f(f(

g(0) -> g(f(0))

R

↳Dependency Pair Analysis

G(0) -> G(f(0))

G(0) -> F(0)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**G(0) -> G(f(0))**

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

g(0) -> g(f(0))

The following dependency pair can be strictly oriented:

G(0) -> G(f(0))

The following rules can be oriented:

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

g(0) -> g(f(0))

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

0 > f

resulting in one new DP problem.

Used Argument Filtering System:

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

f(x) -> f_{1}

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

g(0) -> g(f(0))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes