YES
0 QTRS
↳1 DependencyPairsProof (⇔, 205 ms)
↳2 QDP
↳3 DependencyGraphProof (⇔, 0 ms)
↳4 AND
↳5 QDP
↳6 UsableRulesProof (⇔, 0 ms)
↳7 QDP
↳8 DependencyGraphProof (⇔, 0 ms)
↳9 QDP
↳10 QDPOrderProof (⇔, 78 ms)
↳11 QDP
↳12 PisEmptyProof (⇔, 0 ms)
↳13 YES
↳14 QDP
↳15 UsableRulesProof (⇔, 0 ms)
↳16 QDP
↳17 QDPOrderProof (⇔, 30 ms)
↳18 QDP
↳19 PisEmptyProof (⇔, 0 ms)
↳20 YES
0(1(1(x))) → 1(0(2(1(x))))
0(1(1(x))) → 1(1(0(3(2(x)))))
0(1(1(x))) → 1(4(0(0(2(1(x))))))
0(1(4(x))) → 1(4(0(3(x))))
0(1(4(x))) → 4(0(2(1(x))))
0(1(4(x))) → 4(0(2(1(3(x)))))
0(4(1(x))) → 0(2(4(1(x))))
0(4(1(x))) → 4(0(2(1(x))))
0(4(1(x))) → 4(0(3(1(x))))
0(4(1(x))) → 1(4(4(0(2(x)))))
0(4(1(x))) → 2(1(4(0(2(x)))))
0(5(4(x))) → 1(4(0(0(2(5(x))))))
0(5(4(x))) → 4(0(2(5(2(5(x))))))
0(5(4(x))) → 5(0(4(0(3(3(x))))))
4(2(1(x))) → 4(0(2(1(x))))
4(2(1(x))) → 1(2(4(0(2(x)))))
0(1(0(4(x)))) → 0(0(2(2(1(4(x))))))
0(1(1(2(x)))) → 5(1(0(2(1(x)))))
0(1(1(3(x)))) → 1(1(5(0(3(x)))))
0(1(4(1(x)))) → 1(0(2(4(1(x)))))
0(1(4(3(x)))) → 1(0(2(4(3(x)))))
0(1(4(3(x)))) → 4(0(2(1(3(x)))))
0(4(1(2(x)))) → 2(0(3(1(4(x)))))
0(4(2(1(x)))) → 0(4(3(0(2(1(x))))))
0(5(0(4(x)))) → 1(5(4(0(0(2(x))))))
0(5(1(3(x)))) → 1(1(5(0(3(x)))))
0(5(1(3(x)))) → 5(3(1(0(3(x)))))
0(5(4(1(x)))) → 4(1(5(4(0(2(x))))))
0(5(4(3(x)))) → 0(2(5(0(3(4(x))))))
0(5(4(3(x)))) → 1(5(3(4(0(3(x))))))
1(0(5(4(x)))) → 1(4(5(0(3(3(x))))))
1(0(5(4(x)))) → 5(5(1(0(2(4(x))))))
1(4(2(1(x)))) → 4(0(2(1(2(1(x))))))
4(1(2(1(x)))) → 4(1(0(2(1(x)))))
4(1(2(1(x)))) → 3(4(0(2(1(1(x))))))
4(3(2(1(x)))) → 0(3(4(0(2(1(x))))))
0(0(1(2(3(x))))) → 1(0(3(0(0(2(x))))))
0(0(5(1(2(x))))) → 0(0(2(5(0(1(x))))))
0(0(5(1(3(x))))) → 4(5(0(0(3(1(x))))))
0(1(3(4(2(x))))) → 1(3(4(3(0(2(x))))))
0(4(5(3(4(x))))) → 0(3(2(5(4(4(x))))))
0(5(0(2(2(x))))) → 0(0(2(5(2(4(x))))))
0(5(1(1(3(x))))) → 0(3(2(1(1(5(x))))))
0(5(1(4(3(x))))) → 3(0(2(1(5(4(x))))))
0(5(5(1(2(x))))) → 1(5(3(0(2(5(x))))))
1(0(1(2(4(x))))) → 1(1(0(2(3(4(x))))))
1(4(2(1(2(x))))) → 0(2(2(1(1(4(x))))))
4(0(0(5(4(x))))) → 5(0(0(4(4(5(x))))))
4(2(5(4(1(x))))) → 4(4(1(5(3(2(x))))))
01(1(1(x))) → 11(0(2(1(x))))
01(1(1(x))) → 01(2(1(x)))
01(1(1(x))) → 11(1(0(3(2(x)))))
01(1(1(x))) → 11(0(3(2(x))))
01(1(1(x))) → 01(3(2(x)))
01(1(1(x))) → 11(4(0(0(2(1(x))))))
01(1(1(x))) → 41(0(0(2(1(x)))))
01(1(1(x))) → 01(0(2(1(x))))
01(1(4(x))) → 11(4(0(3(x))))
01(1(4(x))) → 41(0(3(x)))
01(1(4(x))) → 01(3(x))
01(1(4(x))) → 41(0(2(1(x))))
01(1(4(x))) → 01(2(1(x)))
01(1(4(x))) → 11(x)
01(1(4(x))) → 41(0(2(1(3(x)))))
01(1(4(x))) → 01(2(1(3(x))))
01(1(4(x))) → 11(3(x))
01(4(1(x))) → 01(2(4(1(x))))
01(4(1(x))) → 41(0(2(1(x))))
01(4(1(x))) → 01(2(1(x)))
01(4(1(x))) → 41(0(3(1(x))))
01(4(1(x))) → 01(3(1(x)))
01(4(1(x))) → 11(4(4(0(2(x)))))
01(4(1(x))) → 41(4(0(2(x))))
01(4(1(x))) → 41(0(2(x)))
01(4(1(x))) → 01(2(x))
01(4(1(x))) → 11(4(0(2(x))))
01(5(4(x))) → 11(4(0(0(2(5(x))))))
01(5(4(x))) → 41(0(0(2(5(x)))))
01(5(4(x))) → 01(0(2(5(x))))
01(5(4(x))) → 01(2(5(x)))
01(5(4(x))) → 41(0(2(5(2(5(x))))))
01(5(4(x))) → 01(2(5(2(5(x)))))
01(5(4(x))) → 01(4(0(3(3(x)))))
01(5(4(x))) → 41(0(3(3(x))))
01(5(4(x))) → 01(3(3(x)))
41(2(1(x))) → 41(0(2(1(x))))
41(2(1(x))) → 01(2(1(x)))
41(2(1(x))) → 11(2(4(0(2(x)))))
41(2(1(x))) → 41(0(2(x)))
41(2(1(x))) → 01(2(x))
01(1(0(4(x)))) → 01(0(2(2(1(4(x))))))
01(1(0(4(x)))) → 01(2(2(1(4(x)))))
01(1(0(4(x)))) → 11(4(x))
01(1(1(2(x)))) → 11(0(2(1(x))))
01(1(1(2(x)))) → 01(2(1(x)))
01(1(1(2(x)))) → 11(x)
01(1(1(3(x)))) → 11(1(5(0(3(x)))))
01(1(1(3(x)))) → 11(5(0(3(x))))
01(1(1(3(x)))) → 01(3(x))
01(1(4(1(x)))) → 11(0(2(4(1(x)))))
01(1(4(1(x)))) → 01(2(4(1(x))))
01(1(4(3(x)))) → 11(0(2(4(3(x)))))
01(1(4(3(x)))) → 01(2(4(3(x))))
01(1(4(3(x)))) → 41(0(2(1(3(x)))))
01(1(4(3(x)))) → 01(2(1(3(x))))
01(1(4(3(x)))) → 11(3(x))
01(4(1(2(x)))) → 01(3(1(4(x))))
01(4(1(2(x)))) → 11(4(x))
01(4(1(2(x)))) → 41(x)
01(4(2(1(x)))) → 01(4(3(0(2(1(x))))))
01(4(2(1(x)))) → 41(3(0(2(1(x)))))
01(4(2(1(x)))) → 01(2(1(x)))
01(5(0(4(x)))) → 11(5(4(0(0(2(x))))))
01(5(0(4(x)))) → 41(0(0(2(x))))
01(5(0(4(x)))) → 01(0(2(x)))
01(5(0(4(x)))) → 01(2(x))
01(5(1(3(x)))) → 11(1(5(0(3(x)))))
01(5(1(3(x)))) → 11(5(0(3(x))))
01(5(1(3(x)))) → 01(3(x))
01(5(1(3(x)))) → 11(0(3(x)))
01(5(4(1(x)))) → 41(1(5(4(0(2(x))))))
01(5(4(1(x)))) → 11(5(4(0(2(x)))))
01(5(4(1(x)))) → 41(0(2(x)))
01(5(4(1(x)))) → 01(2(x))
01(5(4(3(x)))) → 01(2(5(0(3(4(x))))))
01(5(4(3(x)))) → 01(3(4(x)))
01(5(4(3(x)))) → 41(x)
01(5(4(3(x)))) → 11(5(3(4(0(3(x))))))
01(5(4(3(x)))) → 41(0(3(x)))
01(5(4(3(x)))) → 01(3(x))
11(0(5(4(x)))) → 11(4(5(0(3(3(x))))))
11(0(5(4(x)))) → 41(5(0(3(3(x)))))
11(0(5(4(x)))) → 01(3(3(x)))
11(0(5(4(x)))) → 11(0(2(4(x))))
11(0(5(4(x)))) → 01(2(4(x)))
11(4(2(1(x)))) → 41(0(2(1(2(1(x))))))
11(4(2(1(x)))) → 01(2(1(2(1(x)))))
11(4(2(1(x)))) → 11(2(1(x)))
41(1(2(1(x)))) → 41(1(0(2(1(x)))))
41(1(2(1(x)))) → 11(0(2(1(x))))
41(1(2(1(x)))) → 01(2(1(x)))
41(1(2(1(x)))) → 41(0(2(1(1(x)))))
41(1(2(1(x)))) → 01(2(1(1(x))))
41(1(2(1(x)))) → 11(1(x))
41(3(2(1(x)))) → 01(3(4(0(2(1(x))))))
41(3(2(1(x)))) → 41(0(2(1(x))))
41(3(2(1(x)))) → 01(2(1(x)))
01(0(1(2(3(x))))) → 11(0(3(0(0(2(x))))))
01(0(1(2(3(x))))) → 01(3(0(0(2(x)))))
01(0(1(2(3(x))))) → 01(0(2(x)))
01(0(1(2(3(x))))) → 01(2(x))
01(0(5(1(2(x))))) → 01(0(2(5(0(1(x))))))
01(0(5(1(2(x))))) → 01(2(5(0(1(x)))))
01(0(5(1(2(x))))) → 01(1(x))
01(0(5(1(2(x))))) → 11(x)
01(0(5(1(3(x))))) → 41(5(0(0(3(1(x))))))
01(0(5(1(3(x))))) → 01(0(3(1(x))))
01(0(5(1(3(x))))) → 01(3(1(x)))
01(0(5(1(3(x))))) → 11(x)
01(1(3(4(2(x))))) → 11(3(4(3(0(2(x))))))
01(1(3(4(2(x))))) → 41(3(0(2(x))))
01(1(3(4(2(x))))) → 01(2(x))
01(4(5(3(4(x))))) → 01(3(2(5(4(4(x))))))
01(4(5(3(4(x))))) → 41(4(x))
01(5(0(2(2(x))))) → 01(0(2(5(2(4(x))))))
01(5(0(2(2(x))))) → 01(2(5(2(4(x)))))
01(5(0(2(2(x))))) → 41(x)
01(5(1(1(3(x))))) → 01(3(2(1(1(5(x))))))
01(5(1(1(3(x))))) → 11(1(5(x)))
01(5(1(1(3(x))))) → 11(5(x))
01(5(1(4(3(x))))) → 01(2(1(5(4(x)))))
01(5(1(4(3(x))))) → 11(5(4(x)))
01(5(1(4(3(x))))) → 41(x)
01(5(5(1(2(x))))) → 11(5(3(0(2(5(x))))))
01(5(5(1(2(x))))) → 01(2(5(x)))
11(0(1(2(4(x))))) → 11(1(0(2(3(4(x))))))
11(0(1(2(4(x))))) → 11(0(2(3(4(x)))))
11(0(1(2(4(x))))) → 01(2(3(4(x))))
11(4(2(1(2(x))))) → 01(2(2(1(1(4(x))))))
11(4(2(1(2(x))))) → 11(1(4(x)))
11(4(2(1(2(x))))) → 11(4(x))
11(4(2(1(2(x))))) → 41(x)
41(0(0(5(4(x))))) → 01(0(4(4(5(x)))))
41(0(0(5(4(x))))) → 01(4(4(5(x))))
41(0(0(5(4(x))))) → 41(4(5(x)))
41(0(0(5(4(x))))) → 41(5(x))
41(2(5(4(1(x))))) → 41(4(1(5(3(2(x))))))
41(2(5(4(1(x))))) → 41(1(5(3(2(x)))))
41(2(5(4(1(x))))) → 11(5(3(2(x))))
0(1(1(x))) → 1(0(2(1(x))))
0(1(1(x))) → 1(1(0(3(2(x)))))
0(1(1(x))) → 1(4(0(0(2(1(x))))))
0(1(4(x))) → 1(4(0(3(x))))
0(1(4(x))) → 4(0(2(1(x))))
0(1(4(x))) → 4(0(2(1(3(x)))))
0(4(1(x))) → 0(2(4(1(x))))
0(4(1(x))) → 4(0(2(1(x))))
0(4(1(x))) → 4(0(3(1(x))))
0(4(1(x))) → 1(4(4(0(2(x)))))
0(4(1(x))) → 2(1(4(0(2(x)))))
0(5(4(x))) → 1(4(0(0(2(5(x))))))
0(5(4(x))) → 4(0(2(5(2(5(x))))))
0(5(4(x))) → 5(0(4(0(3(3(x))))))
4(2(1(x))) → 4(0(2(1(x))))
4(2(1(x))) → 1(2(4(0(2(x)))))
0(1(0(4(x)))) → 0(0(2(2(1(4(x))))))
0(1(1(2(x)))) → 5(1(0(2(1(x)))))
0(1(1(3(x)))) → 1(1(5(0(3(x)))))
0(1(4(1(x)))) → 1(0(2(4(1(x)))))
0(1(4(3(x)))) → 1(0(2(4(3(x)))))
0(1(4(3(x)))) → 4(0(2(1(3(x)))))
0(4(1(2(x)))) → 2(0(3(1(4(x)))))
0(4(2(1(x)))) → 0(4(3(0(2(1(x))))))
0(5(0(4(x)))) → 1(5(4(0(0(2(x))))))
0(5(1(3(x)))) → 1(1(5(0(3(x)))))
0(5(1(3(x)))) → 5(3(1(0(3(x)))))
0(5(4(1(x)))) → 4(1(5(4(0(2(x))))))
0(5(4(3(x)))) → 0(2(5(0(3(4(x))))))
0(5(4(3(x)))) → 1(5(3(4(0(3(x))))))
1(0(5(4(x)))) → 1(4(5(0(3(3(x))))))
1(0(5(4(x)))) → 5(5(1(0(2(4(x))))))
1(4(2(1(x)))) → 4(0(2(1(2(1(x))))))
4(1(2(1(x)))) → 4(1(0(2(1(x)))))
4(1(2(1(x)))) → 3(4(0(2(1(1(x))))))
4(3(2(1(x)))) → 0(3(4(0(2(1(x))))))
0(0(1(2(3(x))))) → 1(0(3(0(0(2(x))))))
0(0(5(1(2(x))))) → 0(0(2(5(0(1(x))))))
0(0(5(1(3(x))))) → 4(5(0(0(3(1(x))))))
0(1(3(4(2(x))))) → 1(3(4(3(0(2(x))))))
0(4(5(3(4(x))))) → 0(3(2(5(4(4(x))))))
0(5(0(2(2(x))))) → 0(0(2(5(2(4(x))))))
0(5(1(1(3(x))))) → 0(3(2(1(1(5(x))))))
0(5(1(4(3(x))))) → 3(0(2(1(5(4(x))))))
0(5(5(1(2(x))))) → 1(5(3(0(2(5(x))))))
1(0(1(2(4(x))))) → 1(1(0(2(3(4(x))))))
1(4(2(1(2(x))))) → 0(2(2(1(1(4(x))))))
4(0(0(5(4(x))))) → 5(0(0(4(4(5(x))))))
4(2(5(4(1(x))))) → 4(4(1(5(3(2(x))))))
41(1(2(1(x)))) → 11(1(x))
11(4(2(1(2(x))))) → 11(1(4(x)))
11(4(2(1(2(x))))) → 11(4(x))
11(4(2(1(2(x))))) → 41(x)
0(1(1(x))) → 1(0(2(1(x))))
0(1(1(x))) → 1(1(0(3(2(x)))))
0(1(1(x))) → 1(4(0(0(2(1(x))))))
0(1(4(x))) → 1(4(0(3(x))))
0(1(4(x))) → 4(0(2(1(x))))
0(1(4(x))) → 4(0(2(1(3(x)))))
0(4(1(x))) → 0(2(4(1(x))))
0(4(1(x))) → 4(0(2(1(x))))
0(4(1(x))) → 4(0(3(1(x))))
0(4(1(x))) → 1(4(4(0(2(x)))))
0(4(1(x))) → 2(1(4(0(2(x)))))
0(5(4(x))) → 1(4(0(0(2(5(x))))))
0(5(4(x))) → 4(0(2(5(2(5(x))))))
0(5(4(x))) → 5(0(4(0(3(3(x))))))
4(2(1(x))) → 4(0(2(1(x))))
4(2(1(x))) → 1(2(4(0(2(x)))))
0(1(0(4(x)))) → 0(0(2(2(1(4(x))))))
0(1(1(2(x)))) → 5(1(0(2(1(x)))))
0(1(1(3(x)))) → 1(1(5(0(3(x)))))
0(1(4(1(x)))) → 1(0(2(4(1(x)))))
0(1(4(3(x)))) → 1(0(2(4(3(x)))))
0(1(4(3(x)))) → 4(0(2(1(3(x)))))
0(4(1(2(x)))) → 2(0(3(1(4(x)))))
0(4(2(1(x)))) → 0(4(3(0(2(1(x))))))
0(5(0(4(x)))) → 1(5(4(0(0(2(x))))))
0(5(1(3(x)))) → 1(1(5(0(3(x)))))
0(5(1(3(x)))) → 5(3(1(0(3(x)))))
0(5(4(1(x)))) → 4(1(5(4(0(2(x))))))
0(5(4(3(x)))) → 0(2(5(0(3(4(x))))))
0(5(4(3(x)))) → 1(5(3(4(0(3(x))))))
