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