YES
0 QTRS
↳1 QTRSRRRProof (⇔, 118 ms)
↳2 QTRS
↳3 DependencyPairsProof (⇔, 8 ms)
↳4 QDP
↳5 DependencyGraphProof (⇔, 0 ms)
↳6 TRUE
0(1(0(2(x)))) → 2(2(2(x)))
0(1(1(1(x)))) → 3(1(0(x)))
4(5(1(4(x)))) → 1(5(4(4(x))))
1(2(0(4(1(x))))) → 2(5(2(2(x))))
1(5(1(0(3(x))))) → 5(5(0(3(x))))
1(3(5(1(0(4(x)))))) → 4(0(0(0(1(4(x))))))
3(3(1(4(5(4(5(5(x)))))))) → 3(5(3(2(0(5(2(x)))))))
4(2(5(3(1(0(0(5(2(x))))))))) → 4(4(1(5(3(5(3(2(x))))))))
2(2(1(1(0(2(0(1(2(3(x)))))))))) → 5(4(4(5(2(5(5(2(3(x)))))))))
2(2(2(3(3(4(3(3(5(4(5(x))))))))))) → 5(5(4(2(5(3(5(3(2(0(5(x)))))))))))
4(2(1(1(5(1(0(0(0(2(5(x))))))))))) → 5(5(0(3(0(1(4(5(2(5(x))))))))))
5(4(5(4(2(0(2(2(3(0(0(2(x)))))))))))) → 5(3(4(5(0(3(2(1(1(2(2(x)))))))))))
0(2(1(1(3(1(5(0(5(2(3(1(4(x))))))))))))) → 3(0(1(5(1(4(4(5(0(5(1(1(4(x)))))))))))))
1(1(2(4(2(2(2(1(1(3(4(1(2(x))))))))))))) → 1(5(0(3(4(1(0(5(2(2(2(3(x))))))))))))
1(4(0(0(2(4(0(3(3(2(0(3(1(x))))))))))))) → 1(5(0(5(0(2(0(5(1(0(1(2(5(5(x))))))))))))))
4(1(4(1(3(0(0(2(1(5(4(1(0(0(x)))))))))))))) → 2(3(0(2(5(4(4(3(0(4(1(2(0(x)))))))))))))
4(2(4(4(0(0(0(4(0(3(5(0(3(3(x)))))))))))))) → 5(1(0(1(0(1(3(5(3(5(5(0(0(3(x))))))))))))))
1(2(5(3(3(0(2(2(5(3(2(3(3(3(2(1(x)))))))))))))))) → 1(1(0(0(4(1(2(1(0(5(0(0(3(5(0(4(1(x)))))))))))))))))
3(1(2(5(0(3(4(3(1(5(4(1(5(2(0(5(x)))))))))))))))) → 3(1(0(4(2(0(5(2(4(4(2(2(1(1(1(5(x))))))))))))))))
1(3(4(5(1(0(0(3(1(2(4(2(3(5(2(0(4(1(x)))))))))))))))))) → 1(3(0(0(4(2(2(5(3(1(0(1(2(1(5(0(1(4(1(x)))))))))))))))))))
1(0(3(3(2(5(0(0(3(0(3(2(4(1(4(0(2(4(2(x))))))))))))))))))) → 4(3(4(2(1(4(2(4(3(3(2(2(2(1(1(1(5(3(2(x)))))))))))))))))))
5(3(2(1(0(1(3(1(3(3(0(0(3(2(5(3(0(3(0(x))))))))))))))))))) → 5(1(0(3(2(4(0(0(3(2(1(5(1(3(0(5(1(3(1(x)))))))))))))))))))
0(2(2(3(3(5(0(0(5(0(3(1(3(0(1(2(1(5(5(1(x)))))))))))))))))))) → 0(0(3(2(5(2(5(2(3(2(1(2(5(4(3(4(5(0(4(x)))))))))))))))))))
1(0(4(2(3(3(5(4(3(5(0(2(0(4(5(0(2(0(2(4(x)))))))))))))))))))) → 4(5(4(5(4(1(1(2(5(0(4(3(1(5(4(3(1(5(4(0(4(x)))))))))))))))))))))
1(4(2(3(1(3(4(2(4(1(5(1(4(0(4(5(2(0(0(3(4(x))))))))))))))))))))) → 4(3(4(1(3(5(1(1(4(3(1(5(1(3(1(2(4(2(1(3(x))))))))))))))))))))
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
POL(0(x1)) = 235 + x1
POL(1(x1)) = 191 + x1
POL(2(x1)) = 157 + x1
POL(3(x1)) = 381 + x1
POL(4(x1)) = 237 + x1
POL(5(x1)) = 136 + x1
0(1(0(2(x)))) → 2(2(2(x)))
0(1(1(1(x)))) → 3(1(0(x)))
1(2(0(4(1(x))))) → 2(5(2(2(x))))
1(5(1(0(3(x))))) → 5(5(0(3(x))))
1(3(5(1(0(4(x)))))) → 4(0(0(0(1(4(x))))))
3(3(1(4(5(4(5(5(x)))))))) → 3(5(3(2(0(5(2(x)))))))
4(2(5(3(1(0(0(5(2(x))))))))) → 4(4(1(5(3(5(3(2(x))))))))
2(2(1(1(0(2(0(1(2(3(x)))))))))) → 5(4(4(5(2(5(5(2(3(x)))))))))
2(2(2(3(3(4(3(3(5(4(5(x))))))))))) → 5(5(4(2(5(3(5(3(2(0(5(x)))))))))))
4(2(1(1(5(1(0(0(0(2(5(x))))))))))) → 5(5(0(3(0(1(4(5(2(5(x))))))))))
5(4(5(4(2(0(2(2(3(0(0(2(x)))))))))))) → 5(3(4(5(0(3(2(1(1(2(2(x)))))))))))
0(2(1(1(3(1(5(0(5(2(3(1(4(x))))))))))))) → 3(0(1(5(1(4(4(5(0(5(1(1(4(x)))))))))))))
1(1(2(4(2(2(2(1(1(3(4(1(2(x))))))))))))) → 1(5(0(3(4(1(0(5(2(2(2(3(x))))))))))))
1(4(0(0(2(4(0(3(3(2(0(3(1(x))))))))))))) → 1(5(0(5(0(2(0(5(1(0(1(2(5(5(x))))))))))))))
4(1(4(1(3(0(0(2(1(5(4(1(0(0(x)))))))))))))) → 2(3(0(2(5(4(4(3(0(4(1(2(0(x)))))))))))))
4(2(4(4(0(0(0(4(0(3(5(0(3(3(x)))))))))))))) → 5(1(0(1(0(1(3(5(3(5(5(0(0(3(x))))))))))))))
1(2(5(3(3(0(2(2(5(3(2(3(3(3(2(1(x)))))))))))))))) → 1(1(0(0(4(1(2(1(0(5(0(0(3(5(0(4(1(x)))))))))))))))))
3(1(2(5(0(3(4(3(1(5(4(1(5(2(0(5(x)))))))))))))))) → 3(1(0(4(2(0(5(2(4(4(2(2(1(1(1(5(x))))))))))))))))
1(3(4(5(1(0(0(3(1(2(4(2(3(5(2(0(4(1(x)))))))))))))))))) → 1(3(0(0(4(2(2(5(3(1(0(1(2(1(5(0(1(4(1(x)))))))))))))))))))
1(0(3(3(2(5(0(0(3(0(3(2(4(1(4(0(2(4(2(x))))))))))))))))))) → 4(3(4(2(1(4(2(4(3(3(2(2(2(1(1(1(5(3(2(x)))))))))))))))))))
5(3(2(1(0(1(3(1(3(3(0(0(3(2(5(3(0(3(0(x))))))))))))))))))) → 5(1(0(3(2(4(0(0(3(2(1(5(1(3(0(5(1(3(1(x)))))))))))))))))))
0(2(2(3(3(5(0(0(5(0(3(1(3(0(1(2(1(5(5(1(x)))))))))))))))))))) → 0(0(3(2(5(2(5(2(3(2(1(2(5(4(3(4(5(0(4(x)))))))))))))))))))
1(0(4(2(3(3(5(4(3(5(0(2(0(4(5(0(2(0(2(4(x)))))))))))))))))))) → 4(5(4(5(4(1(1(2(5(0(4(3(1(5(4(3(1(5(4(0(4(x)))))))))))))))))))))
1(4(2(3(1(3(4(2(4(1(5(1(4(0(4(5(2(0(0(3(4(x))))))))))))))))))))) → 4(3(4(1(3(5(1(1(4(3(1(5(1(3(1(2(4(2(1(3(x))))))))))))))))))))
4(5(1(4(x)))) → 1(5(4(4(x))))
41(5(1(4(x)))) → 41(4(x))
4(5(1(4(x)))) → 1(5(4(4(x))))