f1(b2(a, z)) -> z
b2(y, b2(a, z)) -> b2(f1(c3(y, y, a)), b2(f1(z), a))
f1(f1(f1(c3(z, x, a)))) -> b2(f1(x), z)
↳ QTRS
↳ DependencyPairsProof
f1(b2(a, z)) -> z
b2(y, b2(a, z)) -> b2(f1(c3(y, y, a)), b2(f1(z), a))
f1(f1(f1(c3(z, x, a)))) -> b2(f1(x), z)
B2(y, b2(a, z)) -> B2(f1(c3(y, y, a)), b2(f1(z), a))
B2(y, b2(a, z)) -> F1(c3(y, y, a))
F1(f1(f1(c3(z, x, a)))) -> F1(x)
B2(y, b2(a, z)) -> F1(z)
B2(y, b2(a, z)) -> B2(f1(z), a)
F1(f1(f1(c3(z, x, a)))) -> B2(f1(x), z)
f1(b2(a, z)) -> z
b2(y, b2(a, z)) -> b2(f1(c3(y, y, a)), b2(f1(z), a))
f1(f1(f1(c3(z, x, a)))) -> b2(f1(x), z)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
B2(y, b2(a, z)) -> B2(f1(c3(y, y, a)), b2(f1(z), a))
B2(y, b2(a, z)) -> F1(c3(y, y, a))
F1(f1(f1(c3(z, x, a)))) -> F1(x)
B2(y, b2(a, z)) -> F1(z)
B2(y, b2(a, z)) -> B2(f1(z), a)
F1(f1(f1(c3(z, x, a)))) -> B2(f1(x), z)
f1(b2(a, z)) -> z
b2(y, b2(a, z)) -> b2(f1(c3(y, y, a)), b2(f1(z), a))
f1(f1(f1(c3(z, x, a)))) -> b2(f1(x), z)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
B2(y, b2(a, z)) -> B2(f1(c3(y, y, a)), b2(f1(z), a))
F1(f1(f1(c3(z, x, a)))) -> F1(x)
B2(y, b2(a, z)) -> F1(z)
F1(f1(f1(c3(z, x, a)))) -> B2(f1(x), z)
f1(b2(a, z)) -> z
b2(y, b2(a, z)) -> b2(f1(c3(y, y, a)), b2(f1(z), a))
f1(f1(f1(c3(z, x, a)))) -> b2(f1(x), z)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B2(y, b2(a, z)) -> F1(z)
Used ordering: Polynomial interpretation [21]:
B2(y, b2(a, z)) -> B2(f1(c3(y, y, a)), b2(f1(z), a))
F1(f1(f1(c3(z, x, a)))) -> F1(x)
F1(f1(f1(c3(z, x, a)))) -> B2(f1(x), z)
POL(B2(x1, x2)) = x2
POL(F1(x1)) = x1
POL(a) = 0
POL(b2(x1, x2)) = 1 + x2
POL(c3(x1, x2, x3)) = x1 + x2
POL(f1(x1)) = x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
B2(y, b2(a, z)) -> B2(f1(c3(y, y, a)), b2(f1(z), a))
F1(f1(f1(c3(z, x, a)))) -> F1(x)
F1(f1(f1(c3(z, x, a)))) -> B2(f1(x), z)
f1(b2(a, z)) -> z
b2(y, b2(a, z)) -> b2(f1(c3(y, y, a)), b2(f1(z), a))
f1(f1(f1(c3(z, x, a)))) -> b2(f1(x), z)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
B2(y, b2(a, z)) -> B2(f1(c3(y, y, a)), b2(f1(z), a))
f1(b2(a, z)) -> z
b2(y, b2(a, z)) -> b2(f1(c3(y, y, a)), b2(f1(z), a))
f1(f1(f1(c3(z, x, a)))) -> b2(f1(x), z)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
F1(f1(f1(c3(z, x, a)))) -> F1(x)
f1(b2(a, z)) -> z
b2(y, b2(a, z)) -> b2(f1(c3(y, y, a)), b2(f1(z), a))
f1(f1(f1(c3(z, x, a)))) -> b2(f1(x), z)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F1(f1(f1(c3(z, x, a)))) -> F1(x)
POL(F1(x1)) = x1
POL(a) = 1
POL(c3(x1, x2, x3)) = x2 + x3
POL(f1(x1)) = x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
f1(b2(a, z)) -> z
b2(y, b2(a, z)) -> b2(f1(c3(y, y, a)), b2(f1(z), a))
f1(f1(f1(c3(z, x, a)))) -> b2(f1(x), z)