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))

innermost

The following dependency pairs can be strictly oriented:

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

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

There are no usable rules for innermost w.r.t. to the AFS that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(G(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(h(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(F(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes