f(a, f(

R

↳Dependency Pair Analysis

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

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Usable Rules (Innermost)

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

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

innermost

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

R

↳DPs

→DP Problem 1

↳UsableRules

→DP Problem 2

↳Argument Filtering and Ordering

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

none

innermost

The following dependency pair can be strictly oriented:

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

There are no usable rules w.r.t. the AFS that need to be oriented.

Used ordering: Lexicographic Path Order with Precedence:

trivial

resulting in one new DP problem.

Used Argument Filtering System:

F(x,_{1}x) -> F(_{2}x,_{1}x)_{2}

f(x,_{1}x) -> f(_{2}x,_{1}x)_{2}

R

↳DPs

→DP Problem 1

↳UsableRules

→DP Problem 2

↳AFS

...

→DP Problem 3

↳Dependency Graph

none

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes