b(a, b(c(z, x, y), a)) → b(b(z, c(y, z, a)), x)
f(c(a, b(b(z, a), y), x)) → f(c(x, b(z, x), y))
c(f(c(a, y, a)), x, z) → f(b(b(z, z), f(b(y, b(x, a)))))
↳ QTRS
↳ DependencyPairsProof
b(a, b(c(z, x, y), a)) → b(b(z, c(y, z, a)), x)
f(c(a, b(b(z, a), y), x)) → f(c(x, b(z, x), y))
c(f(c(a, y, a)), x, z) → f(b(b(z, z), f(b(y, b(x, a)))))
C(f(c(a, y, a)), x, z) → B(b(z, z), f(b(y, b(x, a))))
B(a, b(c(z, x, y), a)) → C(y, z, a)
F(c(a, b(b(z, a), y), x)) → B(z, x)
F(c(a, b(b(z, a), y), x)) → F(c(x, b(z, x), y))
B(a, b(c(z, x, y), a)) → B(z, c(y, z, a))
C(f(c(a, y, a)), x, z) → B(z, z)
B(a, b(c(z, x, y), a)) → B(b(z, c(y, z, a)), x)
C(f(c(a, y, a)), x, z) → B(y, b(x, a))
C(f(c(a, y, a)), x, z) → B(x, a)
C(f(c(a, y, a)), x, z) → F(b(b(z, z), f(b(y, b(x, a)))))
F(c(a, b(b(z, a), y), x)) → C(x, b(z, x), y)
C(f(c(a, y, a)), x, z) → F(b(y, b(x, a)))
b(a, b(c(z, x, y), a)) → b(b(z, c(y, z, a)), x)
f(c(a, b(b(z, a), y), x)) → f(c(x, b(z, x), y))
c(f(c(a, y, a)), x, z) → f(b(b(z, z), f(b(y, b(x, a)))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
C(f(c(a, y, a)), x, z) → B(b(z, z), f(b(y, b(x, a))))
B(a, b(c(z, x, y), a)) → C(y, z, a)
F(c(a, b(b(z, a), y), x)) → B(z, x)
F(c(a, b(b(z, a), y), x)) → F(c(x, b(z, x), y))
B(a, b(c(z, x, y), a)) → B(z, c(y, z, a))
C(f(c(a, y, a)), x, z) → B(z, z)
B(a, b(c(z, x, y), a)) → B(b(z, c(y, z, a)), x)
C(f(c(a, y, a)), x, z) → B(y, b(x, a))
C(f(c(a, y, a)), x, z) → B(x, a)
C(f(c(a, y, a)), x, z) → F(b(b(z, z), f(b(y, b(x, a)))))
F(c(a, b(b(z, a), y), x)) → C(x, b(z, x), y)
C(f(c(a, y, a)), x, z) → F(b(y, b(x, a)))
b(a, b(c(z, x, y), a)) → b(b(z, c(y, z, a)), x)
f(c(a, b(b(z, a), y), x)) → f(c(x, b(z, x), y))
c(f(c(a, y, a)), x, z) → f(b(b(z, z), f(b(y, b(x, a)))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
B(a, b(c(z, x, y), a)) → C(y, z, a)
C(f(c(a, y, a)), x, z) → B(y, b(x, a))
b(a, b(c(z, x, y), a)) → b(b(z, c(y, z, a)), x)
f(c(a, b(b(z, a), y), x)) → f(c(x, b(z, x), y))
c(f(c(a, y, a)), x, z) → f(b(b(z, z), f(b(y, b(x, a)))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(a, b(c(z, x, y), a)) → C(y, z, a)
Used ordering: Polynomial interpretation [25,35]:
C(f(c(a, y, a)), x, z) → B(y, b(x, a))
The value of delta used in the strict ordering is 1.
POL(a) = 0
POL(C(x1, x2, x3)) = x_2
POL(f(x1)) = 0
POL(b(x1, x2)) = (2)x_1
POL(c(x1, x2, x3)) = 1 + (2)x_1 + (4)x_3
POL(B(x1, x2)) = (1/2)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
C(f(c(a, y, a)), x, z) → B(y, b(x, a))
b(a, b(c(z, x, y), a)) → b(b(z, c(y, z, a)), x)
f(c(a, b(b(z, a), y), x)) → f(c(x, b(z, x), y))
c(f(c(a, y, a)), x, z) → f(b(b(z, z), f(b(y, b(x, a)))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
F(c(a, b(b(z, a), y), x)) → F(c(x, b(z, x), y))
b(a, b(c(z, x, y), a)) → b(b(z, c(y, z, a)), x)
f(c(a, b(b(z, a), y), x)) → f(c(x, b(z, x), y))
c(f(c(a, y, a)), x, z) → f(b(b(z, z), f(b(y, b(x, a)))))