1(0(5(4(x)))) → 1(4(5(0(3(3(x))))))
1(0(5(4(x)))) → 5(5(1(0(2(4(x))))))
1(4(2(1(x)))) → 4(0(2(1(2(1(x))))))
4(1(2(1(x)))) → 4(1(0(2(1(x)))))
4(1(2(1(x)))) → 3(4(0(2(1(1(x))))))
4(3(2(1(x)))) → 0(3(4(0(2(1(x))))))
0(0(1(2(3(x))))) → 1(0(3(0(0(2(x))))))
0(0(5(1(2(x))))) → 0(0(2(5(0(1(x))))))
0(0(5(1(3(x))))) → 4(5(0(0(3(1(x))))))
0(1(3(4(2(x))))) → 1(3(4(3(0(2(x))))))
0(4(5(3(4(x))))) → 0(3(2(5(4(4(x))))))
0(5(0(2(2(x))))) → 0(0(2(5(2(4(x))))))
0(5(1(1(3(x))))) → 0(3(2(1(1(5(x))))))
0(5(1(4(3(x))))) → 3(0(2(1(5(4(x))))))
0(5(5(1(2(x))))) → 1(5(3(0(2(5(x))))))
1(0(1(2(4(x))))) → 1(1(0(2(3(4(x))))))
1(4(2(1(2(x))))) → 0(2(2(1(1(4(x))))))
4(0(0(5(4(x))))) → 5(0(0(4(4(5(x))))))
4(2(5(4(1(x))))) → 4(4(1(5(3(2(x))))))
41(1(2(1(x)))) → 11(1(x))
11(4(2(1(2(x))))) → 11(1(4(x)))
11(4(2(1(2(x))))) → 11(4(x))
11(4(2(1(2(x))))) → 41(x)
4(2(1(x))) → 4(0(2(1(x))))
4(2(1(x))) → 1(2(4(0(2(x)))))
4(1(2(1(x)))) → 4(1(0(2(1(x)))))
4(1(2(1(x)))) → 3(4(0(2(1(1(x))))))
4(3(2(1(x)))) → 0(3(4(0(2(1(x))))))
4(0(0(5(4(x))))) → 5(0(0(4(4(5(x))))))
4(2(5(4(1(x))))) → 4(4(1(5(3(2(x))))))
1(0(5(4(x)))) → 1(4(5(0(3(3(x))))))
1(0(5(4(x)))) → 5(5(1(0(2(4(x))))))
1(4(2(1(x)))) → 4(0(2(1(2(1(x))))))
1(0(1(2(4(x))))) → 1(1(0(2(3(4(x))))))
1(4(2(1(2(x))))) → 0(2(2(1(1(4(x))))))
11(4(2(1(2(x))))) → 11(4(x))
4(2(1(x))) → 4(0(2(1(x))))
4(2(1(x))) → 1(2(4(0(2(x)))))
4(1(2(1(x)))) → 4(1(0(2(1(x)))))
4(1(2(1(x)))) → 3(4(0(2(1(1(x))))))
4(3(2(1(x)))) → 0(3(4(0(2(1(x))))))
4(0(0(5(4(x))))) → 5(0(0(4(4(5(x))))))
4(2(5(4(1(x))))) → 4(4(1(5(3(2(x))))))
1(0(5(4(x)))) → 1(4(5(0(3(3(x))))))
1(0(5(4(x)))) → 5(5(1(0(2(4(x))))))
1(4(2(1(x)))) → 4(0(2(1(2(1(x))))))
1(0(1(2(4(x))))) → 1(1(0(2(3(4(x))))))
1(4(2(1(2(x))))) → 0(2(2(1(1(4(x))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
11(4(2(1(2(x))))) → 11(4(x))
POL(0(x1)) = 0
POL(1(x1)) = x1
POL(11(x1)) = x1
POL(2(x1)) = 1 + x1
POL(3(x1)) = 0
POL(4(x1)) = x1
POL(5(x1)) = 0
4(2(1(x))) → 4(0(2(1(x))))
4(2(1(x))) → 1(2(4(0(2(x)))))
4(1(2(1(x)))) → 4(1(0(2(1(x)))))
4(1(2(1(x)))) → 3(4(0(2(1(1(x))))))
4(3(2(1(x)))) → 0(3(4(0(2(1(x))))))
4(0(0(5(4(x))))) → 5(0(0(4(4(5(x))))))
4(2(5(4(1(x))))) → 4(4(1(5(3(2(x))))))
4(2(1(x))) → 4(0(2(1(x))))
4(2(1(x))) → 1(2(4(0(2(x)))))
4(1(2(1(x)))) → 4(1(0(2(1(x)))))
4(1(2(1(x)))) → 3(4(0(2(1(1(x))))))
4(3(2(1(x)))) → 0(3(4(0(2(1(x))))))
4(0(0(5(4(x))))) → 5(0(0(4(4(5(x))))))
4(2(5(4(1(x))))) → 4(4(1(5(3(2(x))))))
1(0(5(4(x)))) → 1(4(5(0(3(3(x))))))
1(0(5(4(x)))) → 5(5(1(0(2(4(x))))))
1(4(2(1(x)))) → 4(0(2(1(2(1(x))))))
1(0(1(2(4(x))))) → 1(1(0(2(3(4(x))))))
1(4(2(1(2(x))))) → 0(2(2(1(1(4(x))))))
01(0(5(1(2(x))))) → 01(1(x))
0(1(1(x))) → 1(0(2(1(x))))
0(1(1(x))) → 1(1(0(3(2(x)))))
0(1(1(x))) → 1(4(0(0(2(1(x))))))
0(1(4(x))) → 1(4(0(3(x))))
0(1(4(x))) → 4(0(2(1(x))))
0(1(4(x))) → 4(0(2(1(3(x)))))
0(4(1(x))) → 0(2(4(1(x))))
0(4(1(x))) → 4(0(2(1(x))))
0(4(1(x))) → 4(0(3(1(x))))
0(4(1(x))) → 1(4(4(0(2(x)))))
0(4(1(x))) → 2(1(4(0(2(x)))))
0(5(4(x))) → 1(4(0(0(2(5(x))))))
0(5(4(x))) → 4(0(2(5(2(5(x))))))
0(5(4(x))) → 5(0(4(0(3(3(x))))))
4(2(1(x))) → 4(0(2(1(x))))
4(2(1(x))) → 1(2(4(0(2(x)))))
0(1(0(4(x)))) → 0(0(2(2(1(4(x))))))
0(1(1(2(x)))) → 5(1(0(2(1(x)))))
0(1(1(3(x)))) → 1(1(5(0(3(x)))))
0(1(4(1(x)))) → 1(0(2(4(1(x)))))
0(1(4(3(x)))) → 1(0(2(4(3(x)))))
0(1(4(3(x)))) → 4(0(2(1(3(x)))))
0(4(1(2(x)))) → 2(0(3(1(4(x)))))
0(4(2(1(x)))) → 0(4(3(0(2(1(x))))))
0(5(0(4(x)))) → 1(5(4(0(0(2(x))))))
0(5(1(3(x)))) → 1(1(5(0(3(x)))))
0(5(1(3(x)))) → 5(3(1(0(3(x)))))
0(5(4(1(x)))) → 4(1(5(4(0(2(x))))))
0(5(4(3(x)))) → 0(2(5(0(3(4(x))))))
0(5(4(3(x)))) → 1(5(3(4(0(3(x))))))
1(0(5(4(x)))) → 1(4(5(0(3(3(x))))))
1(0(5(4(x)))) → 5(5(1(0(2(4(x))))))
1(4(2(1(x)))) → 4(0(2(1(2(1(x))))))
4(1(2(1(x)))) → 4(1(0(2(1(x)))))
4(1(2(1(x)))) → 3(4(0(2(1(1(x))))))
4(3(2(1(x)))) → 0(3(4(0(2(1(x))))))
0(0(1(2(3(x))))) → 1(0(3(0(0(2(x))))))
0(0(5(1(2(x))))) → 0(0(2(5(0(1(x))))))
0(0(5(1(3(x))))) → 4(5(0(0(3(1(x))))))
0(1(3(4(2(x))))) → 1(3(4(3(0(2(x))))))
0(4(5(3(4(x))))) → 0(3(2(5(4(4(x))))))
0(5(0(2(2(x))))) → 0(0(2(5(2(4(x))))))
0(5(1(1(3(x))))) → 0(3(2(1(1(5(x))))))
0(5(1(4(3(x))))) → 3(0(2(1(5(4(x))))))
0(5(5(1(2(x))))) → 1(5(3(0(2(5(x))))))
1(0(1(2(4(x))))) → 1(1(0(2(3(4(x))))))
1(4(2(1(2(x))))) → 0(2(2(1(1(4(x))))))
4(0(0(5(4(x))))) → 5(0(0(4(4(5(x))))))
4(2(5(4(1(x))))) → 4(4(1(5(3(2(x))))))
01(0(5(1(2(x))))) → 01(1(x))
1(0(5(4(x)))) → 1(4(5(0(3(3(x))))))
1(0(5(4(x)))) → 5(5(1(0(2(4(x))))))
1(4(2(1(x)))) → 4(0(2(1(2(1(x))))))
1(0(1(2(4(x))))) → 1(1(0(2(3(4(x))))))
1(4(2(1(2(x))))) → 0(2(2(1(1(4(x))))))
4(2(1(x))) → 4(0(2(1(x))))
4(2(1(x))) → 1(2(4(0(2(x)))))
4(1(2(1(x)))) → 4(1(0(2(1(x)))))
4(1(2(1(x)))) → 3(4(0(2(1(1(x))))))
4(3(2(1(x)))) → 0(3(4(0(2(1(x))))))
4(0(0(5(4(x))))) → 5(0(0(4(4(5(x))))))
4(2(5(4(1(x))))) → 4(4(1(5(3(2(x))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
01(0(5(1(2(x))))) → 01(1(x))
POL(0(x1)) = 1 + x1
POL(01(x1)) = x1
POL(1(x1)) = 1
POL(2(x1)) = 0
POL(3(x1)) = 0
POL(4(x1)) = 0
POL(5(x1)) = x1
1(0(5(4(x)))) → 1(4(5(0(3(3(x))))))
1(0(5(4(x)))) → 5(5(1(0(2(4(x))))))
1(4(2(1(x)))) → 4(0(2(1(2(1(x))))))
1(0(1(2(4(x))))) → 1(1(0(2(3(4(x))))))
1(4(2(1(2(x))))) → 0(2(2(1(1(4(x))))))
1(0(5(4(x)))) → 1(4(5(0(3(3(x))))))
1(0(5(4(x)))) → 5(5(1(0(2(4(x))))))
1(4(2(1(x)))) → 4(0(2(1(2(1(x))))))
1(0(1(2(4(x))))) → 1(1(0(2(3(4(x))))))
1(4(2(1(2(x))))) → 0(2(2(1(1(4(x))))))
4(2(1(x))) → 4(0(2(1(x))))
4(2(1(x))) → 1(2(4(0(2(x)))))
4(1(2(1(x)))) → 4(1(0(2(1(x)))))
4(1(2(1(x)))) → 3(4(0(2(1(1(x))))))
4(3(2(1(x)))) → 0(3(4(0(2(1(x))))))
4(0(0(5(4(x))))) → 5(0(0(4(4(5(x))))))
4(2(5(4(1(x))))) → 4(4(1(5(3(2(x))))))