Termination w.r.t. Q of the following Term Rewriting System could not be shown:
Q restricted rewrite system:
The TRS R consists of the following rules:
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)
Q is empty.
↳ QTRS
↳ DependencyPairsProof
Q restricted rewrite system:
The TRS R consists of the following rules:
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)
Q is empty.
Using Dependency Pairs [1,13] we result in the following initial DP problem:
Q DP problem:
The TRS P consists of the following rules:
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)
The TRS R consists of the following rules:
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)
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
Q DP problem:
The TRS P consists of the following rules:
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)
The TRS R consists of the following rules:
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)
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [13,14,18] contains 1 SCC with 2 less nodes.
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
Q DP problem:
The TRS P consists of the following rules:
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)
The TRS R consists of the following rules:
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)
Q is empty.
We have to consider all minimal (P,Q,R)-chains.