f(f(

g(g(

R

↳Dependency Pair Analysis

F(f(x)) -> G(f(x))

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

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

The following dependency pairs can be strictly oriented:

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

F(f(x)) -> G(f(x))

The following usable rules w.r.t. to the AFS can be oriented:

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

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

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

{F, f, g} > G

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}

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes