app(app(apply,

R

↳Dependency Pair Analysis

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

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

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

innermost

The following dependency pair can be strictly oriented:

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

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

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Dependency Graph

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes