a(a(x1)) → b(c(x1))
a(b(x1)) → c(a(x1))
c(c(x1)) → a(b(x1))
↳ QTRS
↳ DependencyPairsProof
a(a(x1)) → b(c(x1))
a(b(x1)) → c(a(x1))
c(c(x1)) → a(b(x1))
A(a(x1)) → C(x1)
C(c(x1)) → A(b(x1))
A(b(x1)) → C(a(x1))
A(b(x1)) → A(x1)
a(a(x1)) → b(c(x1))
a(b(x1)) → c(a(x1))
c(c(x1)) → a(b(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
A(a(x1)) → C(x1)
C(c(x1)) → A(b(x1))
A(b(x1)) → C(a(x1))
A(b(x1)) → A(x1)
a(a(x1)) → b(c(x1))
a(b(x1)) → c(a(x1))
c(c(x1)) → a(b(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(x1)) → C(x1)
A(b(x1)) → A(x1)
Used ordering: Polynomial interpretation [25,35]:
C(c(x1)) → A(b(x1))
A(b(x1)) → C(a(x1))
The value of delta used in the strict ordering is 1/8.
POL(C(x1)) = (1/2)x_1
POL(c(x1)) = 1/4 + x_1
POL(a(x1)) = 1/4 + x_1
POL(A(x1)) = (1/2)x_1
POL(b(x1)) = 1/4 + x_1
a(a(x1)) → b(c(x1))
c(c(x1)) → a(b(x1))
a(b(x1)) → c(a(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
C(c(x1)) → A(b(x1))
A(b(x1)) → C(a(x1))
a(a(x1)) → b(c(x1))
a(b(x1)) → c(a(x1))
c(c(x1)) → a(b(x1))