h(f(

g(

R

↳Dependency Pair Analysis

H(f(x),y) -> G(x,y)

G(x,y) -> H(x,y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**G( x, y) -> H(x, y)**

h(f(x),y) -> f(g(x,y))

g(x,y) -> h(x,y)

The following dependency pair can be strictly oriented:

H(f(x),y) -> G(x,y)

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:

{H, G}

resulting in one new DP problem.

Used Argument Filtering System:

G(x,_{1}x) -> G(_{2}x,_{1}x)_{2}

H(x,_{1}x) -> H(_{2}x,_{1}x)_{2}

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

**G( x, y) -> H(x, y)**

h(f(x),y) -> f(g(x,y))

g(x,y) -> h(x,y)

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes