a(x1) → b(c(x1))
a(b(x1)) → c(a(x1))
c(c(c(x1))) → a(b(x1))
↳ QTRS
↳ DependencyPairsProof
a(x1) → b(c(x1))
a(b(x1)) → c(a(x1))
c(c(c(x1))) → a(b(x1))
C(c(c(x1))) → A(b(x1))
A(x1) → C(x1)
A(b(x1)) → C(a(x1))
A(b(x1)) → A(x1)
a(x1) → b(c(x1))
a(b(x1)) → c(a(x1))
c(c(c(x1))) → a(b(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
C(c(c(x1))) → A(b(x1))
A(x1) → C(x1)
A(b(x1)) → C(a(x1))
A(b(x1)) → A(x1)
a(x1) → b(c(x1))
a(b(x1)) → c(a(x1))
c(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(x1) → C(x1)
A(b(x1)) → A(x1)
Used ordering: Polynomial interpretation [25,35]:
C(c(c(x1))) → A(b(x1))
A(b(x1)) → C(a(x1))
The value of delta used in the strict ordering is 2.
POL(C(x1)) = (2)x_1
POL(c(x1)) = 1 + x_1
POL(a(x1)) = 2 + x_1
POL(A(x1)) = 2 + (2)x_1
POL(b(x1)) = 1 + x_1
a(x1) → b(c(x1))
c(c(c(x1))) → a(b(x1))
a(b(x1)) → c(a(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
C(c(c(x1))) → A(b(x1))
A(b(x1)) → C(a(x1))
a(x1) → b(c(x1))
a(b(x1)) → c(a(x1))
c(c(c(x1))) → a(b(x1))