(x))) → AB_{RIGHT4_1}(Right4_{a_1}(x))
AA_{RIGHT4_1}(Right4_{b_1}(b_{b_1}(x))) → AA_{AB_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
AA_{RIGHT4_1}(Right4_{b_1}(b_{b_1}(x))) → AB_{RIGHT4_1}(Right4_{b_1}(x))
AA_{RIGHT4_1}(Right4_{b_1}(b_{b_1}(x))) → RIGHT4_{B_1}(x)
AA_{RIGHT4_1}(Right4_{b_1}(b_{a_1}(x))) → AA_{AB_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
AA_{RIGHT4_1}(Right4_{b_1}(b_{a_1}(x))) → AB_{RIGHT4_1}(Right4_{a_1}(x))
AB_{RIGHT5_1}(Right5_{b_1}(b_{b_1}(x))) → AB_{AB_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
AB_{RIGHT5_1}(Right5_{b_1}(b_{b_1}(x))) → AB_{RIGHT5_1}(Right5_{b_1}(x))
AB_{RIGHT5_1}(Right5_{b_1}(b_{b_1}(x))) → RIGHT5_{B_1}(x)
AB_{RIGHT5_1}(Right5_{b_1}(b_{a_1}(x))) → AB_{AB_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
AB_{RIGHT5_1}(Right5_{b_1}(b_{a_1}(x))) → AB_{RIGHT5_1}(Right5_{a_1}(x))
AA_{RIGHT5_1}(Right5_{b_1}(b_{b_1}(x))) → AA_{AB_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
AA_{RIGHT5_1}(Right5_{b_1}(b_{b_1}(x))) → AB_{RIGHT5_1}(Right5_{b_1}(x))
AA_{RIGHT5_1}(Right5_{b_1}(b_{b_1}(x))) → RIGHT5_{B_1}(x)
AA_{RIGHT5_1}(Right5_{b_1}(b_{a_1}(x))) → AA_{AB_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
AA_{RIGHT5_1}(Right5_{b_1}(b_{a_1}(x))) → AB_{RIGHT5_1}(Right5_{a_1}(x))
AB_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → AB_{AA_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
AB_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → AA_{RIGHT1_1}(Right1_{b_1}(x))
AB_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → RIGHT1_{B_1}(x)
AB_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AB_{AA_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
AB_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AA_{RIGHT1_1}(Right1_{a_1}(x))
AA_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → AA_{AA_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
AA_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → AA_{RIGHT1_1}(Right1_{b_1}(x))
AA_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → RIGHT1_{B_1}(x)
AA_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AA_{AA_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
AA_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AA_{RIGHT1_1}(Right1_{a_1}(x))
AB_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → AB_{AA_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
AB_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → AA_{RIGHT2_1}(Right2_{b_1}(x))
AB_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → RIGHT2_{B_1}(x)
AB_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AB_{AA_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
AB_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AA_{RIGHT2_1}(Right2_{a_1}(x))
AA_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → AA_{AA_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
AA_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → AA_{RIGHT2_1}(Right2_{b_1}(x))
AA_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → RIGHT2_{B_1}(x)
AA_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AA_{AA_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
AA_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AA_{RIGHT2_1}(Right2_{a_1}(x))
WAIT_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → WAIT_{AA_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
WAIT_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → AA_{RIGHT3_1}(Right3_{b_1}(x))
WAIT_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → RIGHT3_{B_1}(x)
WAIT_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → WAIT_{AA_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
WAIT_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{RIGHT3_1}(Right3_{a_1}(x))
AB_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → AB_{AA_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
AB_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → AA_{RIGHT3_1}(Right3_{b_1}(x))
AB_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → RIGHT3_{B_1}(x)
AB_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AB_{AA_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
AB_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{RIGHT3_1}(Right3_{a_1}(x))
AA_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → AA_{AA_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
AA_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → AA_{RIGHT3_1}(Right3_{b_1}(x))
AA_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → RIGHT3_{B_1}(x)
AA_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{AA_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
AA_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{RIGHT3_1}(Right3_{a_1}(x))
AB_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → AB_{AA_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
AB_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → AA_{RIGHT4_1}(Right4_{b_1}(x))
AB_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → RIGHT4_{B_1}(x)
AB_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AB_{AA_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
AB_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AA_{RIGHT4_1}(Right4_{a_1}(x))
AA_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → AA_{AA_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
AA_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → AA_{RIGHT4_1}(Right4_{b_1}(x))
AA_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → RIGHT4_{B_1}(x)
AA_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AA_{AA_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
AA_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AA_{RIGHT4_1}(Right4_{a_1}(x))
AB_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → AB_{AA_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
AB_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → AA_{RIGHT5_1}(Right5_{b_1}(x))
AB_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → RIGHT5_{B_1}(x)
AB_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AB_{AA_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
AB_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AA_{RIGHT5_1}(Right5_{a_1}(x))
AA_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → AA_{AA_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
AA_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → AA_{RIGHT5_1}(Right5_{b_1}(x))
AA_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → RIGHT5_{B_1}(x)
AA_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AA_{AA_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
AA_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AA_{RIGHT5_1}(Right5_{a_1}(x))
WAIT_{AB_1}(Ab_{Left_1}(Left_{b_1}(x))) → LEFT_{B_1}(b_{b_1}(x))
WAIT_{AB_1}(Ab_{Left_1}(Left_{b_1}(x))) → B_{B_1}(x)
WAIT_{AB_1}(Ab_{Left_1}(Left_{a_1}(x))) → LEFT_{B_1}(b_{a_1}(x))
AB_{AB_1}(Ab_{Left_1}(Left_{b_1}(x))) → LEFT_{B_1}(b_{b_1}(x))
AB_{AB_1}(Ab_{Left_1}(Left_{b_1}(x))) → B_{B_1}(x)
AB_{AB_1}(Ab_{Left_1}(Left_{a_1}(x))) → LEFT_{B_1}(b_{a_1}(x))
AA_{AB_1}(Ab_{Left_1}(Left_{b_1}(x))) → LEFT_{B_1}(b_{b_1}(x))
AA_{AB_1}(Ab_{Left_1}(Left_{b_1}(x))) → B_{B_1}(x)
AA_{AB_1}(Ab_{Left_1}(Left_{a_1}(x))) → LEFT_{B_1}(b_{a_1}(x))
WAIT_{AA_1}(Aa_{Left_1}(Left_{b_1}(x))) → A_{B_1}(x)
AB_{AA_1}(Aa_{Left_1}(Left_{b_1}(x))) → A_{B_1}(x)
AA_{AA_1}(Aa_{Left_1}(Left_{b_1}(x))) → A_{B_1}(x)
BEGIN_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → BEGIN_{BEGIN_1}(Begin_{b_1}(x))
B_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → B_{BEGIN_1}(Begin_{b_1}(x))
A_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → A_{BEGIN_1}(Begin_{b_1}(x))
WAIT_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → WAIT_{BEGIN_1}(Begin_{b_1}(x))
RIGHT1_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT1_{BEGIN_1}(Begin_{b_1}(x))
RIGHT2_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT2_{BEGIN_1}(Begin_{b_1}(x))
RIGHT3_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT3_{BEGIN_1}(Begin_{b_1}(x))
RIGHT4_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT4_{BEGIN_1}(Begin_{b_1}(x))
RIGHT5_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT5_{BEGIN_1}(Begin_{b_1}(x))
END_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → END_{BEGIN_1}(Begin_{b_1}(x))
LEFT_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → LEFT_{BEGIN_1}(Begin_{b_1}(x))
AB_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → AB_{BEGIN_1}(Begin_{b_1}(x))
AA_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → AA_{BEGIN_1}(Begin_{b_1}(x))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{a_1}(a_{b_1}(x)))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{a_1}(a_{a_1}(x)))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{a_1}(a_{b_1}(x)))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{a_1}(a_{a_1}(x)))
RIGHT1_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
RIGHT1_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
RIGHT1_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
RIGHT1_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
RIGHT1_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{a_1}(a_{b_1}(x)))
RIGHT1_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)
RIGHT1_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))))
RIGHT1_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))
RIGHT1_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))
RIGHT1_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))
RIGHT1_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{a_1}(a_{a_1}(x)))
RIGHT2_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
RIGHT2_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
RIGHT2_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
RIGHT2_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
RIGHT2_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{a_1}(a_{b_1}(x)))
RIGHT2_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)
RIGHT2_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))))
RIGHT2_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))
RIGHT2_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))
RIGHT2_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))
RIGHT2_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{a_1}(a_{a_1}(x)))
RIGHT3_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
RIGHT3_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
RIGHT3_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
RIGHT3_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
RIGHT3_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{a_1}(a_{b_1}(x)))
RIGHT3_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)
RIGHT3_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))))
RIGHT3_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))
RIGHT3_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))
RIGHT3_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))
RIGHT3_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{a_1}(a_{a_1}(x)))
RIGHT4_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
RIGHT4_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
RIGHT4_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
RIGHT4_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
RIGHT4_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{a_1}(a_{b_1}(x)))
RIGHT4_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)
RIGHT4_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))))
RIGHT4_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))
RIGHT4_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))
RIGHT4_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))
RIGHT4_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{a_1}(a_{a_1}(x)))
RIGHT5_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
RIGHT5_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
RIGHT5_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
RIGHT5_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
RIGHT5_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{a_1}(a_{b_1}(x)))
RIGHT5_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)
RIGHT5_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))))
RIGHT5_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))
RIGHT5_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))
RIGHT5_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))
RIGHT5_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{a_1}(a_{a_1}(x)))
LEFT_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
LEFT_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
LEFT_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
LEFT_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
LEFT_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{a_1}(a_{b_1}(x)))
LEFT_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)
LEFT_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))))
LEFT_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))
LEFT_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x)))))
LEFT_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))
LEFT_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → B_{B_1}(b_{a_1}(a_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(17) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 19 SCCs with 355 less nodes.

(18) Complex Obligation (AND)

(19) Obligation:

Q DP problem:
The TRS P consists of the following rules:

A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(20) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(21) Obligation:

Q DP problem:
The TRS P consists of the following rules:

A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)

The TRS R consists of the following rules:

a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(22) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → B_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))
A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(x)
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation:
POL( A_{B_1}(x1) ) = x1

POL( b_{a_1}(x1) ) = x1 + 2

POL( B_{B_1}(x1) ) = x1 + 1

POL( a_{b_1}(x1) ) = 2x1

POL( b_{b_1}(x1) ) = 2x1 + 2

POL( a_{a_1}(x1) ) = x1


The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(23) Obligation:

Q DP problem:
The TRS P consists of the following rules:

A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))

The TRS R consists of the following rules:

a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(24) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


A_{B_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → A_{B_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x)))))))
The remaining pairs can at least be oriented weakly.
Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:

POL(A_{B_1}(x1)) = 0A +
[-I,0A,0A]
·x1

POL(b_{b_1}(x1)) =
/0A\
|0A|
\-I/
 +
/-I0A0A\
|0A-I0A|
\-I-I0A/
·x1

POL(b_{a_1}(x1)) =
/0A\
|0A|
\-I/
 +
/-I0A0A\
|0A-I-I|
\-I-I-I/
·x1

POL(a_{b_1}(x1)) =
/0A\
|0A|
\1A/
 +
/-I-I0A\
|0A0A0A|
\-I0A1A/
·x1

POL(a_{a_1}(x1)) =
/0A\
|-I|
\-I/
 +
/0A-I-I\
|0A-I0A|
\-I-I-I/
·x1

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(25) Obligation:

Q DP problem:
P is empty.
The TRS R consists of the following rules:

a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(26) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(27) YES

(28) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT5_1}(Right5_{b_1}(b_{a_1}(x))) → AB_{RIGHT5_1}(Right5_{a_1}(x))
AB_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → AA_{RIGHT5_1}(Right5_{b_1}(x))
AA_{RIGHT5_1}(Right5_{b_1}(b_{b_1}(x))) → AB_{RIGHT5_1}(Right5_{b_1}(x))
AB_{RIGHT5_1}(Right5_{b_1}(b_{b_1}(x))) → AB_{RIGHT5_1}(Right5_{b_1}(x))
AB_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AA_{RIGHT5_1}(Right5_{a_1}(x))
AA_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → AA_{RIGHT5_1}(Right5_{b_1}(x))
AA_{RIGHT5_1}(Right5_{b_1}(b_{a_1}(x))) → AB_{RIGHT5_1}(Right5_{a_1}(x))
AA_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AA_{RIGHT5_1}(Right5_{a_1}(x))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(29) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(30) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT5_1}(Right5_{b_1}(b_{a_1}(x))) → AB_{RIGHT5_1}(Right5_{a_1}(x))
AB_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → AA_{RIGHT5_1}(Right5_{b_1}(x))
AA_{RIGHT5_1}(Right5_{b_1}(b_{b_1}(x))) → AB_{RIGHT5_1}(Right5_{b_1}(x))
AB_{RIGHT5_1}(Right5_{b_1}(b_{b_1}(x))) → AB_{RIGHT5_1}(Right5_{b_1}(x))
AB_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AA_{RIGHT5_1}(Right5_{a_1}(x))
AA_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → AA_{RIGHT5_1}(Right5_{b_1}(x))
AA_{RIGHT5_1}(Right5_{b_1}(b_{a_1}(x))) → AB_{RIGHT5_1}(Right5_{a_1}(x))
AA_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AA_{RIGHT5_1}(Right5_{a_1}(x))

The TRS R consists of the following rules:

Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(31) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AB_{RIGHT5_1}(Right5_{b_1}(b_{a_1}(x))) → AB_{RIGHT5_1}(Right5_{a_1}(x))
AA_{RIGHT5_1}(Right5_{b_1}(b_{b_1}(x))) → AB_{RIGHT5_1}(Right5_{b_1}(x))
AB_{RIGHT5_1}(Right5_{b_1}(b_{b_1}(x))) → AB_{RIGHT5_1}(Right5_{b_1}(x))
AA_{RIGHT5_1}(Right5_{b_1}(b_{a_1}(x))) → AB_{RIGHT5_1}(Right5_{a_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(AA_{RIGHT5_1}(x1)) = x1   
POL(AB_{RIGHT5_1}(x1)) = x1   
POL(Right5_{a_1}(x1)) = x1   
POL(Right5_{b_1}(x1)) = x1   
POL(a_{a_1}(x1)) = x1   
POL(a_{b_1}(x1)) = x1   
POL(b_{a_1}(x1)) = 1 + x1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(32) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → AA_{RIGHT5_1}(Right5_{b_1}(x))
AB_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AA_{RIGHT5_1}(Right5_{a_1}(x))
AA_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → AA_{RIGHT5_1}(Right5_{b_1}(x))
AA_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AA_{RIGHT5_1}(Right5_{a_1}(x))

The TRS R consists of the following rules:

Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(33) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

(34) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AA_{RIGHT5_1}(Right5_{a_1}(x))
AA_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → AA_{RIGHT5_1}(Right5_{b_1}(x))

The TRS R consists of the following rules:

Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(35) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AA_{RIGHT5_1}(Right5_{a_1}(a_{b_1}(x))) → AA_{RIGHT5_1}(Right5_{b_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:

POL(AA_{RIGHT5_1}(x1)) = 0A +
[0A,0A,0A]
·x1

POL(Right5_{a_1}(x1)) =
/0A\
|0A|
\0A/
 +
/0A1A0A\
|0A0A-I|
\-I-I-I/
·x1

POL(a_{a_1}(x1)) =
/0A\
|-I|
\-I/
 +
/-I-I-I\
|0A0A0A|
\-I-I-I/
·x1

POL(a_{b_1}(x1)) =
/-I\
|0A|
\0A/
 +
/0A0A0A\
|0A0A1A|
\0A0A0A/
·x1

POL(Right5_{b_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A0A1A\
|0A0A1A|
\0A0A0A/
·x1

POL(b_{b_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A-I0A\
|-I-I0A|
\-I0A-I/
·x1

POL(b_{a_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A-I-I\
|0A-I0A|
\-I-I-I/
·x1

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(36) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AA_{RIGHT5_1}(Right5_{a_1}(x))

The TRS R consists of the following rules:

Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(37) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(38) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AA_{RIGHT5_1}(Right5_{a_1}(x))

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(39) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AA_{RIGHT5_1}(Right5_{a_1}(a_{a_1}(x))) → AA_{RIGHT5_1}(Right5_{a_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(AA_{RIGHT5_1}(x1)) = x1   
POL(Right5_{a_1}(x1)) = x1   
POL(a_{a_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
none

(40) Obligation:

Q DP problem:
P is empty.
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(41) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(42) YES

(43) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT4_1}(Right4_{b_1}(b_{a_1}(x))) → AB_{RIGHT4_1}(Right4_{a_1}(x))
AB_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → AA_{RIGHT4_1}(Right4_{b_1}(x))
AA_{RIGHT4_1}(Right4_{b_1}(b_{b_1}(x))) → AB_{RIGHT4_1}(Right4_{b_1}(x))
AB_{RIGHT4_1}(Right4_{b_1}(b_{b_1}(x))) → AB_{RIGHT4_1}(Right4_{b_1}(x))
AB_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AA_{RIGHT4_1}(Right4_{a_1}(x))
AA_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → AA_{RIGHT4_1}(Right4_{b_1}(x))
AA_{RIGHT4_1}(Right4_{b_1}(b_{a_1}(x))) → AB_{RIGHT4_1}(Right4_{a_1}(x))
AA_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AA_{RIGHT4_1}(Right4_{a_1}(x))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(44) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(45) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT4_1}(Right4_{b_1}(b_{a_1}(x))) → AB_{RIGHT4_1}(Right4_{a_1}(x))
AB_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → AA_{RIGHT4_1}(Right4_{b_1}(x))
AA_{RIGHT4_1}(Right4_{b_1}(b_{b_1}(x))) → AB_{RIGHT4_1}(Right4_{b_1}(x))
AB_{RIGHT4_1}(Right4_{b_1}(b_{b_1}(x))) → AB_{RIGHT4_1}(Right4_{b_1}(x))
AB_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AA_{RIGHT4_1}(Right4_{a_1}(x))
AA_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → AA_{RIGHT4_1}(Right4_{b_1}(x))
AA_{RIGHT4_1}(Right4_{b_1}(b_{a_1}(x))) → AB_{RIGHT4_1}(Right4_{a_1}(x))
AA_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AA_{RIGHT4_1}(Right4_{a_1}(x))

The TRS R consists of the following rules:

Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(46) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AB_{RIGHT4_1}(Right4_{b_1}(b_{a_1}(x))) → AB_{RIGHT4_1}(Right4_{a_1}(x))
AA_{RIGHT4_1}(Right4_{b_1}(b_{b_1}(x))) → AB_{RIGHT4_1}(Right4_{b_1}(x))
AB_{RIGHT4_1}(Right4_{b_1}(b_{b_1}(x))) → AB_{RIGHT4_1}(Right4_{b_1}(x))
AA_{RIGHT4_1}(Right4_{b_1}(b_{a_1}(x))) → AB_{RIGHT4_1}(Right4_{a_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation:
POL( AA_{RIGHT4_1}(x1) ) = max{0, 2x1 - 2}

POL( AB_{RIGHT4_1}(x1) ) = max{0, 2x1 - 2}

POL( Right4_{b_1}(x1) ) = 2x1 + 1

POL( b_{b_1}(x1) ) = 2x1 + 2

POL( b_{a_1}(x1) ) = 2x1 + 2

POL( a_{b_1}(x1) ) = x1

POL( Right4_{a_1}(x1) ) = 2x1 + 1

POL( a_{a_1}(x1) ) = x1


The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(47) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → AA_{RIGHT4_1}(Right4_{b_1}(x))
AB_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AA_{RIGHT4_1}(Right4_{a_1}(x))
AA_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → AA_{RIGHT4_1}(Right4_{b_1}(x))
AA_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AA_{RIGHT4_1}(Right4_{a_1}(x))

The TRS R consists of the following rules:

Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(48) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

(49) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AA_{RIGHT4_1}(Right4_{a_1}(x))
AA_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → AA_{RIGHT4_1}(Right4_{b_1}(x))

The TRS R consists of the following rules:

Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(50) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AA_{RIGHT4_1}(Right4_{a_1}(a_{b_1}(x))) → AA_{RIGHT4_1}(Right4_{b_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:

POL(AA_{RIGHT4_1}(x1)) = 0A +
[0A,0A,0A]
·x1

POL(Right4_{a_1}(x1)) =
/0A\
|0A|
\0A/
 +
/0A1A0A\
|0A0A-I|
\-I-I-I/
·x1

POL(a_{a_1}(x1)) =
/0A\
|-I|
\-I/
 +
/-I-I-I\
|0A0A0A|
\-I-I-I/
·x1

POL(a_{b_1}(x1)) =
/-I\
|0A|
\0A/
 +
/0A0A0A\
|0A0A1A|
\0A0A0A/
·x1

POL(Right4_{b_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A0A1A\
|0A0A1A|
\0A0A0A/
·x1

POL(b_{b_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A-I0A\
|-I-I0A|
\-I0A-I/
·x1

POL(b_{a_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A-I-I\
|0A-I0A|
\-I-I-I/
·x1

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(51) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AA_{RIGHT4_1}(Right4_{a_1}(x))

The TRS R consists of the following rules:

Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(52) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(53) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AA_{RIGHT4_1}(Right4_{a_1}(x))

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(54) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AA_{RIGHT4_1}(Right4_{a_1}(a_{a_1}(x))) → AA_{RIGHT4_1}(Right4_{a_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(AA_{RIGHT4_1}(x1)) = x1   
POL(Right4_{a_1}(x1)) = x1   
POL(a_{a_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
none

(55) Obligation:

Q DP problem:
P is empty.
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(56) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(57) YES

(58) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT2_1}(Right2_{b_1}(b_{a_1}(x))) → AB_{RIGHT2_1}(Right2_{a_1}(x))
AB_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → AA_{RIGHT2_1}(Right2_{b_1}(x))
AA_{RIGHT2_1}(Right2_{b_1}(b_{b_1}(x))) → AB_{RIGHT2_1}(Right2_{b_1}(x))
AB_{RIGHT2_1}(Right2_{b_1}(b_{b_1}(x))) → AB_{RIGHT2_1}(Right2_{b_1}(x))
AB_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AA_{RIGHT2_1}(Right2_{a_1}(x))
AA_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → AA_{RIGHT2_1}(Right2_{b_1}(x))
AA_{RIGHT2_1}(Right2_{b_1}(b_{a_1}(x))) → AB_{RIGHT2_1}(Right2_{a_1}(x))
AA_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AA_{RIGHT2_1}(Right2_{a_1}(x))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(59) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(60) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT2_1}(Right2_{b_1}(b_{a_1}(x))) → AB_{RIGHT2_1}(Right2_{a_1}(x))
AB_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → AA_{RIGHT2_1}(Right2_{b_1}(x))
AA_{RIGHT2_1}(Right2_{b_1}(b_{b_1}(x))) → AB_{RIGHT2_1}(Right2_{b_1}(x))
AB_{RIGHT2_1}(Right2_{b_1}(b_{b_1}(x))) → AB_{RIGHT2_1}(Right2_{b_1}(x))
AB_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AA_{RIGHT2_1}(Right2_{a_1}(x))
AA_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → AA_{RIGHT2_1}(Right2_{b_1}(x))
AA_{RIGHT2_1}(Right2_{b_1}(b_{a_1}(x))) → AB_{RIGHT2_1}(Right2_{a_1}(x))
AA_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AA_{RIGHT2_1}(Right2_{a_1}(x))

The TRS R consists of the following rules:

Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(61) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AB_{RIGHT2_1}(Right2_{b_1}(b_{a_1}(x))) → AB_{RIGHT2_1}(Right2_{a_1}(x))
AA_{RIGHT2_1}(Right2_{b_1}(b_{b_1}(x))) → AB_{RIGHT2_1}(Right2_{b_1}(x))
AB_{RIGHT2_1}(Right2_{b_1}(b_{b_1}(x))) → AB_{RIGHT2_1}(Right2_{b_1}(x))
AA_{RIGHT2_1}(Right2_{b_1}(b_{a_1}(x))) → AB_{RIGHT2_1}(Right2_{a_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(AA_{RIGHT2_1}(x1)) = x1   
POL(AB_{RIGHT2_1}(x1)) = x1   
POL(Right2_{a_1}(x1)) = x1   
POL(Right2_{b_1}(x1)) = x1   
POL(a_{a_1}(x1)) = x1   
POL(a_{b_1}(x1)) = x1   
POL(b_{a_1}(x1)) = 1 + x1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(62) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → AA_{RIGHT2_1}(Right2_{b_1}(x))
AB_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AA_{RIGHT2_1}(Right2_{a_1}(x))
AA_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → AA_{RIGHT2_1}(Right2_{b_1}(x))
AA_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AA_{RIGHT2_1}(Right2_{a_1}(x))

The TRS R consists of the following rules:

Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(63) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

(64) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AA_{RIGHT2_1}(Right2_{a_1}(x))
AA_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → AA_{RIGHT2_1}(Right2_{b_1}(x))

The TRS R consists of the following rules:

Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(65) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AA_{RIGHT2_1}(Right2_{a_1}(a_{b_1}(x))) → AA_{RIGHT2_1}(Right2_{b_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:

POL(AA_{RIGHT2_1}(x1)) = 0A +
[0A,0A,0A]
·x1

POL(Right2_{a_1}(x1)) =
/0A\
|0A|
\0A/
 +
/0A1A0A\
|0A0A-I|
\-I-I-I/
·x1

POL(a_{a_1}(x1)) =
/0A\
|-I|
\-I/
 +
/-I-I-I\
|0A0A0A|
\-I-I-I/
·x1

POL(a_{b_1}(x1)) =
/-I\
|0A|
\0A/
 +
/0A0A0A\
|0A0A1A|
\0A0A0A/
·x1

POL(Right2_{b_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A0A1A\
|0A0A1A|
\0A0A0A/
·x1

POL(b_{b_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A-I0A\
|-I-I0A|
\-I0A-I/
·x1

POL(b_{a_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A-I-I\
|0A-I0A|
\-I-I-I/
·x1

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(66) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AA_{RIGHT2_1}(Right2_{a_1}(x))

The TRS R consists of the following rules:

Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(67) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(68) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AA_{RIGHT2_1}(Right2_{a_1}(x))

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(69) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AA_{RIGHT2_1}(Right2_{a_1}(a_{a_1}(x))) → AA_{RIGHT2_1}(Right2_{a_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(AA_{RIGHT2_1}(x1)) = x1   
POL(Right2_{a_1}(x1)) = x1   
POL(a_{a_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
none

(70) Obligation:

Q DP problem:
P is empty.
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(71) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(72) YES

(73) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT1_1}(Right1_{b_1}(b_{a_1}(x))) → AB_{RIGHT1_1}(Right1_{a_1}(x))
AB_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → AA_{RIGHT1_1}(Right1_{b_1}(x))
AA_{RIGHT1_1}(Right1_{b_1}(b_{b_1}(x))) → AB_{RIGHT1_1}(Right1_{b_1}(x))
AB_{RIGHT1_1}(Right1_{b_1}(b_{b_1}(x))) → AB_{RIGHT1_1}(Right1_{b_1}(x))
AB_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AA_{RIGHT1_1}(Right1_{a_1}(x))
AA_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → AA_{RIGHT1_1}(Right1_{b_1}(x))
AA_{RIGHT1_1}(Right1_{b_1}(b_{a_1}(x))) → AB_{RIGHT1_1}(Right1_{a_1}(x))
AA_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AA_{RIGHT1_1}(Right1_{a_1}(x))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(74) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(75) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT1_1}(Right1_{b_1}(b_{a_1}(x))) → AB_{RIGHT1_1}(Right1_{a_1}(x))
AB_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → AA_{RIGHT1_1}(Right1_{b_1}(x))
AA_{RIGHT1_1}(Right1_{b_1}(b_{b_1}(x))) → AB_{RIGHT1_1}(Right1_{b_1}(x))
AB_{RIGHT1_1}(Right1_{b_1}(b_{b_1}(x))) → AB_{RIGHT1_1}(Right1_{b_1}(x))
AB_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AA_{RIGHT1_1}(Right1_{a_1}(x))
AA_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → AA_{RIGHT1_1}(Right1_{b_1}(x))
AA_{RIGHT1_1}(Right1_{b_1}(b_{a_1}(x))) → AB_{RIGHT1_1}(Right1_{a_1}(x))
AA_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AA_{RIGHT1_1}(Right1_{a_1}(x))

The TRS R consists of the following rules:

Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(76) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AB_{RIGHT1_1}(Right1_{b_1}(b_{a_1}(x))) → AB_{RIGHT1_1}(Right1_{a_1}(x))
AA_{RIGHT1_1}(Right1_{b_1}(b_{b_1}(x))) → AB_{RIGHT1_1}(Right1_{b_1}(x))
AB_{RIGHT1_1}(Right1_{b_1}(b_{b_1}(x))) → AB_{RIGHT1_1}(Right1_{b_1}(x))
AA_{RIGHT1_1}(Right1_{b_1}(b_{a_1}(x))) → AB_{RIGHT1_1}(Right1_{a_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(AA_{RIGHT1_1}(x1)) = x1   
POL(AB_{RIGHT1_1}(x1)) = x1   
POL(Right1_{a_1}(x1)) = x1   
POL(Right1_{b_1}(x1)) = x1   
POL(a_{a_1}(x1)) = x1   
POL(a_{b_1}(x1)) = x1   
POL(b_{a_1}(x1)) = 1 + x1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(77) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → AA_{RIGHT1_1}(Right1_{b_1}(x))
AB_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AA_{RIGHT1_1}(Right1_{a_1}(x))
AA_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → AA_{RIGHT1_1}(Right1_{b_1}(x))
AA_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AA_{RIGHT1_1}(Right1_{a_1}(x))

The TRS R consists of the following rules:

Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(78) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

(79) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AA_{RIGHT1_1}(Right1_{a_1}(x))
AA_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → AA_{RIGHT1_1}(Right1_{b_1}(x))

The TRS R consists of the following rules:

Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(80) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AA_{RIGHT1_1}(Right1_{a_1}(a_{b_1}(x))) → AA_{RIGHT1_1}(Right1_{b_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:

POL(AA_{RIGHT1_1}(x1)) = 0A +
[0A,0A,0A]
·x1

POL(Right1_{a_1}(x1)) =
/0A\
|0A|
\0A/
 +
/0A1A0A\
|0A0A-I|
\-I-I-I/
·x1

POL(a_{a_1}(x1)) =
/0A\
|-I|
\-I/
 +
/-I-I-I\
|0A0A0A|
\-I-I-I/
·x1

POL(a_{b_1}(x1)) =
/-I\
|0A|
\0A/
 +
/0A0A0A\
|0A0A1A|
\0A0A0A/
·x1

POL(Right1_{b_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A0A1A\
|0A0A1A|
\0A0A0A/
·x1

POL(b_{b_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A-I0A\
|-I-I0A|
\-I0A-I/
·x1

POL(b_{a_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A-I-I\
|0A-I0A|
\-I-I-I/
·x1

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(81) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AA_{RIGHT1_1}(Right1_{a_1}(x))

The TRS R consists of the following rules:

Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(82) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(83) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AA_{RIGHT1_1}(Right1_{a_1}(x))

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(84) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AA_{RIGHT1_1}(Right1_{a_1}(a_{a_1}(x))) → AA_{RIGHT1_1}(Right1_{a_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(AA_{RIGHT1_1}(x1)) = x1   
POL(Right1_{a_1}(x1)) = x1   
POL(a_{a_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
none

(85) Obligation:

Q DP problem:
P is empty.
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(86) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(87) YES

(88) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT3_1}(Right3_{b_1}(b_{a_1}(x))) → AB_{RIGHT3_1}(Right3_{a_1}(x))
AB_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → AA_{RIGHT3_1}(Right3_{b_1}(x))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → AB_{RIGHT3_1}(Right3_{b_1}(x))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → AB_{RIGHT3_1}(Right3_{b_1}(x))
AB_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{RIGHT3_1}(Right3_{a_1}(x))
AA_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → AA_{RIGHT3_1}(Right3_{b_1}(x))
AA_{RIGHT3_1}(Right3_{b_1}(b_{a_1}(x))) → AB_{RIGHT3_1}(Right3_{a_1}(x))
AA_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{RIGHT3_1}(Right3_{a_1}(x))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(89) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(90) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT3_1}(Right3_{b_1}(b_{a_1}(x))) → AB_{RIGHT3_1}(Right3_{a_1}(x))
AB_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → AA_{RIGHT3_1}(Right3_{b_1}(x))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → AB_{RIGHT3_1}(Right3_{b_1}(x))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → AB_{RIGHT3_1}(Right3_{b_1}(x))
AB_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{RIGHT3_1}(Right3_{a_1}(x))
AA_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → AA_{RIGHT3_1}(Right3_{b_1}(x))
AA_{RIGHT3_1}(Right3_{b_1}(b_{a_1}(x))) → AB_{RIGHT3_1}(Right3_{a_1}(x))
AA_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{RIGHT3_1}(Right3_{a_1}(x))

The TRS R consists of the following rules:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(91) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AB_{RIGHT3_1}(Right3_{b_1}(b_{a_1}(x))) → AB_{RIGHT3_1}(Right3_{a_1}(x))
AA_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → AB_{RIGHT3_1}(Right3_{b_1}(x))
AB_{RIGHT3_1}(Right3_{b_1}(b_{b_1}(x))) → AB_{RIGHT3_1}(Right3_{b_1}(x))
AA_{RIGHT3_1}(Right3_{b_1}(b_{a_1}(x))) → AB_{RIGHT3_1}(Right3_{a_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial Order [NEGPOLO,POLO] with Interpretation:
POL( AA_{RIGHT3_1}(x1) ) = max{0, 2x1 - 2}

POL( AB_{RIGHT3_1}(x1) ) = max{0, 2x1 - 2}

POL( Right3_{b_1}(x1) ) = 2x1 + 1

POL( b_{b_1}(x1) ) = 2x1 + 2

POL( b_{a_1}(x1) ) = 2x1 + 2

POL( a_{b_1}(x1) ) = x1

POL( Right3_{a_1}(x1) ) = 2x1 + 1

POL( a_{a_1}(x1) ) = x1


The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(92) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → AA_{RIGHT3_1}(Right3_{b_1}(x))
AB_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{RIGHT3_1}(Right3_{a_1}(x))
AA_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → AA_{RIGHT3_1}(Right3_{b_1}(x))
AA_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{RIGHT3_1}(Right3_{a_1}(x))

The TRS R consists of the following rules:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(93) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

(94) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{RIGHT3_1}(Right3_{a_1}(x))
AA_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → AA_{RIGHT3_1}(Right3_{b_1}(x))

The TRS R consists of the following rules:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(95) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AA_{RIGHT3_1}(Right3_{a_1}(a_{b_1}(x))) → AA_{RIGHT3_1}(Right3_{b_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Matrix interpretation [MATRO] with arctic natural numbers [ARCTIC]:

POL(AA_{RIGHT3_1}(x1)) = 0A +
[0A,0A,0A]
·x1

POL(Right3_{a_1}(x1)) =
/0A\
|0A|
\0A/
 +
/0A1A0A\
|0A0A-I|
\-I-I-I/
·x1

POL(a_{a_1}(x1)) =
/0A\
|-I|
\-I/
 +
/-I-I-I\
|0A0A0A|
\-I-I-I/
·x1

POL(a_{b_1}(x1)) =
/-I\
|0A|
\0A/
 +
/0A0A0A\
|0A0A1A|
\0A0A0A/
·x1

POL(Right3_{b_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A0A1A\
|0A0A1A|
\0A0A0A/
·x1

POL(b_{b_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A-I0A\
|-I-I0A|
\-I0A-I/
·x1

POL(b_{a_1}(x1)) =
/-I\
|-I|
\-I/
 +
/0A-I-I\
|0A-I0A|
\-I-I-I/
·x1

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(96) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{RIGHT3_1}(Right3_{a_1}(x))

The TRS R consists of the following rules:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(97) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(98) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{RIGHT3_1}(Right3_{a_1}(x))

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(99) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AA_{RIGHT3_1}(Right3_{a_1}(a_{a_1}(x))) → AA_{RIGHT3_1}(Right3_{a_1}(x))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(AA_{RIGHT3_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = x1   
POL(a_{a_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
none

(100) Obligation:

Q DP problem:
P is empty.
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(101) PisEmptyProof (EQUIVALENT transformation)

The TRS P is empty. Hence, there is no (P,Q,R) chain.

