f(f(a,

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

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

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

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

Furthermore,

R

↳OC

→TRS2

↳DPs

→DP Problem 1

↳Usable Rules (Innermost)

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

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

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

↳Instantiation Transformation

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

none

innermost

On this DP problem, an Instantiation SCC transformation can be performed.

As a result of transforming the rule

one new Dependency Pair is created:

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

F(f(a, f(a, a)), a) -> F(f(f(a, a), f(a, a)), a)

The transformation is resulting in no new DP problems.

Duration:

0:00 minutes