(0) Obligation:

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

f(x, y) → x
g(a) → h(a, b, a)
i(x) → f(x, x)
h(x, x, y) → g(x)

Q is empty.

(1) AAECC Innermost (EQUIVALENT transformation)

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

f(x, y) → x
i(x) → f(x, x)

The TRS R 2 is

g(a) → h(a, b, a)
h(x, x, y) → g(x)

The signature Sigma is {g, h}

(2) Obligation:

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

f(x, y) → x
g(a) → h(a, b, a)
i(x) → f(x, x)
h(x, x, y) → g(x)

The set Q consists of the following terms:

f(x0, x1)
g(a)
i(x0)
h(x0, 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:

G(a) → H(a, b, a)
I(x) → F(x, x)
H(x, x, y) → G(x)

The TRS R consists of the following rules:

f(x, y) → x
g(a) → h(a, b, a)
i(x) → f(x, x)
h(x, x, y) → g(x)

The set Q consists of the following terms:

f(x0, x1)
g(a)
i(x0)
h(x0, 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 0 SCCs with 3 less nodes.

(6) TRUE