f(

b -> c

R

↳Overlay and local confluence Check

The TRS is overlay and locally confluent (all critical pairs are trivially joinable).Hence, we can switch to innermost.

R

↳OC

→TRS2

↳Dependency Pair Analysis

F(x,x) -> F(a, b)

F(x,x) -> B

Furthermore,

R

↳OC

→TRS2

↳DPs

→DP Problem 1

↳Usable Rules (Innermost)

**F( x, x) -> F(a, b)**

f(x,x) -> f(a, b)

b -> c

innermost

As we are in the innermost case, we can delete all 1 non-usable-rules.

R

↳OC

→TRS2

↳DPs

→DP Problem 1

↳UsableRules

...

→DP Problem 2

↳Rewriting Transformation

**F( x, x) -> F(a, b)**

b -> c

innermost

On this DP problem, a Rewriting SCC transformation can be performed.

As a result of transforming the rule

one new Dependency Pair is created:

F(x,x) -> F(a, b)

F(x,x) -> F(a, c)

The transformation is resulting in no new DP problems.

Duration:

0:00 minutes