(102) YES

(103) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → AA_{BEGIN_1}(Begin_{b_1}(x))
AA_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → AA_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
AA_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → AA_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(104) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(105) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → AA_{BEGIN_1}(Begin_{b_1}(x))
AA_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → AA_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
AA_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → AA_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(106) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AA_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → AA_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
AA_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → AA_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(AA_{BEGIN_1}(x1)) = x1   
POL(AA_{WAIT_1}(x1)) = x1   
POL(Aa_{Aa_1}(x1)) = 0   
POL(Aa_{Ab_1}(x1)) = 0   
POL(Aa_{Left_1}(x1)) = 0   
POL(Aa_{Right3_1}(x1)) = 0   
POL(Ab_{Aa_1}(x1)) = 0   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = 0   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = 0   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = 0   
POL(Left_{b_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = 0   
POL(Right3_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = 0   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 0   
POL(a_{a_1}(x1)) = 0   
POL(a_{b_1}(x1)) = 0   
POL(b_{a_1}(x1)) = 1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(107) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AA_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → AA_{BEGIN_1}(Begin_{b_1}(x))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(108) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(109) TRUE

(110) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → AB_{BEGIN_1}(Begin_{b_1}(x))
AB_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → AB_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
AB_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → AB_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(111) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(112) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → AB_{BEGIN_1}(Begin_{b_1}(x))
AB_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → AB_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
AB_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → AB_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(113) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


AB_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → AB_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
AB_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → AB_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(AB_{BEGIN_1}(x1)) = x1   
POL(AB_{WAIT_1}(x1)) = x1   
POL(Aa_{Aa_1}(x1)) = 0   
POL(Aa_{Ab_1}(x1)) = 0   
POL(Aa_{Left_1}(x1)) = 0   
POL(Aa_{Right3_1}(x1)) = 0   
POL(Ab_{Aa_1}(x1)) = 0   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = 0   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = 0   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = 0   
POL(Left_{b_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = 0   
POL(Right3_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = 0   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 0   
POL(a_{a_1}(x1)) = 0   
POL(a_{b_1}(x1)) = 0   
POL(b_{a_1}(x1)) = 1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(114) Obligation:

Q DP problem:
The TRS P consists of the following rules:

AB_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → AB_{BEGIN_1}(Begin_{b_1}(x))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(115) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(116) TRUE

(117) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LEFT_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → LEFT_{BEGIN_1}(Begin_{b_1}(x))
LEFT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → LEFT_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
LEFT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → LEFT_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(118) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(119) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LEFT_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → LEFT_{BEGIN_1}(Begin_{b_1}(x))
LEFT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → LEFT_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
LEFT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → LEFT_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(120) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


LEFT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → LEFT_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
LEFT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → LEFT_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = 0   
POL(Aa_{Ab_1}(x1)) = 0   
POL(Aa_{Left_1}(x1)) = 0   
POL(Aa_{Right3_1}(x1)) = 0   
POL(Ab_{Aa_1}(x1)) = 0   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = 0   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = 0   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(LEFT_{BEGIN_1}(x1)) = x1   
POL(LEFT_{WAIT_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = 0   
POL(Left_{b_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = 0   
POL(Right3_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = 0   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 0   
POL(a_{a_1}(x1)) = 0   
POL(a_{b_1}(x1)) = 0   
POL(b_{a_1}(x1)) = 1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(121) Obligation:

Q DP problem:
The TRS P consists of the following rules:

LEFT_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → LEFT_{BEGIN_1}(Begin_{b_1}(x))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(122) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(123) TRUE

(124) Obligation:

Q DP problem:
The TRS P consists of the following rules:

END_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → END_{BEGIN_1}(Begin_{b_1}(x))
END_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → END_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
END_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → END_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(125) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(126) Obligation:

Q DP problem:
The TRS P consists of the following rules:

END_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → END_{BEGIN_1}(Begin_{b_1}(x))
END_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → END_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
END_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → END_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(127) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


END_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → END_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
END_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → END_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = 0   
POL(Aa_{Ab_1}(x1)) = 0   
POL(Aa_{Left_1}(x1)) = 0   
POL(Aa_{Right3_1}(x1)) = 0   
POL(Ab_{Aa_1}(x1)) = 0   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(END_{BEGIN_1}(x1)) = x1   
POL(END_{WAIT_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = 0   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = 0   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = 0   
POL(Left_{b_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = 0   
POL(Right3_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = 0   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 0   
POL(a_{a_1}(x1)) = 0   
POL(a_{b_1}(x1)) = 0   
POL(b_{a_1}(x1)) = 1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(128) Obligation:

Q DP problem:
The TRS P consists of the following rules:

END_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → END_{BEGIN_1}(Begin_{b_1}(x))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(129) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(130) TRUE

(131) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT5_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT5_{BEGIN_1}(Begin_{b_1}(x))
RIGHT5_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT5_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT5_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT5_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(132) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(133) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT5_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT5_{BEGIN_1}(Begin_{b_1}(x))
RIGHT5_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT5_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT5_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT5_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(134) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


RIGHT5_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT5_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT5_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT5_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = 0   
POL(Aa_{Ab_1}(x1)) = 0   
POL(Aa_{Left_1}(x1)) = 0   
POL(Aa_{Right3_1}(x1)) = 0   
POL(Ab_{Aa_1}(x1)) = 0   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = 0   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = 0   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = 0   
POL(Left_{b_1}(x1)) = x1   
POL(RIGHT5_{BEGIN_1}(x1)) = x1   
POL(RIGHT5_{WAIT_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = 0   
POL(Right3_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = 0   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 0   
POL(a_{a_1}(x1)) = 0   
POL(a_{b_1}(x1)) = 0   
POL(b_{a_1}(x1)) = 1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(135) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT5_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT5_{BEGIN_1}(Begin_{b_1}(x))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(136) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(137) TRUE

(138) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT4_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT4_{BEGIN_1}(Begin_{b_1}(x))
RIGHT4_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT4_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT4_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT4_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(139) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(140) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT4_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT4_{BEGIN_1}(Begin_{b_1}(x))
RIGHT4_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT4_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT4_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT4_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(141) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


