a(x1) → b(x1)
b(b(x1)) → c(x1)
c(a(c(x1))) → a(b(c(a(x1))))
↳ QTRS
↳ DependencyPairsProof
a(x1) → b(x1)
b(b(x1)) → c(x1)
c(a(c(x1))) → a(b(c(a(x1))))
B(b(x1)) → C(x1)
A(x1) → B(x1)
C(a(c(x1))) → B(c(a(x1)))
C(a(c(x1))) → A(x1)
C(a(c(x1))) → C(a(x1))
C(a(c(x1))) → A(b(c(a(x1))))
a(x1) → b(x1)
b(b(x1)) → c(x1)
c(a(c(x1))) → a(b(c(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
B(b(x1)) → C(x1)
A(x1) → B(x1)
C(a(c(x1))) → B(c(a(x1)))
C(a(c(x1))) → A(x1)
C(a(c(x1))) → C(a(x1))
C(a(c(x1))) → A(b(c(a(x1))))
a(x1) → b(x1)
b(b(x1)) → c(x1)
c(a(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(a(c(x1))) → B(c(a(x1)))
C(a(c(x1))) → A(x1)
C(a(c(x1))) → C(a(x1))
Used ordering: Polynomial interpretation [25,35]:
B(b(x1)) → C(x1)
A(x1) → B(x1)
C(a(c(x1))) → A(b(c(a(x1))))
The value of delta used in the strict ordering is 4.
POL(C(x1)) = 4 + (4)x_1
POL(c(x1)) = 2 + x_1
POL(B(x1)) = (4)x_1
POL(a(x1)) = 1 + x_1
POL(A(x1)) = (4)x_1
POL(b(x1)) = 1 + x_1
a(x1) → b(x1)
b(b(x1)) → c(x1)
c(a(c(x1))) → a(b(c(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
B(b(x1)) → C(x1)
A(x1) → B(x1)
C(a(c(x1))) → A(b(c(a(x1))))
a(x1) → b(x1)
b(b(x1)) → c(x1)
c(a(c(x1))) → a(b(c(a(x1))))