a(a(s(s(x1)))) → s(s(a(a(x1))))
b(b(a(a(b(b(s(s(x1)))))))) → a(a(b(b(s(s(a(a(x1))))))))
b(b(a(a(b(b(b(b(x1)))))))) → a(a(b(b(a(a(b(b(x1))))))))
a(a(b(b(a(a(a(a(x1)))))))) → b(b(a(a(b(b(a(a(x1))))))))
↳ QTRS
↳ DependencyPairsProof
a(a(s(s(x1)))) → s(s(a(a(x1))))
b(b(a(a(b(b(s(s(x1)))))))) → a(a(b(b(s(s(a(a(x1))))))))
b(b(a(a(b(b(b(b(x1)))))))) → a(a(b(b(a(a(b(b(x1))))))))
a(a(b(b(a(a(a(a(x1)))))))) → b(b(a(a(b(b(a(a(x1))))))))
B(b(a(a(b(b(b(b(x1)))))))) → A(b(b(a(a(b(b(x1)))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(a(a(x1)))
B(b(a(a(b(b(s(s(x1)))))))) → A(a(b(b(s(s(a(a(x1))))))))
A(a(b(b(a(a(a(a(x1)))))))) → A(a(b(b(a(a(x1))))))
B(b(a(a(b(b(b(b(x1)))))))) → A(a(b(b(a(a(b(b(x1))))))))
B(b(a(a(b(b(s(s(x1)))))))) → A(x1)
A(a(s(s(x1)))) → A(x1)
B(b(a(a(b(b(s(s(x1)))))))) → A(b(b(s(s(a(a(x1)))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(b(a(a(b(b(a(a(x1))))))))
B(b(a(a(b(b(b(b(x1)))))))) → B(a(a(b(b(x1)))))
B(b(a(a(b(b(b(b(x1)))))))) → A(b(b(x1)))
A(a(s(s(x1)))) → A(a(x1))
B(b(a(a(b(b(b(b(x1)))))))) → B(b(a(a(b(b(x1))))))
B(b(a(a(b(b(b(b(x1)))))))) → A(a(b(b(x1))))
A(a(b(b(a(a(a(a(x1)))))))) → B(a(a(b(b(a(a(x1)))))))
B(b(a(a(b(b(s(s(x1)))))))) → B(b(s(s(a(a(x1))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(b(a(a(x1))))
A(a(b(b(a(a(a(a(x1)))))))) → A(b(b(a(a(x1)))))
B(b(a(a(b(b(s(s(x1)))))))) → B(s(s(a(a(x1)))))
B(b(a(a(b(b(s(s(x1)))))))) → A(a(x1))
a(a(s(s(x1)))) → s(s(a(a(x1))))
b(b(a(a(b(b(s(s(x1)))))))) → a(a(b(b(s(s(a(a(x1))))))))
b(b(a(a(b(b(b(b(x1)))))))) → a(a(b(b(a(a(b(b(x1))))))))
a(a(b(b(a(a(a(a(x1)))))))) → b(b(a(a(b(b(a(a(x1))))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
B(b(a(a(b(b(b(b(x1)))))))) → A(b(b(a(a(b(b(x1)))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(a(a(x1)))
B(b(a(a(b(b(s(s(x1)))))))) → A(a(b(b(s(s(a(a(x1))))))))
A(a(b(b(a(a(a(a(x1)))))))) → A(a(b(b(a(a(x1))))))
B(b(a(a(b(b(b(b(x1)))))))) → A(a(b(b(a(a(b(b(x1))))))))
B(b(a(a(b(b(s(s(x1)))))))) → A(x1)
A(a(s(s(x1)))) → A(x1)
B(b(a(a(b(b(s(s(x1)))))))) → A(b(b(s(s(a(a(x1)))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(b(a(a(b(b(a(a(x1))))))))
B(b(a(a(b(b(b(b(x1)))))))) → B(a(a(b(b(x1)))))
B(b(a(a(b(b(b(b(x1)))))))) → A(b(b(x1)))
A(a(s(s(x1)))) → A(a(x1))
B(b(a(a(b(b(b(b(x1)))))))) → B(b(a(a(b(b(x1))))))
B(b(a(a(b(b(b(b(x1)))))))) → A(a(b(b(x1))))
A(a(b(b(a(a(a(a(x1)))))))) → B(a(a(b(b(a(a(x1)))))))
B(b(a(a(b(b(s(s(x1)))))))) → B(b(s(s(a(a(x1))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(b(a(a(x1))))
A(a(b(b(a(a(a(a(x1)))))))) → A(b(b(a(a(x1)))))
B(b(a(a(b(b(s(s(x1)))))))) → B(s(s(a(a(x1)))))
B(b(a(a(b(b(s(s(x1)))))))) → A(a(x1))
a(a(s(s(x1)))) → s(s(a(a(x1))))
b(b(a(a(b(b(s(s(x1)))))))) → a(a(b(b(s(s(a(a(x1))))))))
b(b(a(a(b(b(b(b(x1)))))))) → a(a(b(b(a(a(b(b(x1))))))))
a(a(b(b(a(a(a(a(x1)))))))) → b(b(a(a(b(b(a(a(x1))))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
B(b(a(a(b(b(b(b(x1)))))))) → A(b(b(a(a(b(b(x1)))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(a(a(x1)))
A(a(b(b(a(a(a(a(x1)))))))) → A(a(b(b(a(a(x1))))))
B(b(a(a(b(b(b(b(x1)))))))) → A(a(b(b(a(a(b(b(x1))))))))
B(b(a(a(b(b(s(s(x1)))))))) → A(x1)
A(a(s(s(x1)))) → A(x1)
A(a(b(b(a(a(a(a(x1)))))))) → B(b(a(a(b(b(a(a(x1))))))))
B(b(a(a(b(b(b(b(x1)))))))) → B(a(a(b(b(x1)))))
B(b(a(a(b(b(b(b(x1)))))))) → A(b(b(x1)))
B(b(a(a(b(b(b(b(x1)))))))) → A(a(b(b(x1))))
A(a(s(s(x1)))) → A(a(x1))
B(b(a(a(b(b(b(b(x1)))))))) → B(b(a(a(b(b(x1))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(a(a(b(b(a(a(x1)))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(b(a(a(x1))))
A(a(b(b(a(a(a(a(x1)))))))) → A(b(b(a(a(x1)))))
B(b(a(a(b(b(s(s(x1)))))))) → A(a(x1))
a(a(s(s(x1)))) → s(s(a(a(x1))))
b(b(a(a(b(b(s(s(x1)))))))) → a(a(b(b(s(s(a(a(x1))))))))
b(b(a(a(b(b(b(b(x1)))))))) → a(a(b(b(a(a(b(b(x1))))))))
a(a(b(b(a(a(a(a(x1)))))))) → b(b(a(a(b(b(a(a(x1))))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(b(a(a(b(b(b(b(x1)))))))) → A(b(b(a(a(b(b(x1)))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(a(a(x1)))
A(a(b(b(a(a(a(a(x1)))))))) → A(a(b(b(a(a(x1))))))
B(b(a(a(b(b(s(s(x1)))))))) → A(x1)
A(a(s(s(x1)))) → A(x1)
B(b(a(a(b(b(b(b(x1)))))))) → B(a(a(b(b(x1)))))
B(b(a(a(b(b(b(b(x1)))))))) → A(b(b(x1)))
B(b(a(a(b(b(b(b(x1)))))))) → A(a(b(b(x1))))
B(b(a(a(b(b(b(b(x1)))))))) → B(b(a(a(b(b(x1))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(a(a(b(b(a(a(x1)))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(b(a(a(x1))))
A(a(b(b(a(a(a(a(x1)))))))) → A(b(b(a(a(x1)))))
B(b(a(a(b(b(s(s(x1)))))))) → A(a(x1))
Used ordering: Polynomial interpretation [25,35]:
B(b(a(a(b(b(b(b(x1)))))))) → A(a(b(b(a(a(b(b(x1))))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(b(a(a(b(b(a(a(x1))))))))
A(a(s(s(x1)))) → A(a(x1))
The value of delta used in the strict ordering is 16.
POL(B(x1)) = (4)x_1
POL(a(x1)) = 4 + (4)x_1
POL(A(x1)) = (4)x_1
POL(s(x1)) = x_1
POL(b(x1)) = 4 + (4)x_1
a(a(s(s(x1)))) → s(s(a(a(x1))))
b(b(a(a(b(b(s(s(x1)))))))) → a(a(b(b(s(s(a(a(x1))))))))
b(b(a(a(b(b(b(b(x1)))))))) → a(a(b(b(a(a(b(b(x1))))))))
a(a(b(b(a(a(a(a(x1)))))))) → b(b(a(a(b(b(a(a(x1))))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
A(a(s(s(x1)))) → A(a(x1))
B(b(a(a(b(b(b(b(x1)))))))) → A(a(b(b(a(a(b(b(x1))))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(b(a(a(b(b(a(a(x1))))))))
a(a(s(s(x1)))) → s(s(a(a(x1))))
b(b(a(a(b(b(s(s(x1)))))))) → a(a(b(b(s(s(a(a(x1))))))))
b(b(a(a(b(b(b(b(x1)))))))) → a(a(b(b(a(a(b(b(x1))))))))
a(a(b(b(a(a(a(a(x1)))))))) → b(b(a(a(b(b(a(a(x1))))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(s(s(x1)))) → A(a(x1))
Used ordering: Polynomial interpretation [25,35]:
B(b(a(a(b(b(b(b(x1)))))))) → A(a(b(b(a(a(b(b(x1))))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(b(a(a(b(b(a(a(x1))))))))
The value of delta used in the strict ordering is 2.
POL(B(x1)) = 0
POL(a(x1)) = x_1
POL(A(x1)) = x_1
POL(s(x1)) = 1 + x_1
POL(b(x1)) = 0
a(a(s(s(x1)))) → s(s(a(a(x1))))
b(b(a(a(b(b(s(s(x1)))))))) → a(a(b(b(s(s(a(a(x1))))))))
b(b(a(a(b(b(b(b(x1)))))))) → a(a(b(b(a(a(b(b(x1))))))))
a(a(b(b(a(a(a(a(x1)))))))) → b(b(a(a(b(b(a(a(x1))))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
B(b(a(a(b(b(b(b(x1)))))))) → A(a(b(b(a(a(b(b(x1))))))))
A(a(b(b(a(a(a(a(x1)))))))) → B(b(a(a(b(b(a(a(x1))))))))
a(a(s(s(x1)))) → s(s(a(a(x1))))
b(b(a(a(b(b(s(s(x1)))))))) → a(a(b(b(s(s(a(a(x1))))))))
b(b(a(a(b(b(b(b(x1)))))))) → a(a(b(b(a(a(b(b(x1))))))))
a(a(b(b(a(a(a(a(x1)))))))) → b(b(a(a(b(b(a(a(x1))))))))