f(g(

f(g(

R

↳Dependency Pair Analysis

F(g(x)) -> F(x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**F(g( x)) -> F(x)**

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

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

innermost

The following dependency pair can be strictly oriented:

F(g(x)) -> F(x)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(F(x)_{1})= x _{1}_{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes