a(x1) → b(c(x1))
b(a(b(x1))) → c(x1)
c(c(x1)) → a(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
a(x1) → b(c(x1))
b(a(b(x1))) → c(x1)
c(c(x1)) → a(a(b(x1)))
C(c(x1)) → A(a(b(x1)))
A(x1) → B(c(x1))
C(c(x1)) → A(b(x1))
A(x1) → C(x1)
C(c(x1)) → B(x1)
B(a(b(x1))) → C(x1)
a(x1) → b(c(x1))
b(a(b(x1))) → c(x1)
c(c(x1)) → a(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
C(c(x1)) → A(a(b(x1)))
A(x1) → B(c(x1))
C(c(x1)) → A(b(x1))
A(x1) → C(x1)
C(c(x1)) → B(x1)
B(a(b(x1))) → C(x1)
a(x1) → b(c(x1))
b(a(b(x1))) → c(x1)
c(c(x1)) → a(a(b(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(c(x1)) → A(b(x1))
C(c(x1)) → B(x1)
Used ordering: Polynomial interpretation [25,35]:
C(c(x1)) → A(a(b(x1)))
A(x1) → B(c(x1))
A(x1) → C(x1)
B(a(b(x1))) → C(x1)
The value of delta used in the strict ordering is 1/4.
POL(C(x1)) = 1 + (1/2)x_1
POL(c(x1)) = 1/2 + x_1
POL(B(x1)) = 3/4 + (1/2)x_1
POL(a(x1)) = 1/2 + x_1
POL(A(x1)) = 1 + (1/2)x_1
POL(b(x1)) = x_1
b(a(b(x1))) → c(x1)
c(c(x1)) → a(a(b(x1)))
a(x1) → b(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
A(x1) → B(c(x1))
C(c(x1)) → A(a(b(x1)))
A(x1) → C(x1)
B(a(b(x1))) → C(x1)
a(x1) → b(c(x1))
b(a(b(x1))) → c(x1)
c(c(x1)) → a(a(b(x1)))