f(f(

f(g(f(

R

↳Dependency Pair Analysis

F(f(X)) -> F(g(f(g(f(X)))))

F(f(X)) -> F(g(f(X)))

F(g(f(X))) -> F(g(X))

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

**F(g(f( X))) -> F(g(X))**

f(f(X)) -> f(g(f(g(f(X)))))

f(g(f(X))) -> f(g(X))

The following dependency pair can be strictly oriented:

F(g(f(X))) -> F(g(X))

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

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Dependency Graph

f(f(X)) -> f(g(f(g(f(X)))))

f(g(f(X))) -> f(g(X))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes