f(f(

g(0) -> g(f(0))

R

↳Dependency Pair Analysis

G(0) -> G(f(0))

G(0) -> F(0)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**G(0) -> G(f(0))**

f(f(x)) -> f(x)

g(0) -> g(f(0))

innermost

The following dependency pair can be strictly oriented:

G(0) -> G(f(0))

The following usable rule for innermost w.r.t. to the AFS can be oriented:

f(f(x)) -> f(x)

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(0)= 1 _{ }^{ }_{ }^{ }POL(G(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(f)= 0 _{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

G(x) -> G(_{1}x)_{1}

f(x) -> f_{1}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

f(f(x)) -> f(x)

g(0) -> g(f(0))

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes