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