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