app(app(apply,

R

↳Dependency Pair Analysis

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

The following dependency pair can be strictly oriented:

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

The following rule can be oriented:

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(apply)= 0 _{ }^{ }_{ }^{ }POL(APP(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(app(x)_{1}, x_{2})= 1 + x _{1}+ x_{2}_{ }^{ }

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

↳AFS

→DP Problem 2

↳Dependency Graph

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes