(0) Obligation:

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

f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)
ab
ac

Q is empty.

(1) AAECC Innermost (EQUIVALENT transformation)

We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none

The TRS R 2 is

f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)
ab
ac

The signature Sigma is {c, a, f, g, b}

(2) Obligation:

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

f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)
ab
ac

The set Q consists of the following terms:

f(x0, x1, x2)
g(0, 1, x0)
a

(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(x, y, z) → G(x, y, z)
G(0, 1, x) → F(x, x, x)

The TRS R consists of the following rules:

f(x, y, z) → g(x, y, z)
g(0, 1, x) → f(x, x, x)
ab
ac

The set Q consists of the following terms:

f(x0, x1, x2)
g(0, 1, x0)
a

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