(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
b(a, f(b(b(z, y), a))) → z
c(c(z, x, a), a, y) → f(f(c(y, a, f(c(z, y, x)))))
f(f(c(a, y, z))) → b(y, b(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:
C(c(z, x, a), a, y) → F(f(c(y, a, f(c(z, y, x)))))
C(c(z, x, a), a, y) → F(c(y, a, f(c(z, y, x))))
C(c(z, x, a), a, y) → C(y, a, f(c(z, y, x)))
C(c(z, x, a), a, y) → F(c(z, y, x))
C(c(z, x, a), a, y) → C(z, y, x)
F(f(c(a, y, z))) → B(y, b(z, z))
F(f(c(a, y, z))) → B(z, z)
The TRS R consists of the following rules:
b(a, f(b(b(z, y), a))) → z
c(c(z, x, a), a, y) → f(f(c(y, a, f(c(z, y, x)))))
f(f(c(a, y, z))) → b(y, b(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 5 less nodes.
(4) Obligation:
Q DP problem:
The TRS P consists of the following rules:
C(c(z, x, a), a, y) → C(z, y, x)
C(c(z, x, a), a, y) → C(y, a, f(c(z, y, x)))
The TRS R consists of the following rules:
b(a, f(b(b(z, y), a))) → z
c(c(z, x, a), a, y) → f(f(c(y, a, f(c(z, y, x)))))
f(f(c(a, y, z))) → b(y, b(z, z))
Q is empty.
We have to consider all minimal (P,Q,R)-chains.