g(f(

h(

R

↳Dependency Pair Analysis

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

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

innermost

The following dependency pair can be strictly oriented:

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

There are no usable rules for innermost 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:

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

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

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

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes