f(

g(h(

g(h(

R

↳Dependency Pair Analysis

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

G(h(x),y) -> F(x,y)

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

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

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

The following dependency pairs can be strictly oriented:

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

G(h(x),y) -> F(x,y)

The following rules can be oriented:

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

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

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

Used ordering: Homeomorphic Embedding Order with EMB

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

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

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

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes