a(a(x1)) → b(x1)
a(a(a(x1))) → a(b(a(x1)))
a(b(a(x1))) → b(b(b(x1)))
a(a(a(a(x1)))) → a(a(b(a(a(x1)))))
a(a(b(a(x1)))) → a(b(b(a(b(x1)))))
a(b(a(a(x1)))) → b(a(b(b(a(x1)))))
a(b(b(a(x1)))) → b(b(b(b(b(x1)))))
a(a(a(a(a(x1))))) → a(a(a(b(a(a(a(x1)))))))
a(a(a(b(a(x1))))) → a(a(b(b(a(a(b(x1)))))))
a(a(b(a(a(x1))))) → a(b(a(b(a(b(a(x1)))))))
a(a(b(b(a(x1))))) → a(b(b(b(a(b(b(x1)))))))
a(b(a(a(a(x1))))) → b(a(a(b(b(a(a(x1)))))))
a(b(a(b(a(x1))))) → b(a(b(b(b(a(b(x1)))))))
a(b(b(a(a(x1))))) → b(b(a(b(b(b(a(x1)))))))
a(b(b(b(a(x1))))) → b(b(b(b(b(b(b(x1)))))))
↳ QTRS
↳ DependencyPairsProof
a(a(x1)) → b(x1)
a(a(a(x1))) → a(b(a(x1)))
a(b(a(x1))) → b(b(b(x1)))
a(a(a(a(x1)))) → a(a(b(a(a(x1)))))
a(a(b(a(x1)))) → a(b(b(a(b(x1)))))
a(b(a(a(x1)))) → b(a(b(b(a(x1)))))
a(b(b(a(x1)))) → b(b(b(b(b(x1)))))
a(a(a(a(a(x1))))) → a(a(a(b(a(a(a(x1)))))))
a(a(a(b(a(x1))))) → a(a(b(b(a(a(b(x1)))))))
a(a(b(a(a(x1))))) → a(b(a(b(a(b(a(x1)))))))
a(a(b(b(a(x1))))) → a(b(b(b(a(b(b(x1)))))))
a(b(a(a(a(x1))))) → b(a(a(b(b(a(a(x1)))))))
a(b(a(b(a(x1))))) → b(a(b(b(b(a(b(x1)))))))
a(b(b(a(a(x1))))) → b(b(a(b(b(b(a(x1)))))))
a(b(b(b(a(x1))))) → b(b(b(b(b(b(b(x1)))))))
A(b(b(a(a(x1))))) → A(b(b(b(a(x1)))))
A(a(b(b(a(x1))))) → A(b(b(b(a(b(b(x1)))))))
A(a(a(a(x1)))) → A(a(b(a(a(x1)))))
A(a(b(a(a(x1))))) → A(b(a(x1)))
A(b(a(a(a(x1))))) → A(a(b(b(a(a(x1))))))
A(a(b(a(x1)))) → A(b(x1))
A(a(b(a(a(x1))))) → A(b(a(b(a(x1)))))
A(a(a(a(a(x1))))) → A(b(a(a(a(x1)))))
A(a(a(b(a(x1))))) → A(b(x1))
A(b(a(b(a(x1))))) → A(b(b(b(a(b(x1))))))
A(b(a(a(a(x1))))) → A(b(b(a(a(x1)))))
A(a(b(b(a(x1))))) → A(b(b(x1)))
A(a(a(a(a(x1))))) → A(a(b(a(a(a(x1))))))
A(a(a(b(a(x1))))) → A(a(b(x1)))
A(b(a(b(a(x1))))) → A(b(x1))
A(a(a(x1))) → A(b(a(x1)))
A(a(a(b(a(x1))))) → A(b(b(a(a(b(x1))))))
A(a(a(a(x1)))) → A(b(a(a(x1))))
A(a(a(a(a(x1))))) → A(a(a(b(a(a(a(x1)))))))
A(a(b(a(a(x1))))) → A(b(a(b(a(b(a(x1)))))))
A(b(a(a(x1)))) → A(b(b(a(x1))))
A(a(b(a(x1)))) → A(b(b(a(b(x1)))))
A(a(a(b(a(x1))))) → A(a(b(b(a(a(b(x1)))))))
a(a(x1)) → b(x1)
a(a(a(x1))) → a(b(a(x1)))
a(b(a(x1))) → b(b(b(x1)))
a(a(a(a(x1)))) → a(a(b(a(a(x1)))))
a(a(b(a(x1)))) → a(b(b(a(b(x1)))))
a(b(a(a(x1)))) → b(a(b(b(a(x1)))))
a(b(b(a(x1)))) → b(b(b(b(b(x1)))))
a(a(a(a(a(x1))))) → a(a(a(b(a(a(a(x1)))))))
a(a(a(b(a(x1))))) → a(a(b(b(a(a(b(x1)))))))
a(a(b(a(a(x1))))) → a(b(a(b(a(b(a(x1)))))))
a(a(b(b(a(x1))))) → a(b(b(b(a(b(b(x1)))))))
a(b(a(a(a(x1))))) → b(a(a(b(b(a(a(x1)))))))
a(b(a(b(a(x1))))) → b(a(b(b(b(a(b(x1)))))))
a(b(b(a(a(x1))))) → b(b(a(b(b(b(a(x1)))))))
a(b(b(b(a(x1))))) → b(b(b(b(b(b(b(x1)))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
A(b(b(a(a(x1))))) → A(b(b(b(a(x1)))))
A(a(b(b(a(x1))))) → A(b(b(b(a(b(b(x1)))))))
A(a(a(a(x1)))) → A(a(b(a(a(x1)))))
A(a(b(a(a(x1))))) → A(b(a(x1)))
A(b(a(a(a(x1))))) → A(a(b(b(a(a(x1))))))
A(a(b(a(x1)))) → A(b(x1))
A(a(b(a(a(x1))))) → A(b(a(b(a(x1)))))
A(a(a(a(a(x1))))) → A(b(a(a(a(x1)))))
A(a(a(b(a(x1))))) → A(b(x1))
A(b(a(b(a(x1))))) → A(b(b(b(a(b(x1))))))
A(b(a(a(a(x1))))) → A(b(b(a(a(x1)))))
A(a(b(b(a(x1))))) → A(b(b(x1)))
A(a(a(a(a(x1))))) → A(a(b(a(a(a(x1))))))
A(a(a(b(a(x1))))) → A(a(b(x1)))
A(b(a(b(a(x1))))) → A(b(x1))
A(a(a(x1))) → A(b(a(x1)))
A(a(a(b(a(x1))))) → A(b(b(a(a(b(x1))))))
A(a(a(a(x1)))) → A(b(a(a(x1))))
A(a(a(a(a(x1))))) → A(a(a(b(a(a(a(x1)))))))
A(a(b(a(a(x1))))) → A(b(a(b(a(b(a(x1)))))))
A(b(a(a(x1)))) → A(b(b(a(x1))))
A(a(b(a(x1)))) → A(b(b(a(b(x1)))))
A(a(a(b(a(x1))))) → A(a(b(b(a(a(b(x1)))))))
a(a(x1)) → b(x1)
a(a(a(x1))) → a(b(a(x1)))
a(b(a(x1))) → b(b(b(x1)))
a(a(a(a(x1)))) → a(a(b(a(a(x1)))))
a(a(b(a(x1)))) → a(b(b(a(b(x1)))))
a(b(a(a(x1)))) → b(a(b(b(a(x1)))))
a(b(b(a(x1)))) → b(b(b(b(b(x1)))))
a(a(a(a(a(x1))))) → a(a(a(b(a(a(a(x1)))))))
a(a(a(b(a(x1))))) → a(a(b(b(a(a(b(x1)))))))
a(a(b(a(a(x1))))) → a(b(a(b(a(b(a(x1)))))))
a(a(b(b(a(x1))))) → a(b(b(b(a(b(b(x1)))))))
a(b(a(a(a(x1))))) → b(a(a(b(b(a(a(x1)))))))
a(b(a(b(a(x1))))) → b(a(b(b(b(a(b(x1)))))))
a(b(b(a(a(x1))))) → b(b(a(b(b(b(a(x1)))))))
a(b(b(b(a(x1))))) → b(b(b(b(b(b(b(x1)))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
A(a(a(a(x1)))) → A(a(b(a(a(x1)))))
A(a(b(a(a(x1))))) → A(b(a(x1)))
A(b(a(a(a(x1))))) → A(a(b(b(a(a(x1))))))
A(a(b(a(x1)))) → A(b(x1))
A(a(b(a(a(x1))))) → A(b(a(b(a(x1)))))
A(a(a(a(a(x1))))) → A(b(a(a(a(x1)))))
A(a(a(b(a(x1))))) → A(b(x1))
A(a(a(a(a(x1))))) → A(a(b(a(a(a(x1))))))
A(a(a(b(a(x1))))) → A(a(b(x1)))
A(b(a(b(a(x1))))) → A(b(x1))
A(a(a(x1))) → A(b(a(x1)))
A(a(a(a(x1)))) → A(b(a(a(x1))))
A(a(a(a(a(x1))))) → A(a(a(b(a(a(a(x1)))))))
A(a(b(a(a(x1))))) → A(b(a(b(a(b(a(x1)))))))
A(a(a(b(a(x1))))) → A(a(b(b(a(a(b(x1)))))))
a(a(x1)) → b(x1)
a(a(a(x1))) → a(b(a(x1)))
a(b(a(x1))) → b(b(b(x1)))
a(a(a(a(x1)))) → a(a(b(a(a(x1)))))
a(a(b(a(x1)))) → a(b(b(a(b(x1)))))
a(b(a(a(x1)))) → b(a(b(b(a(x1)))))
a(b(b(a(x1)))) → b(b(b(b(b(x1)))))
a(a(a(a(a(x1))))) → a(a(a(b(a(a(a(x1)))))))
a(a(a(b(a(x1))))) → a(a(b(b(a(a(b(x1)))))))
a(a(b(a(a(x1))))) → a(b(a(b(a(b(a(x1)))))))
a(a(b(b(a(x1))))) → a(b(b(b(a(b(b(x1)))))))
a(b(a(a(a(x1))))) → b(a(a(b(b(a(a(x1)))))))
a(b(a(b(a(x1))))) → b(a(b(b(b(a(b(x1)))))))
a(b(b(a(a(x1))))) → b(b(a(b(b(b(a(x1)))))))
a(b(b(b(a(x1))))) → b(b(b(b(b(b(b(x1)))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(a(a(x1)))) → A(a(b(a(a(x1)))))
A(a(b(a(a(x1))))) → A(b(a(x1)))
A(b(a(a(a(x1))))) → A(a(b(b(a(a(x1))))))
A(a(b(a(x1)))) → A(b(x1))
A(a(b(a(a(x1))))) → A(b(a(b(a(x1)))))
A(a(a(a(a(x1))))) → A(b(a(a(a(x1)))))
A(a(a(b(a(x1))))) → A(b(x1))
A(a(a(a(a(x1))))) → A(a(b(a(a(a(x1))))))
A(a(a(b(a(x1))))) → A(a(b(x1)))
A(b(a(b(a(x1))))) → A(b(x1))
A(a(a(x1))) → A(b(a(x1)))
A(a(a(a(x1)))) → A(b(a(a(x1))))
A(a(a(a(a(x1))))) → A(a(a(b(a(a(a(x1)))))))
A(a(b(a(a(x1))))) → A(b(a(b(a(b(a(x1)))))))
A(a(a(b(a(x1))))) → A(a(b(b(a(a(b(x1)))))))
The value of delta used in the strict ordering is 25/256.
POL(a(x1)) = 1/2 + (9/4)x_1
POL(A(x1)) = (1/2)x_1
POL(b(x1)) = (1/4)x_1
a(a(b(b(a(x1))))) → a(b(b(b(a(b(b(x1)))))))
a(b(a(a(a(x1))))) → b(a(a(b(b(a(a(x1)))))))
a(a(b(a(a(x1))))) → a(b(a(b(a(b(a(x1)))))))
a(b(b(b(a(x1))))) → b(b(b(b(b(b(b(x1)))))))
a(b(a(b(a(x1))))) → b(a(b(b(b(a(b(x1)))))))
a(b(b(a(a(x1))))) → b(b(a(b(b(b(a(x1)))))))
a(a(a(x1))) → a(b(a(x1)))
a(a(x1)) → b(x1)
a(b(a(x1))) → b(b(b(x1)))
a(b(a(a(x1)))) → b(a(b(b(a(x1)))))
a(a(b(a(x1)))) → a(b(b(a(b(x1)))))
a(a(a(a(a(x1))))) → a(a(a(b(a(a(a(x1)))))))
a(a(a(b(a(x1))))) → a(a(b(b(a(a(b(x1)))))))
a(a(a(a(x1)))) → a(a(b(a(a(x1)))))
a(b(b(a(x1)))) → b(b(b(b(b(x1)))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a(a(x1)) → b(x1)
a(a(a(x1))) → a(b(a(x1)))
a(b(a(x1))) → b(b(b(x1)))
a(a(a(a(x1)))) → a(a(b(a(a(x1)))))
a(a(b(a(x1)))) → a(b(b(a(b(x1)))))
a(b(a(a(x1)))) → b(a(b(b(a(x1)))))
a(b(b(a(x1)))) → b(b(b(b(b(x1)))))
a(a(a(a(a(x1))))) → a(a(a(b(a(a(a(x1)))))))
a(a(a(b(a(x1))))) → a(a(b(b(a(a(b(x1)))))))
a(a(b(a(a(x1))))) → a(b(a(b(a(b(a(x1)))))))
a(a(b(b(a(x1))))) → a(b(b(b(a(b(b(x1)))))))
a(b(a(a(a(x1))))) → b(a(a(b(b(a(a(x1)))))))
a(b(a(b(a(x1))))) → b(a(b(b(b(a(b(x1)))))))
a(b(b(a(a(x1))))) → b(b(a(b(b(b(a(x1)))))))
a(b(b(b(a(x1))))) → b(b(b(b(b(b(b(x1)))))))