(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(c(a, z, x)) → b(a, z)
b(x, b(z, y)) → f(b(f(f(z)), c(x, z, y)))
b(y, z) → z
Q is empty.
(1) DependencyPairsProof (EQUIVALENT transformation)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
(2) Obligation:
Q DP problem:
The TRS P consists of the following rules:
F(c(a, z, x)) → B(a, z)
B(x, b(z, y)) → F(b(f(f(z)), c(x, z, y)))
B(x, b(z, y)) → B(f(f(z)), c(x, z, y))
B(x, b(z, y)) → F(f(z))
B(x, b(z, y)) → F(z)
The TRS R consists of the following rules:
f(c(a, z, x)) → b(a, z)
b(x, b(z, y)) → f(b(f(f(z)), c(x, z, y)))
b(y, z) → z
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
(3) DependencyGraphProof (EQUIVALENT transformation)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
B(x, b(z, y)) → F(b(f(f(z)), c(x, z, y)))
F(c(a, z, x)) → B(a, z)
B(x, b(z, y)) → F(f(z))
B(x, b(z, y)) → F(z)
The TRS R consists of the following rules:
f(c(a, z, x)) → b(a, z)
b(x, b(z, y)) → f(b(f(f(z)), c(x, z, y)))
b(y, z) → z
Q is empty.
We have to consider all minimal (P,Q,R)-chains.