a(x1) → b(x1)
a(a(x1)) → a(b(a(x1)))
a(b(x1)) → b(b(b(x1)))
a(a(a(x1))) → a(a(b(a(a(x1)))))
a(a(b(x1))) → a(b(b(a(b(x1)))))
a(b(a(x1))) → b(a(b(b(a(x1)))))
a(b(b(x1))) → b(b(b(b(b(x1)))))
b(a(x1)) → b(b(b(x1)))
a(b(a(x1))) → a(b(b(a(b(x1)))))
b(a(a(x1))) → b(a(b(b(a(x1)))))
b(b(a(x1))) → b(b(b(b(b(x1)))))
↳ QTRS
↳ DependencyPairsProof
a(x1) → b(x1)
a(a(x1)) → a(b(a(x1)))
a(b(x1)) → b(b(b(x1)))
a(a(a(x1))) → a(a(b(a(a(x1)))))
a(a(b(x1))) → a(b(b(a(b(x1)))))
a(b(a(x1))) → b(a(b(b(a(x1)))))
a(b(b(x1))) → b(b(b(b(b(x1)))))
b(a(x1)) → b(b(b(x1)))
a(b(a(x1))) → a(b(b(a(b(x1)))))
b(a(a(x1))) → b(a(b(b(a(x1)))))
b(b(a(x1))) → b(b(b(b(b(x1)))))
A(a(b(x1))) → A(b(b(a(b(x1)))))
B(a(a(x1))) → B(b(a(x1)))
A(a(x1)) → A(b(a(x1)))
B(b(a(x1))) → B(b(b(b(x1))))
B(b(a(x1))) → B(b(b(x1)))
B(a(x1)) → B(x1)
A(a(x1)) → B(a(x1))
B(a(a(x1))) → B(a(x1))
B(b(a(x1))) → B(x1)
A(b(a(x1))) → B(a(b(b(a(x1)))))
A(b(x1)) → B(b(b(x1)))
A(b(a(x1))) → B(b(a(b(x1))))
B(a(x1)) → B(b(b(x1)))
A(b(a(x1))) → B(b(a(x1)))
B(b(a(x1))) → B(b(b(b(b(x1)))))
A(b(b(x1))) → B(b(b(b(x1))))
A(a(a(x1))) → A(b(a(a(x1))))
A(b(a(x1))) → B(a(b(x1)))
B(a(a(x1))) → B(a(b(b(a(x1)))))
A(b(x1)) → B(b(x1))
A(a(a(x1))) → B(a(a(x1)))
A(a(a(x1))) → A(a(b(a(a(x1)))))
B(a(x1)) → B(b(x1))
A(b(a(x1))) → A(b(b(a(b(x1)))))
A(x1) → B(x1)
A(b(a(x1))) → B(x1)
B(b(a(x1))) → B(b(x1))
A(a(b(x1))) → B(b(a(b(x1))))
A(b(a(x1))) → A(b(b(a(x1))))
A(b(b(x1))) → B(b(b(x1)))
A(a(b(x1))) → B(a(b(x1)))
B(a(a(x1))) → A(b(b(a(x1))))
A(b(b(x1))) → B(b(b(b(b(x1)))))
A(b(a(x1))) → A(b(x1))
a(x1) → b(x1)
a(a(x1)) → a(b(a(x1)))
a(b(x1)) → b(b(b(x1)))
a(a(a(x1))) → a(a(b(a(a(x1)))))
a(a(b(x1))) → a(b(b(a(b(x1)))))
a(b(a(x1))) → b(a(b(b(a(x1)))))
a(b(b(x1))) → b(b(b(b(b(x1)))))
b(a(x1)) → b(b(b(x1)))
a(b(a(x1))) → a(b(b(a(b(x1)))))
b(a(a(x1))) → b(a(b(b(a(x1)))))
b(b(a(x1))) → b(b(b(b(b(x1)))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
A(a(b(x1))) → A(b(b(a(b(x1)))))
B(a(a(x1))) → B(b(a(x1)))
A(a(x1)) → A(b(a(x1)))
B(b(a(x1))) → B(b(b(b(x1))))
B(b(a(x1))) → B(b(b(x1)))
B(a(x1)) → B(x1)
A(a(x1)) → B(a(x1))
B(a(a(x1))) → B(a(x1))
B(b(a(x1))) → B(x1)
A(b(a(x1))) → B(a(b(b(a(x1)))))
A(b(x1)) → B(b(b(x1)))
A(b(a(x1))) → B(b(a(b(x1))))
B(a(x1)) → B(b(b(x1)))
A(b(a(x1))) → B(b(a(x1)))
B(b(a(x1))) → B(b(b(b(b(x1)))))
A(b(b(x1))) → B(b(b(b(x1))))
A(a(a(x1))) → A(b(a(a(x1))))
A(b(a(x1))) → B(a(b(x1)))
B(a(a(x1))) → B(a(b(b(a(x1)))))
A(b(x1)) → B(b(x1))
A(a(a(x1))) → B(a(a(x1)))
A(a(a(x1))) → A(a(b(a(a(x1)))))
B(a(x1)) → B(b(x1))
A(b(a(x1))) → A(b(b(a(b(x1)))))
A(x1) → B(x1)
A(b(a(x1))) → B(x1)
B(b(a(x1))) → B(b(x1))
A(a(b(x1))) → B(b(a(b(x1))))
A(b(a(x1))) → A(b(b(a(x1))))
A(b(b(x1))) → B(b(b(x1)))
A(a(b(x1))) → B(a(b(x1)))
B(a(a(x1))) → A(b(b(a(x1))))
A(b(b(x1))) → B(b(b(b(b(x1)))))
A(b(a(x1))) → A(b(x1))
a(x1) → b(x1)
a(a(x1)) → a(b(a(x1)))
a(b(x1)) → b(b(b(x1)))
a(a(a(x1))) → a(a(b(a(a(x1)))))
a(a(b(x1))) → a(b(b(a(b(x1)))))
a(b(a(x1))) → b(a(b(b(a(x1)))))
a(b(b(x1))) → b(b(b(b(b(x1)))))
b(a(x1)) → b(b(b(x1)))
a(b(a(x1))) → a(b(b(a(b(x1)))))
b(a(a(x1))) → b(a(b(b(a(x1)))))
b(b(a(x1))) → 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(b(x1))) → A(b(b(a(b(x1)))))
A(a(x1)) → A(b(a(x1)))
A(a(x1)) → B(a(x1))
A(a(a(x1))) → A(b(a(a(x1))))
A(a(a(x1))) → B(a(a(x1)))
A(a(b(x1))) → B(b(a(b(x1))))
A(a(b(x1))) → B(a(b(x1)))
Used ordering: Polynomial interpretation [25,35]:
B(a(a(x1))) → B(b(a(x1)))
B(b(a(x1))) → B(b(b(b(x1))))
B(b(a(x1))) → B(b(b(x1)))
B(a(x1)) → B(x1)
B(a(a(x1))) → B(a(x1))
B(b(a(x1))) → B(x1)
A(b(a(x1))) → B(a(b(b(a(x1)))))
A(b(x1)) → B(b(b(x1)))
A(b(a(x1))) → B(b(a(b(x1))))
B(a(x1)) → B(b(b(x1)))
A(b(a(x1))) → B(b(a(x1)))
B(b(a(x1))) → B(b(b(b(b(x1)))))
A(b(b(x1))) → B(b(b(b(x1))))
A(b(a(x1))) → B(a(b(x1)))
B(a(a(x1))) → B(a(b(b(a(x1)))))
A(b(x1)) → B(b(x1))
A(a(a(x1))) → A(a(b(a(a(x1)))))
B(a(x1)) → B(b(x1))
A(b(a(x1))) → A(b(b(a(b(x1)))))
A(x1) → B(x1)
A(b(a(x1))) → B(x1)
B(b(a(x1))) → B(b(x1))
A(b(a(x1))) → A(b(b(a(x1))))
A(b(b(x1))) → B(b(b(x1)))
B(a(a(x1))) → A(b(b(a(x1))))
A(b(b(x1))) → B(b(b(b(b(x1)))))
A(b(a(x1))) → A(b(x1))
The value of delta used in the strict ordering is 2.
POL(B(x1)) = 0
POL(a(x1)) = 1
POL(A(x1)) = (2)x_1
POL(b(x1)) = 0
a(x1) → b(x1)
a(a(a(x1))) → a(a(b(a(a(x1)))))
a(b(a(x1))) → a(b(b(a(b(x1)))))
a(a(x1)) → a(b(a(x1)))
a(a(b(x1))) → a(b(b(a(b(x1)))))
a(b(x1)) → b(b(b(x1)))
a(b(a(x1))) → b(a(b(b(a(x1)))))
a(b(b(x1))) → b(b(b(b(b(x1)))))
b(b(a(x1))) → b(b(b(b(b(x1)))))
b(a(a(x1))) → b(a(b(b(a(x1)))))
b(a(x1)) → b(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
B(a(a(x1))) → B(b(a(x1)))
B(b(a(x1))) → B(b(b(b(x1))))
B(b(a(x1))) → B(b(b(x1)))
B(a(x1)) → B(x1)
B(a(a(x1))) → B(a(x1))
A(b(x1)) → B(b(b(x1)))
A(b(a(x1))) → B(a(b(b(a(x1)))))
B(b(a(x1))) → B(x1)
A(b(a(x1))) → B(b(a(b(x1))))
B(a(x1)) → B(b(b(x1)))
A(b(a(x1))) → B(b(a(x1)))
A(b(b(x1))) → B(b(b(b(x1))))
B(b(a(x1))) → B(b(b(b(b(x1)))))
A(b(a(x1))) → B(a(b(x1)))
B(a(a(x1))) → B(a(b(b(a(x1)))))
A(b(x1)) → B(b(x1))
A(a(a(x1))) → A(a(b(a(a(x1)))))
B(a(x1)) → B(b(x1))
A(b(a(x1))) → A(b(b(a(b(x1)))))
A(x1) → B(x1)
A(b(a(x1))) → B(x1)
B(b(a(x1))) → B(b(x1))
A(b(a(x1))) → A(b(b(a(x1))))
A(b(b(x1))) → B(b(b(x1)))
B(a(a(x1))) → A(b(b(a(x1))))
A(b(b(x1))) → B(b(b(b(b(x1)))))
A(b(a(x1))) → A(b(x1))
a(x1) → b(x1)
a(a(x1)) → a(b(a(x1)))
a(b(x1)) → b(b(b(x1)))
a(a(a(x1))) → a(a(b(a(a(x1)))))
a(a(b(x1))) → a(b(b(a(b(x1)))))
a(b(a(x1))) → b(a(b(b(a(x1)))))
a(b(b(x1))) → b(b(b(b(b(x1)))))
b(a(x1)) → b(b(b(x1)))
a(b(a(x1))) → a(b(b(a(b(x1)))))
b(a(a(x1))) → b(a(b(b(a(x1)))))
b(b(a(x1))) → 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(x1))) → A(a(b(a(a(x1)))))
Used ordering: Polynomial interpretation [25,35]:
B(a(a(x1))) → B(b(a(x1)))
B(b(a(x1))) → B(b(b(b(x1))))
B(b(a(x1))) → B(b(b(x1)))
B(a(x1)) → B(x1)
B(a(a(x1))) → B(a(x1))
A(b(x1)) → B(b(b(x1)))
A(b(a(x1))) → B(a(b(b(a(x1)))))
B(b(a(x1))) → B(x1)
A(b(a(x1))) → B(b(a(b(x1))))
B(a(x1)) → B(b(b(x1)))
A(b(a(x1))) → B(b(a(x1)))
A(b(b(x1))) → B(b(b(b(x1))))
B(b(a(x1))) → B(b(b(b(b(x1)))))
A(b(a(x1))) → B(a(b(x1)))
B(a(a(x1))) → B(a(b(b(a(x1)))))
A(b(x1)) → B(b(x1))
B(a(x1)) → B(b(x1))
A(b(a(x1))) → A(b(b(a(b(x1)))))
A(x1) → B(x1)
A(b(a(x1))) → B(x1)
B(b(a(x1))) → B(b(x1))
A(b(a(x1))) → A(b(b(a(x1))))
A(b(b(x1))) → B(b(b(x1)))
B(a(a(x1))) → A(b(b(a(x1))))
A(b(b(x1))) → B(b(b(b(b(x1)))))
A(b(a(x1))) → A(b(x1))
The value of delta used in the strict ordering is 8.
POL(B(x1)) = 0
POL(a(x1)) = 1 + (2)x_1
POL(A(x1)) = (4)x_1
POL(b(x1)) = 0
a(x1) → b(x1)
a(a(a(x1))) → a(a(b(a(a(x1)))))
a(b(a(x1))) → a(b(b(a(b(x1)))))
a(a(x1)) → a(b(a(x1)))
a(a(b(x1))) → a(b(b(a(b(x1)))))
a(b(x1)) → b(b(b(x1)))
a(b(a(x1))) → b(a(b(b(a(x1)))))
a(b(b(x1))) → b(b(b(b(b(x1)))))
b(b(a(x1))) → b(b(b(b(b(x1)))))
b(a(a(x1))) → b(a(b(b(a(x1)))))
b(a(x1)) → b(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
B(a(a(x1))) → B(b(a(x1)))
B(b(a(x1))) → B(b(b(b(x1))))
B(b(a(x1))) → B(b(b(x1)))
B(a(x1)) → B(x1)
B(a(a(x1))) → B(a(x1))
B(b(a(x1))) → B(x1)
A(b(a(x1))) → B(a(b(b(a(x1)))))
A(b(x1)) → B(b(b(x1)))
A(b(a(x1))) → B(b(a(b(x1))))
B(a(x1)) → B(b(b(x1)))
A(b(a(x1))) → B(b(a(x1)))
B(b(a(x1))) → B(b(b(b(b(x1)))))
A(b(b(x1))) → B(b(b(b(x1))))
A(b(a(x1))) → B(a(b(x1)))
B(a(a(x1))) → B(a(b(b(a(x1)))))
A(b(x1)) → B(b(x1))
B(a(x1)) → B(b(x1))
A(b(a(x1))) → A(b(b(a(b(x1)))))
A(x1) → B(x1)
A(b(a(x1))) → B(x1)
B(b(a(x1))) → B(b(x1))
A(b(a(x1))) → A(b(b(a(x1))))
A(b(b(x1))) → B(b(b(x1)))
B(a(a(x1))) → A(b(b(a(x1))))
A(b(b(x1))) → B(b(b(b(b(x1)))))
A(b(a(x1))) → A(b(x1))
a(x1) → b(x1)
a(a(x1)) → a(b(a(x1)))
a(b(x1)) → b(b(b(x1)))
a(a(a(x1))) → a(a(b(a(a(x1)))))
a(a(b(x1))) → a(b(b(a(b(x1)))))
a(b(a(x1))) → b(a(b(b(a(x1)))))
a(b(b(x1))) → b(b(b(b(b(x1)))))
b(a(x1)) → b(b(b(x1)))
a(b(a(x1))) → a(b(b(a(b(x1)))))
b(a(a(x1))) → b(a(b(b(a(x1)))))
b(b(a(x1))) → b(b(b(b(b(x1)))))