(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
f(g(x), h(x), y, x) → f(y, y, y, x)
f(x, y, z, 0) → 2
g(0) → 2
h(0) → 2
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(g(x), h(x), y, x) → F(y, y, y, x)
The TRS R consists of the following rules:
f(g(x), h(x), y, x) → f(y, y, y, x)
f(x, y, z, 0) → 2
g(0) → 2
h(0) → 2
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 0 SCCs with 1 less node.
(4) TRUE