b(c(x1)) → a(x1)
b(b(x1)) → a(c(x1))
a(x1) → c(b(x1))
c(c(c(x1))) → b(x1)
↳ QTRS
↳ DependencyPairsProof
b(c(x1)) → a(x1)
b(b(x1)) → a(c(x1))
a(x1) → c(b(x1))
c(c(c(x1))) → b(x1)
A(x1) → C(b(x1))
B(c(x1)) → A(x1)
C(c(c(x1))) → B(x1)
B(b(x1)) → C(x1)
A(x1) → B(x1)
B(b(x1)) → A(c(x1))
b(c(x1)) → a(x1)
b(b(x1)) → a(c(x1))
a(x1) → c(b(x1))
c(c(c(x1))) → b(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
A(x1) → C(b(x1))
B(c(x1)) → A(x1)
C(c(c(x1))) → B(x1)
B(b(x1)) → C(x1)
A(x1) → B(x1)
B(b(x1)) → A(c(x1))
b(c(x1)) → a(x1)
b(b(x1)) → a(c(x1))
a(x1) → c(b(x1))
c(c(c(x1))) → b(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(c(x1)) → A(x1)
B(b(x1)) → C(x1)
B(b(x1)) → A(c(x1))
Used ordering: Polynomial interpretation [25,35]:
A(x1) → C(b(x1))
C(c(c(x1))) → B(x1)
A(x1) → B(x1)
The value of delta used in the strict ordering is 1/8.
POL(C(x1)) = (1/4)x_1
POL(c(x1)) = 1/2 + x_1
POL(B(x1)) = 1/4 + (1/4)x_1
POL(a(x1)) = 3/2 + x_1
POL(A(x1)) = 1/4 + (1/4)x_1
POL(b(x1)) = 1 + x_1
a(x1) → c(b(x1))
b(c(x1)) → a(x1)
b(b(x1)) → a(c(x1))
c(c(c(x1))) → b(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
A(x1) → C(b(x1))
C(c(c(x1))) → B(x1)
A(x1) → B(x1)
b(c(x1)) → a(x1)
b(b(x1)) → a(c(x1))
a(x1) → c(b(x1))
c(c(c(x1))) → b(x1)