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