a(b(x1)) → b(a(a(a(x1))))
b(a(x1)) → a(a(x1))
a(a(x1)) → a(c(b(x1)))
↳ QTRS
↳ DependencyPairsProof
a(b(x1)) → b(a(a(a(x1))))
b(a(x1)) → a(a(x1))
a(a(x1)) → a(c(b(x1)))
A(b(x1)) → A(a(a(x1)))
B(a(x1)) → A(a(x1))
A(b(x1)) → B(a(a(a(x1))))
A(a(x1)) → A(c(b(x1)))
A(b(x1)) → A(a(x1))
A(a(x1)) → B(x1)
A(b(x1)) → A(x1)
a(b(x1)) → b(a(a(a(x1))))
b(a(x1)) → a(a(x1))
a(a(x1)) → a(c(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
A(b(x1)) → A(a(a(x1)))
B(a(x1)) → A(a(x1))
A(b(x1)) → B(a(a(a(x1))))
A(a(x1)) → A(c(b(x1)))
A(b(x1)) → A(a(x1))
A(a(x1)) → B(x1)
A(b(x1)) → A(x1)
a(b(x1)) → b(a(a(a(x1))))
b(a(x1)) → a(a(x1))
a(a(x1)) → a(c(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
A(b(x1)) → A(a(a(x1)))
B(a(x1)) → A(a(x1))
A(b(x1)) → B(a(a(a(x1))))
A(b(x1)) → A(a(x1))
A(a(x1)) → B(x1)
A(b(x1)) → A(x1)
a(b(x1)) → b(a(a(a(x1))))
b(a(x1)) → a(a(x1))
a(a(x1)) → a(c(b(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(b(x1)) → A(a(a(x1)))
A(b(x1)) → B(a(a(a(x1))))
A(b(x1)) → A(a(x1))
A(b(x1)) → A(x1)
Used ordering: Polynomial interpretation [25,35]:
B(a(x1)) → A(a(x1))
A(a(x1)) → B(x1)
The value of delta used in the strict ordering is 1.
POL(c(x1)) = 0
POL(B(x1)) = x_1
POL(a(x1)) = x_1
POL(A(x1)) = x_1
POL(b(x1)) = 1 + (2)x_1
a(b(x1)) → b(a(a(a(x1))))
b(a(x1)) → a(a(x1))
a(a(x1)) → a(c(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
B(a(x1)) → A(a(x1))
A(a(x1)) → B(x1)
a(b(x1)) → b(a(a(a(x1))))
b(a(x1)) → a(a(x1))
a(a(x1)) → a(c(b(x1)))