app(app(apply,

R

↳Dependency Pair Analysis

APP(app(apply,f),x) -> APP(f,x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Usable Rules (Innermost)

**APP(app(apply, f), x) -> APP(f, x)**

app(app(apply,f),x) -> app(f,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

**APP(app(apply, f), x) -> APP(f, x)**

none

innermost

The following dependency pair can be strictly oriented:

APP(app(apply,f),x) -> APP(f,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:

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

app(x,_{1}x) -> app(_{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