(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

f(0, 1, x) → f(h(x), h(x), x)
h(0) → 0
h(g(x, y)) → y

Q is empty.

(1) AAECC Innermost (EQUIVALENT transformation)

We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is

h(0) → 0
h(g(x, y)) → y

The TRS R 2 is

f(0, 1, x) → f(h(x), h(x), x)

The signature Sigma is {f}

(2) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

f(0, 1, x) → f(h(x), h(x), x)
h(0) → 0
h(g(x, y)) → y

The set Q consists of the following terms:

f(0, 1, x0)
h(0)
h(g(x0, x1))

(3) DependencyPairsProof (EQUIVALENT transformation)

Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.

(4) Obligation:

Q DP problem:
The TRS P consists of the following rules:

F(0, 1, x) → F(h(x), h(x), x)
F(0, 1, x) → H(x)

The TRS R consists of the following rules:

f(0, 1, x) → f(h(x), h(x), x)
h(0) → 0
h(g(x, y)) → y

The set Q consists of the following terms:

f(0, 1, x0)
h(0)
h(g(x0, x1))

We have to consider all minimal (P,Q,R)-chains.

(5) DependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.

(6) Obligation:

Q DP problem:
The TRS P consists of the following rules:

F(0, 1, x) → F(h(x), h(x), x)

The TRS R consists of the following rules:

f(0, 1, x) → f(h(x), h(x), x)
h(0) → 0
h(g(x, y)) → y

The set Q consists of the following terms:

f(0, 1, x0)
h(0)
h(g(x0, x1))

We have to consider all minimal (P,Q,R)-chains.