(0) Obligation:

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

f(x, x) → f(a, b)
bc

Q is empty.

(1) AAECC Innermost (EQUIVALENT transformation)

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

bc

The TRS R 2 is

f(x, x) → f(a, b)

The signature Sigma is {f}

(2) Obligation:

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

f(x, x) → f(a, b)
bc

The set Q consists of the following terms:

f(x0, x0)
b

(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, x) → F(a, b)
F(x, x) → B

The TRS R consists of the following rules:

f(x, x) → f(a, b)
bc

The set Q consists of the following terms:

f(x0, x0)
b

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(x, x) → F(a, b)

The TRS R consists of the following rules:

f(x, x) → f(a, b)
bc

The set Q consists of the following terms:

f(x0, x0)
b

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