a(a(x)) → b(b(x))
b(b(a(x))) → a(b(b(x)))
↳ QTRS
↳ DependencyPairsProof
a(a(x)) → b(b(x))
b(b(a(x))) → a(b(b(x)))
B(b(a(x))) → B(b(x))
B(b(a(x))) → B(x)
B(b(a(x))) → A(b(b(x)))
A(a(x)) → B(b(x))
A(a(x)) → B(x)
a(a(x)) → b(b(x))
b(b(a(x))) → a(b(b(x)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
B(b(a(x))) → B(b(x))
B(b(a(x))) → B(x)
B(b(a(x))) → A(b(b(x)))
A(a(x)) → B(b(x))
A(a(x)) → B(x)
a(a(x)) → b(b(x))
b(b(a(x))) → a(b(b(x)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(b(a(x))) → B(b(x))
B(b(a(x))) → B(x)
A(a(x)) → B(x)
Used ordering: Polynomial interpretation [25,35]:
B(b(a(x))) → A(b(b(x)))
A(a(x)) → B(b(x))
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(b(x1)) = 4 + (4)x_1
a(a(x)) → b(b(x))
b(b(a(x))) → a(b(b(x)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
B(b(a(x))) → A(b(b(x)))
A(a(x)) → B(b(x))
a(a(x)) → b(b(x))
b(b(a(x))) → a(b(b(x)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(b(a(x))) → A(b(b(x)))
A(a(x)) → B(b(x))
The value of delta used in the strict ordering is 11.
POL(B(x1)) = 1 + (4)x_1
POL(a(x1)) = 3 + (4)x_1
POL(A(x1)) = 3 + (3)x_1
POL(b(x1)) = (3)x_1
a(a(x)) → b(b(x))
b(b(a(x))) → a(b(b(x)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a(a(x)) → b(b(x))
b(b(a(x))) → a(b(b(x)))