RIGHT4_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT4_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT4_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT4_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = 0   
POL(Aa_{Ab_1}(x1)) = 0   
POL(Aa_{Left_1}(x1)) = 0   
POL(Aa_{Right3_1}(x1)) = 0   
POL(Ab_{Aa_1}(x1)) = 0   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = 0   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = 0   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = 0   
POL(Left_{b_1}(x1)) = x1   
POL(RIGHT4_{BEGIN_1}(x1)) = x1   
POL(RIGHT4_{WAIT_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = 0   
POL(Right3_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = 0   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 0   
POL(a_{a_1}(x1)) = 0   
POL(a_{b_1}(x1)) = 0   
POL(b_{a_1}(x1)) = 1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(142) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT4_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT4_{BEGIN_1}(Begin_{b_1}(x))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(143) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(144) TRUE

(145) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT3_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT3_{BEGIN_1}(Begin_{b_1}(x))
RIGHT3_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT3_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT3_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(146) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(147) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT3_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT3_{BEGIN_1}(Begin_{b_1}(x))
RIGHT3_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT3_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT3_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(148) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


RIGHT3_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT3_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT3_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT3_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = 0   
POL(Aa_{Ab_1}(x1)) = 0   
POL(Aa_{Left_1}(x1)) = 0   
POL(Aa_{Right3_1}(x1)) = 0   
POL(Ab_{Aa_1}(x1)) = 0   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = 0   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = 0   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = 0   
POL(Left_{b_1}(x1)) = x1   
POL(RIGHT3_{BEGIN_1}(x1)) = x1   
POL(RIGHT3_{WAIT_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = 0   
POL(Right3_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = 0   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 0   
POL(a_{a_1}(x1)) = 0   
POL(a_{b_1}(x1)) = 0   
POL(b_{a_1}(x1)) = 1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(149) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT3_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT3_{BEGIN_1}(Begin_{b_1}(x))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(150) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(151) TRUE

(152) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT2_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT2_{BEGIN_1}(Begin_{b_1}(x))
RIGHT2_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT2_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT2_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT2_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(153) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(154) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT2_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT2_{BEGIN_1}(Begin_{b_1}(x))
RIGHT2_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT2_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT2_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT2_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(155) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


RIGHT2_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT2_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT2_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT2_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = 0   
POL(Aa_{Ab_1}(x1)) = 0   
POL(Aa_{Left_1}(x1)) = 0   
POL(Aa_{Right3_1}(x1)) = 0   
POL(Ab_{Aa_1}(x1)) = 0   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = 0   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = 0   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = 0   
POL(Left_{b_1}(x1)) = x1   
POL(RIGHT2_{BEGIN_1}(x1)) = x1   
POL(RIGHT2_{WAIT_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = 0   
POL(Right3_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = 0   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 0   
POL(a_{a_1}(x1)) = 0   
POL(a_{b_1}(x1)) = 0   
POL(b_{a_1}(x1)) = 1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(156) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT2_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT2_{BEGIN_1}(Begin_{b_1}(x))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(157) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(158) TRUE

(159) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT1_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT1_{BEGIN_1}(Begin_{b_1}(x))
RIGHT1_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT1_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT1_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT1_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(160) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(161) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT1_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT1_{BEGIN_1}(Begin_{b_1}(x))
RIGHT1_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT1_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT1_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT1_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(162) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


RIGHT1_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → RIGHT1_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
RIGHT1_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → RIGHT1_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = 0   
POL(Aa_{Ab_1}(x1)) = 0   
POL(Aa_{Left_1}(x1)) = 0   
POL(Aa_{Right3_1}(x1)) = 0   
POL(Ab_{Aa_1}(x1)) = 0   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = 0   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = 0   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = 0   
POL(Left_{b_1}(x1)) = x1   
POL(RIGHT1_{BEGIN_1}(x1)) = x1   
POL(RIGHT1_{WAIT_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = 0   
POL(Right3_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = 0   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 0   
POL(a_{a_1}(x1)) = 0   
POL(a_{b_1}(x1)) = 0   
POL(b_{a_1}(x1)) = 1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(163) Obligation:

Q DP problem:
The TRS P consists of the following rules:

RIGHT1_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → RIGHT1_{BEGIN_1}(Begin_{b_1}(x))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(164) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(165) TRUE

(166) Obligation:

Q DP problem:
The TRS P consists of the following rules:

WAIT_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → WAIT_{BEGIN_1}(Begin_{b_1}(x))
WAIT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
WAIT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(167) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(168) Obligation:

Q DP problem:
The TRS P consists of the following rules:

WAIT_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → WAIT_{BEGIN_1}(Begin_{b_1}(x))
WAIT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
WAIT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(169) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


WAIT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → WAIT_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
WAIT_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → WAIT_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = 0   
POL(Aa_{Ab_1}(x1)) = 0   
POL(Aa_{Left_1}(x1)) = 0   
POL(Aa_{Right3_1}(x1)) = 0   
POL(Ab_{Aa_1}(x1)) = 0   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = 0   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = 0   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = 0   
POL(Left_{b_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = 0   
POL(Right3_{b_1}(x1)) = x1   
POL(WAIT_{BEGIN_1}(x1)) = x1   
POL(WAIT_{WAIT_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = 0   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 0   
POL(a_{a_1}(x1)) = 0   
POL(a_{b_1}(x1)) = 0   
POL(b_{a_1}(x1)) = 1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(170) Obligation:

Q DP problem:
The TRS P consists of the following rules:

WAIT_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → WAIT_{BEGIN_1}(Begin_{b_1}(x))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(171) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(172) TRUE

(173) Obligation:

Q DP problem:
The TRS P consists of the following rules:

A_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → A_{BEGIN_1}(Begin_{b_1}(x))
A_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → A_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
A_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → A_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(174) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(175) Obligation:

Q DP problem:
The TRS P consists of the following rules:

A_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → A_{BEGIN_1}(Begin_{b_1}(x))
A_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → A_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
A_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → A_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(176) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


A_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → A_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
A_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → A_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(A_{BEGIN_1}(x1)) = x1   
POL(A_{WAIT_1}(x1)) = x1   
POL(Aa_{Aa_1}(x1)) = 0   
POL(Aa_{Ab_1}(x1)) = 0   
POL(Aa_{Left_1}(x1)) = 0   
POL(Aa_{Right3_1}(x1)) = 0   
POL(Ab_{Aa_1}(x1)) = 0   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = 0   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = 0   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = 0   
POL(Left_{b_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = 0   
POL(Right3_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = 0   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 0   
POL(a_{a_1}(x1)) = 0   
POL(a_{b_1}(x1)) = 0   
POL(b_{a_1}(x1)) = 1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(177) Obligation:

Q DP problem:
The TRS P consists of the following rules:

A_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → A_{BEGIN_1}(Begin_{b_1}(x))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(178) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(179) TRUE

(180) Obligation:

Q DP problem:
The TRS P consists of the following rules:

B_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → B_{BEGIN_1}(Begin_{b_1}(x))
B_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → B_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
B_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → B_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(181) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(182) Obligation:

Q DP problem:
The TRS P consists of the following rules:

B_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → B_{BEGIN_1}(Begin_{b_1}(x))
B_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → B_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
B_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → B_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(183) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


B_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → B_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
B_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → B_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = 0   
POL(Aa_{Ab_1}(x1)) = 0   
POL(Aa_{Left_1}(x1)) = 0   
POL(Aa_{Right3_1}(x1)) = 0   
POL(Ab_{Aa_1}(x1)) = 0   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(B_{BEGIN_1}(x1)) = x1   
POL(B_{WAIT_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = 0   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = 0   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = 0   
POL(Left_{b_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = 0   
POL(Right3_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = 0   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 0   
POL(a_{a_1}(x1)) = 0   
POL(a_{b_1}(x1)) = 0   
POL(b_{a_1}(x1)) = 1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(184) Obligation:

Q DP problem:
The TRS P consists of the following rules:

B_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → B_{BEGIN_1}(Begin_{b_1}(x))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(185) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(186) TRUE

(187) Obligation:

Q DP problem:
The TRS P consists of the following rules:

BEGIN_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → BEGIN_{BEGIN_1}(Begin_{b_1}(x))
BEGIN_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → BEGIN_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
BEGIN_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → BEGIN_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Begin_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Begin_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
b_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → b_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
a_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → a_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Wait_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Wait_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right1_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right1_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right2_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right2_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right3_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right3_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right4_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right4_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Right5_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Right5_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Left_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Left_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Ab_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Ab_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
Aa_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → Aa_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right5_1}(Right5_{a_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Ab_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{b_1}(x)))
Aa_{Right1_1}(Right1_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right1_1}(Right1_{a_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Ab_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{b_1}(x)))
Aa_{Right2_1}(Right2_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right2_1}(Right2_{a_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Ab_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{b_1}(x)))
Aa_{Right4_1}(Right4_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right4_1}(Right4_{a_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Ab_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{b_1}(x)))
Aa_{Right5_1}(Right5_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right5_1}(Right5_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Begin_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Begin_{Begin_1}(Begin_{b_1}(x))
b_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → b_{Begin_1}(Begin_{b_1}(x))
a_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → a_{Begin_1}(Begin_{b_1}(x))
Wait_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Wait_{Begin_1}(Begin_{b_1}(x))
Right1_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right1_{Begin_1}(Begin_{b_1}(x))
Right2_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right2_{Begin_1}(Begin_{b_1}(x))
Right3_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right3_{Begin_1}(Begin_{b_1}(x))
Right4_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right4_{Begin_1}(Begin_{b_1}(x))
Right5_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Right5_{Begin_1}(Begin_{b_1}(x))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
Left_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Left_{Begin_1}(Begin_{b_1}(x))
Ab_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Ab_{Begin_1}(Begin_{b_1}(x))
Aa_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → Aa_{Begin_1}(Begin_{b_1}(x))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right1_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right1_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right2_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right2_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right4_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right4_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right5_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right5_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(188) UsableRulesProof (EQUIVALENT transformation)

We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R.

(189) Obligation:

Q DP problem:
The TRS P consists of the following rules:

BEGIN_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → BEGIN_{BEGIN_1}(Begin_{b_1}(x))
BEGIN_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → BEGIN_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
BEGIN_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → BEGIN_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(190) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04,JAR06].


The following pairs can be oriented strictly and are deleted.


BEGIN_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → BEGIN_{WAIT_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
BEGIN_{BEGIN_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → BEGIN_{WAIT_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(Aa_{Aa_1}(x1)) = 0   
POL(Aa_{Ab_1}(x1)) = 0   
POL(Aa_{Left_1}(x1)) = 0   
POL(Aa_{Right3_1}(x1)) = 0   
POL(Ab_{Aa_1}(x1)) = 0   
POL(Ab_{Ab_1}(x1)) = 1 + x1   
POL(Ab_{Left_1}(x1)) = x1   
POL(Ab_{Right3_1}(x1)) = x1   
POL(BEGIN_{BEGIN_1}(x1)) = x1   
POL(BEGIN_{WAIT_1}(x1)) = x1   
POL(Begin_{b_1}(x1)) = x1   
POL(End_{Aa_1}(x1)) = x1   
POL(End_{Ab_1}(x1)) = x1   
POL(End_{Begin_1}(x1)) = 0   
POL(End_{End_1}(x1)) = x1   
POL(End_{Left_1}(x1)) = x1   
POL(End_{Right1_1}(x1)) = x1   
POL(End_{Right2_1}(x1)) = x1   
POL(End_{Right3_1}(x1)) = x1   
POL(End_{Right4_1}(x1)) = x1   
POL(End_{Right5_1}(x1)) = x1   
POL(End_{Wait_1}(x1)) = 0   
POL(End_{a_1}(x1)) = x1   
POL(End_{b_1}(x1)) = x1   
POL(Left_{a_1}(x1)) = 0   
POL(Left_{b_1}(x1)) = x1   
POL(Right3_{a_1}(x1)) = 0   
POL(Right3_{b_1}(x1)) = x1   
POL(Wait_{Aa_1}(x1)) = 0   
POL(Wait_{Ab_1}(x1)) = 1 + x1   
POL(Wait_{Left_1}(x1)) = x1   
POL(Wait_{Right3_1}(x1)) = x1   
POL(a_{End_1}(x1)) = 0   
POL(a_{a_1}(x1)) = 0   
POL(a_{b_1}(x1)) = 0   
POL(b_{a_1}(x1)) = 1   
POL(b_{b_1}(x1)) = 1 + x1   

The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:

Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))

(191) Obligation:

Q DP problem:
The TRS P consists of the following rules:

BEGIN_{WAIT_1}(Wait_{Left_1}(Left_{b_1}(x))) → BEGIN_{BEGIN_1}(Begin_{b_1}(x))

The TRS R consists of the following rules:

Wait_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Wait_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Aa_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Wait_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{a_1}(a_{a_1}(x)))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Aa_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Right3_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Right3_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Aa_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Aa_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Aa_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Aa_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{b_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{a_1}(a_{a_1}(x))) → Ab_{Aa_1}(Aa_{Right3_1}(Right3_{a_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Aa_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Aa_{Left_1}(Left_{b_1}(b_{a_1}(x)))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x))))))))
Left_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))))) → Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x))))))))
Ab_{Aa_1}(Aa_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(x)))
Ab_{Aa_1}(Aa_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{a_1}(a_{a_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Ab_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Ab_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Ab_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Ab_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Ab_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Ab_{Left_1}(Left_{b_1}(b_{a_1}(x)))
End_{Wait_1}(Wait_{Left_1}(Left_{b_1}(x))) → End_{Begin_1}(Begin_{b_1}(x))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{b_1}(x)))
End_{Begin_1}(Begin_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x))))) → End_{Wait_1}(Wait_{Right3_1}(Right3_{a_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Begin_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{b_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{a_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Wait_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right1_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right2_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right3_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right4_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Right5_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{End_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Left_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Ab_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x)))))) → Wait_{Left_1}(Left_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(a_{End_1}(End_{Aa_1}(x))))))))))
Wait_{Right3_1}(Right3_{b_1}(b_{b_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{b_1}(x)))
Wait_{Right3_1}(Right3_{b_1}(b_{a_1}(x))) → Wait_{Ab_1}(Ab_{Right3_1}(Right3_{a_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{b_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{b_1}(x)))
Wait_{Ab_1}(Ab_{Left_1}(Left_{a_1}(x))) → Wait_{Left_1}(Left_{b_1}(b_{a_1}(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(192) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(193) TRUE