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

↳Polynomial Ordering

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

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

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

The following dependency pair can be strictly oriented:

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

There are no usable rules using the Ce-refinement that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(G(x)_{1}, x_{2})= x _{1}_{ }^{ }_{ }^{ }POL(H(x)_{1}, x_{2})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(f(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Dependency Graph

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

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

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes