YES Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/ICFP_2010/140654.srs

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

0 QTRS
↳1 FlatCCProof (⇔, 0 ms)
↳2 QTRS
↳3 RootLabelingProof (⇔, 0 ms)
↳4 QTRS
↳5 QTRSRRRProof (⇔, 172 ms)
↳6 QTRS
↳7 QTRSRRRProof (⇔, 4 ms)
↳8 QTRS
↳9 DependencyPairsProof (⇔, 228 ms)
↳10 QDP
↳11 DependencyGraphProof (⇔, 0 ms)
↳12 QDP
↳13 QDPOrderProof (⇔, 252 ms)
↳14 QDP
↳15 PisEmptyProof (⇔, 0 ms)
↳16 YES

(0) Obligation:

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

0(0(0(1(2(1(1(1(0(0(1(0(1(x))))))))))))) → 0(0(1(0(1(1(0(2(0(0(2(0(1(0(1(0(1(x)))))))))))))))))
0(0(1(0(0(1(1(1(0(1(2(0(1(x))))))))))))) → 0(1(1(0(0(1(0(1(1(1(1(0(2(0(1(1(1(x)))))))))))))))))
0(0(1(0(1(0(1(0(0(1(0(2(0(x))))))))))))) → 0(1(1(1(0(1(1(2(1(2(0(1(1(1(0(1(1(x)))))))))))))))))
0(0(1(1(1(1(1(2(1(1(2(1(1(x))))))))))))) → 0(1(2(0(1(0(0(1(2(1(0(0(1(0(1(1(1(x)))))))))))))))))
0(1(0(2(0(2(1(0(0(1(0(1(1(x))))))))))))) → 0(0(0(1(1(1(1(1(0(2(2(0(1(1(1(0(1(x)))))))))))))))))
0(1(0(2(2(1(1(2(1(2(2(0(1(x))))))))))))) → 0(1(2(2(0(0(1(0(1(0(2(1(0(2(2(0(1(x)))))))))))))))))
0(1(1(0(1(1(0(1(0(2(1(0(0(x))))))))))))) → 0(1(2(0(1(1(0(1(1(1(1(1(0(0(1(0(0(x)))))))))))))))))
0(1(1(1(2(1(2(0(1(2(1(0(1(x))))))))))))) → 0(1(0(1(0(1(1(0(0(1(0(2(0(1(0(0(1(x)))))))))))))))))
0(2(0(0(1(1(2(0(1(0(1(0(2(x))))))))))))) → 0(0(1(2(0(0(1(0(1(0(1(1(0(0(1(1(1(x)))))))))))))))))
1(0(2(0(0(2(0(1(2(0(1(0(1(x))))))))))))) → 1(1(0(0(1(0(2(1(2(0(1(1(1(0(1(1(1(x)))))))))))))))))
1(0(2(0(2(1(0(2(0(1(1(2(0(x))))))))))))) → 1(2(0(2(0(0(1(0(1(0(0(0(1(2(0(1(0(x)))))))))))))))))
1(1(0(0(2(2(2(0(1(2(0(1(1(x))))))))))))) → 1(0(1(1(1(0(0(1(2(0(1(2(0(0(0(0(1(x)))))))))))))))))
1(2(0(1(0(2(0(1(0(1(2(1(0(x))))))))))))) → 1(0(1(1(2(0(1(0(0(1(0(0(1(0(1(2(0(x)))))))))))))))))
1(2(1(2(0(0(0(1(1(1(0(0(1(x))))))))))))) → 1(1(1(1(0(2(0(1(1(0(1(1(2(2(0(0(1(x)))))))))))))))))
2(0(0(0(2(2(0(2(2(0(1(0(1(x))))))))))))) → 2(0(0(1(1(2(1(1(2(0(0(1(2(1(2(0(1(x)))))))))))))))))
2(0(2(1(0(0(1(0(0(0(1(1(1(x))))))))))))) → 0(2(1(2(1(0(1(1(1(0(1(0(1(0(0(1(1(x)))))))))))))))))
2(0(2(1(1(1(1(0(2(0(1(0(1(x))))))))))))) → 2(1(2(0(2(0(1(0(1(2(0(1(0(1(1(1(1(x)))))))))))))))))
2(1(2(2(1(1(2(2(0(1(1(0(1(x))))))))))))) → 2(1(1(1(2(0(1(2(2(0(0(0(1(1(1(0(1(x)))))))))))))))))
2(2(1(1(1(1(0(1(1(2(0(1(0(x))))))))))))) → 0(1(0(1(1(1(1(1(2(2(0(1(2(1(1(1(0(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:

0(0(0(1(2(1(1(1(0(0(1(0(1(x))))))))))))) → 0(0(1(0(1(1(0(2(0(0(2(0(1(0(1(0(1(x)))))))))))))))))
0(0(1(0(0(1(1(1(0(1(2(0(1(x))))))))))))) → 0(1(1(0(0(1(0(1(1(1(1(0(2(0(1(1(1(x)))))))))))))))))
0(0(1(0(1(0(1(0(0(1(0(2(0(x))))))))))))) → 0(1(1(1(0(1(1(2(1(2(0(1(1(1(0(1(1(x)))))))))))))))))
0(0(1(1(1(1(1(2(1(1(2(1(1(x))))))))))))) → 0(1(2(0(1(0(0(1(2(1(0(0(1(0(1(1(1(x)))))))))))))))))
0(1(0(2(0(2(1(0(0(1(0(1(1(x))))))))))))) → 0(0(0(1(1(1(1(1(0(2(2(0(1(1(1(0(1(x)))))))))))))))))
0(1(0(2(2(1(1(2(1(2(2(0(1(x))))))))))))) → 0(1(2(2(0(0(1(0(1(0(2(1(0(2(2(0(1(x)))))))))))))))))
0(1(1(0(1(1(0(1(0(2(1(0(0(x))))))))))))) → 0(1(2(0(1(1(0(1(1(1(1(1(0(0(1(0(0(x)))))))))))))))))
0(1(1(1(2(1(2(0(1(2(1(0(1(x))))))))))))) → 0(1(0(1(0(1(1(0(0(1(0(2(0(1(0(0(1(x)))))))))))))))))
0(2(0(0(1(1(2(0(1(0(1(0(2(x))))))))))))) → 0(0(1(2(0(0(1(0(1(0(1(1(0(0(1(1(1(x)))))))))))))))))
1(0(2(0(0(2(0(1(2(0(1(0(1(x))))))))))))) → 1(1(0(0(1(0(2(1(2(0(1(1(1(0(1(1(1(x)))))))))))))))))
1(0(2(0(2(1(0(2(0(1(1(2(0(x))))))))))))) → 1(2(0(2(0(0(1(0(1(0(0(0(1(2(0(1(0(x)))))))))))))))))
1(1(0(0(2(2(2(0(1(2(0(1(1(x))))))))))))) → 1(0(1(1(1(0(0(1(2(0(1(2(0(0(0(0(1(x)))))))))))))))))
1(2(0(1(0(2(0(1(0(1(2(1(0(x))))))))))))) → 1(0(1(1(2(0(1(0(0(1(0(0(1(0(1(2(0(x)))))))))))))))))
1(2(1(2(0(0(0(1(1(1(0(0(1(x))))))))))))) → 1(1(1(1(0(2(0(1(1(0(1(1(2(2(0(0(1(x)))))))))))))))))
2(0(0(0(2(2(0(2(2(0(1(0(1(x))))))))))))) → 2(0(0(1(1(2(1(1(2(0(0(1(2(1(2(0(1(x)))))))))))))))))
2(0(2(1(1(1(1(0(2(0(1(0(1(x))))))))))))) → 2(1(2(0(2(0(1(0(1(2(0(1(0(1(1(1(1(x)))))))))))))))))
2(1(2(2(1(1(2(2(0(1(1(0(1(x))))))))))))) → 2(1(1(1(2(0(1(2(2(0(0(0(1(1(1(0(1(x)))))))))))))))))
0(2(0(2(1(0(0(1(0(0(0(1(1(1(x)))))))))))))) → 0(0(2(1(2(1(0(1(1(1(0(1(0(1(0(0(1(1(x))))))))))))))))))
1(2(0(2(1(0(0(1(0(0(0(1(1(1(x)))))))))))))) → 1(0(2(1(2(1(0(1(1(1(0(1(0(1(0(0(1(1(x))))))))))))))))))
2(2(0(2(1(0(0(1(0(0(0(1(1(1(x)))))))))))))) → 2(0(2(1(2(1(0(1(1(1(0(1(0(1(0(0(1(1(x))))))))))))))))))
0(2(2(1(1(1(1(0(1(1(2(0(1(0(x)))))))))))))) → 0(0(1(0(1(1(1(1(1(2(2(0(1(2(1(1(1(0(x))))))))))))))))))
1(2(2(1(1(1(1(0(1(1(2(0(1(0(x)))))))))))))) → 1(0(1(0(1(1(1(1(1(2(2(0(1(2(1(1(1(0(x))))))))))))))))))
2(2(2(1(1(1(1(0(1(1(2(0(1(0(x)))))))))))))) → 2(0(1(0(1(1(1(1(1(2(2(0(1(2(1(1(1(0(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:

0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))) → 0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x)))))))))))))))))
0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x)))))))))))))))))
0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x)))))))))))))))))
0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x))))))))))))) → 1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x))))))))))))) → 1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))))))
1_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
1_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
1_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))) → 1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x)))))))))))))))))
1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))) → 1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x)))))))))))))))))
1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))) → 1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x)))))))))))))))))
1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
2_{0_1}(0_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
2_{0_1}(0_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
2_{0_1}(0_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
2_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 2_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
2_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 2_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
2_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 2_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))
2_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
2_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
2_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))

Q is empty.

(5) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(0_{0_1}(x1)) = 1 + x1   
POL(0_{1_1}(x1)) = x1   
POL(0_{2_1}(x1)) = 2 + x1   
POL(1_{0_1}(x1)) = x1   
POL(1_{1_1}(x1)) = x1   
POL(1_{2_1}(x1)) = 1 + x1   
POL(2_{0_1}(x1)) = x1   
POL(2_{1_1}(x1)) = 2 + x1   
POL(2_{2_1}(x1)) = 2 + x1   
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))) → 0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(x)))))))))))))))))
0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(x)))))))))))))))))
0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(x)))))))))))))))))
0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x))))))))))))) → 1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x))))))))))))) → 1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))))))
1_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
1_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
1_{1_1}(1_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))) → 1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(x)))))))))))))))))
1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))) → 1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(x)))))))))))))))))
1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))) → 1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(x)))))))))))))))))
1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
2_{1_1}(1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
2_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 2_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
2_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 2_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
2_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 2_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
2_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
2_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
2_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))


(6) Obligation:

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

0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
2_{0_1}(0_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
2_{0_1}(0_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
2_{0_1}(0_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))

Q is empty.

(7) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(0_{0_1}(x1)) = x1   
POL(0_{1_1}(x1)) = x1   
POL(0_{2_1}(x1)) = x1   
POL(1_{0_1}(x1)) = x1   
POL(1_{1_1}(x1)) = x1   
POL(1_{2_1}(x1)) = x1   
POL(2_{0_1}(x1)) = x1   
POL(2_{1_1}(x1)) = x1   
POL(2_{2_1}(x1)) = 1 + x1   
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

2_{0_1}(0_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
2_{0_1}(0_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
2_{0_1}(0_{0_1}(0_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))


(8) Obligation:

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

0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))

Q is empty.

(9) DependencyPairsProof (EQUIVALENT transformation)

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

(10) Obligation:

