a(x1) → b(x1)
a(b(b(x1))) → c(x1)
c(c(x1)) → a(b(c(a(x1))))
↳ QTRS
↳ DependencyPairsProof
a(x1) → b(x1)
a(b(b(x1))) → c(x1)
c(c(x1)) → a(b(c(a(x1))))
C(c(x1)) → A(b(c(a(x1))))
C(c(x1)) → A(x1)
C(c(x1)) → C(a(x1))
A(b(b(x1))) → C(x1)
a(x1) → b(x1)
a(b(b(x1))) → c(x1)
c(c(x1)) → a(b(c(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
C(c(x1)) → A(b(c(a(x1))))
C(c(x1)) → A(x1)
C(c(x1)) → C(a(x1))
A(b(b(x1))) → C(x1)
a(x1) → b(x1)
a(b(b(x1))) → c(x1)
c(c(x1)) → a(b(c(a(x1))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(c(x1)) → A(x1)
C(c(x1)) → C(a(x1))
Used ordering: Polynomial interpretation [25,35]:
C(c(x1)) → A(b(c(a(x1))))
A(b(b(x1))) → C(x1)
The value of delta used in the strict ordering is 1/4.
POL(C(x1)) = 7/4 + (1/4)x_1
POL(c(x1)) = 3/2 + x_1
POL(a(x1)) = 1/2 + x_1
POL(A(x1)) = 3/2 + (1/4)x_1
POL(b(x1)) = 1/2 + x_1
a(x1) → b(x1)
a(b(b(x1))) → c(x1)
c(c(x1)) → a(b(c(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
C(c(x1)) → A(b(c(a(x1))))
A(b(b(x1))) → C(x1)
a(x1) → b(x1)
a(b(b(x1))) → c(x1)
c(c(x1)) → a(b(c(a(x1))))