a(x1) → b(x1)
a(b(x1)) → b(c(a(x1)))
b(x1) → c(x1)
c(b(x1)) → a(x1)
↳ QTRS
↳ DependencyPairsProof
a(x1) → b(x1)
a(b(x1)) → b(c(a(x1)))
b(x1) → c(x1)
c(b(x1)) → a(x1)
C(b(x1)) → A(x1)
A(b(x1)) → B(c(a(x1)))
A(x1) → B(x1)
A(b(x1)) → C(a(x1))
B(x1) → C(x1)
A(b(x1)) → A(x1)
a(x1) → b(x1)
a(b(x1)) → b(c(a(x1)))
b(x1) → c(x1)
c(b(x1)) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
C(b(x1)) → A(x1)
A(b(x1)) → B(c(a(x1)))
A(x1) → B(x1)
A(b(x1)) → C(a(x1))
B(x1) → C(x1)
A(b(x1)) → A(x1)
a(x1) → b(x1)
a(b(x1)) → b(c(a(x1)))
b(x1) → c(x1)
c(b(x1)) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(b(x1)) → A(x1)
A(b(x1)) → A(x1)
Used ordering: Polynomial interpretation [25,35]:
A(b(x1)) → B(c(a(x1)))
A(x1) → B(x1)
A(b(x1)) → C(a(x1))
B(x1) → C(x1)
The value of delta used in the strict ordering is 16.
POL(C(x1)) = (4)x_1
POL(c(x1)) = x_1
POL(B(x1)) = (4)x_1
POL(a(x1)) = 4 + x_1
POL(A(x1)) = (4)x_1
POL(b(x1)) = 4 + x_1
a(x1) → b(x1)
b(x1) → c(x1)
c(b(x1)) → a(x1)
a(b(x1)) → b(c(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
A(b(x1)) → B(c(a(x1)))
A(x1) → B(x1)
A(b(x1)) → C(a(x1))
B(x1) → C(x1)
a(x1) → b(x1)
a(b(x1)) → b(c(a(x1)))
b(x1) → c(x1)
c(b(x1)) → a(x1)