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

↳Argument Filtering and 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 using the Ce-refinement that need to be oriented.

Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:

trivial

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

R

↳DPs

→DP Problem 1

↳AFS

→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