a(a(x1)) → b(b(b(x1)))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
b(x1) → d(d(x1))
c(d(d(x1))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
a(a(x1)) → b(b(b(x1)))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
b(x1) → d(d(x1))
c(d(d(x1))) → a(x1)
C(d(d(x1))) → A(x1)
B(b(x1)) → C(c(x1))
A(a(x1)) → B(b(x1))
B(b(x1)) → C(c(c(x1)))
A(a(x1)) → B(b(b(x1)))
B(b(x1)) → C(x1)
A(a(x1)) → B(x1)
a(a(x1)) → b(b(b(x1)))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
b(x1) → d(d(x1))
c(d(d(x1))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
C(d(d(x1))) → A(x1)
B(b(x1)) → C(c(x1))
A(a(x1)) → B(b(x1))
B(b(x1)) → C(c(c(x1)))
A(a(x1)) → B(b(b(x1)))
B(b(x1)) → C(x1)
A(a(x1)) → B(x1)
a(a(x1)) → b(b(b(x1)))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
b(x1) → d(d(x1))
c(d(d(x1))) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(b(x1)) → C(c(x1))
A(a(x1)) → B(b(x1))
B(b(x1)) → C(c(c(x1)))
B(b(x1)) → C(x1)
A(a(x1)) → B(x1)
Used ordering: Polynomial interpretation [25,35]:
C(d(d(x1))) → A(x1)
A(a(x1)) → B(b(b(x1)))
The value of delta used in the strict ordering is 1/8.
POL(C(x1)) = (1/2)x_1
POL(c(x1)) = 3/2 + x_1
POL(B(x1)) = 1/2 + (1/2)x_1
POL(a(x1)) = 7/2 + x_1
POL(A(x1)) = 1 + (1/2)x_1
POL(d(x1)) = 1 + x_1
POL(b(x1)) = 9/4 + x_1
c(d(d(x1))) → a(x1)
a(a(x1)) → b(b(b(x1)))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
b(x1) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
C(d(d(x1))) → A(x1)
A(a(x1)) → B(b(b(x1)))
a(a(x1)) → b(b(b(x1)))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
b(x1) → d(d(x1))
c(d(d(x1))) → a(x1)