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

0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{2_1}1(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{0_1}1(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}1(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{2_1}1(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{2_1}1(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{0_1}1(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{0_1}1(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{2_1}1(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{2_1}1(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{0_1}1(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}1(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{2_1}1(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{2_1}1(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{0_1}(x))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{2_1}1(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(x))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{2_1}1(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{2_1}(x))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 1_{2_1}1(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 1_{2_1}1(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(x))))
0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(x)))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{2_1}1(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{0_1}1(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{2_1}1(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{2_1}1(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{2_1}1(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{0_1}1(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{2_1}1(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{2_1}1(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{2_1}1(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{0_1}1(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{2_1}1(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))
0_{1_1}1(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{2_1}1(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{2_1}1(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{2_1}1(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{0_1}(x))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{2_1}1(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{2_1}1(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(x))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{2_1}1(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{2_1}1(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))
1_{0_1}1(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{2_1}(x))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{2_1}1(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{0_1}1(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{2_1}1(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{2_1}1(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{2_1}1(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{0_1}1(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{2_1}1(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{2_1}1(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{2_1}1(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{0_1}1(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{2_1}1(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{2_1}1(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x))))))
2_{0_1}1(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{0_1}1(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{2_1}1(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{2_1}1(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}1(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{0_1}1(0_{1_1}(1_{1_1}(1_{0_1}(x))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{0_1}(x)))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{0_1}1(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{2_1}1(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{2_1}1(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}1(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(x))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(x)))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{0_1}1(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{2_1}1(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{2_1}1(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}1(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{0_1}1(0_{1_1}(1_{1_1}(1_{2_1}(x))))
0_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{2_1}(x)))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}1(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{2_1}1(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{2_1}1(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}1(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x)))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{0_1}1(0_{1_1}(1_{1_1}(1_{0_1}(x))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{0_1}(x)))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}1(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{2_1}1(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{2_1}1(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}1(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(x))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(x)))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}1(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{2_1}1(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{2_1}1(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}1(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x)))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{0_1}1(0_{1_1}(1_{1_1}(1_{2_1}(x))))
1_{2_1}1(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{2_1}(x)))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 1_{2_1}1(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 2_{0_1}1(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x)))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 1_{2_1}1(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 1_{2_1}1(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 2_{0_1}1(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x)))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 1_{2_1}1(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 1_{2_1}1(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 2_{0_1}1(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x)))))))
0_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 1_{2_1}1(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 1_{2_1}1(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 2_{0_1}1(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{1_1}1(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x)))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 1_{2_1}1(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 1_{2_1}1(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 2_{0_1}1(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{1_1}1(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x)))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 1_{2_1}1(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 1_{0_1}1(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 1_{2_1}1(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 2_{0_1}1(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{1_1}1(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x)))))))
1_{2_1}1(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 1_{2_1}1(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))

The TRS R consists of the following rules:

0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))

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

(11) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 292 less nodes.

(12) Obligation:

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

0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}1(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}1(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))

The TRS R consists of the following rules:

0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))

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

(13) QDPOrderProof (EQUIVALENT transformation)

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


The following pairs can be oriented strictly and are deleted.


0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}1(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))
0_{0_1}1(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}1(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))
The remaining pairs can at least be oriented weakly.
Used ordering: Polynomial interpretation [POLO]:

POL(0_{0_1}(x1)) = x1   
POL(0_{0_1}1(x1)) = x1   
POL(0_{1_1}(x1)) = 1 + x1   
POL(0_{2_1}(x1)) = 1   
POL(1_{0_1}(x1)) = 0   
POL(1_{1_1}(x1)) = 1   
POL(1_{2_1}(x1)) = 1 + x1   
POL(2_{0_1}(x1)) = 0   
POL(2_{1_1}(x1)) = 1 + x1   
POL(2_{2_1}(x1)) = 0   

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

0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))

(14) Obligation:

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

0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(x))))))))))))) → 0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(x)))))))))))))))))
0_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{2_1}(2_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 0_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
1_{0_1}(0_{2_1}(2_{0_1}(0_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 1_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))))))
2_{0_1}(0_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(x))))))))))))) → 2_{1_1}(1_{2_1}(2_{0_1}(0_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
0_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 0_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{0_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(x))))))))))))))))))
1_{2_1}(2_{0_1}(0_{2_1}(2_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(x)))))))))))))) → 1_{0_1}(0_{2_1}(2_{1_1}(1_{2_1}(2_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
0_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 0_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{0_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{0_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(x))))))))))))))))))
1_{2_1}(2_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{2_1}(2_{0_1}(0_{1_1}(1_{0_1}(0_{2_1}(x)))))))))))))) → 1_{0_1}(0_{1_1}(1_{0_1}(0_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{1_1}(1_{2_1}(2_{2_1}(2_{0_1}(0_{1_1}(1_{2_1}(2_{1_1}(1_{1_1}(1_{1_1}(1_{0_1}(0_{2_1}(x))))))))))))))))))

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

(15) PisEmptyProof (EQUIVALENT transformation)

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

(16) YES