f(

g(0, 1,

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,y,z) -> G(x,y,z)

G(0, 1,x) -> F(x,x,x)

Furthermore,

R

↳OC

→TRS2

↳DPs

→DP Problem 1

↳Usable Rules (Innermost)

**G(0, 1, x) -> F(x, x, x)**

f(x,y,z) -> g(x,y,z)

g(0, 1,x) -> f(x,x,x)

innermost

As we are in the innermost case, we can delete all 2 non-usable-rules.

R

↳OC

→TRS2

↳DPs

→DP Problem 1

↳UsableRules

...

→DP Problem 2

↳Instantiation Transformation

**G(0, 1, x) -> F(x, x, x)**

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(x,y,z) -> G(x,y,z)

F(z',z',z') -> G(z',z',z')

The transformation is resulting in no new DP problems.

Duration:

0:00 minutes