f(g(

f(h(

R

↳Dependency Pair Analysis

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

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

The following dependency pairs can be strictly oriented:

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

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

The following rules can be oriented:

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

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

Used ordering: Homeomorphic Embedding Order with EMB

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

h(x) -> h_{1}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes