g(h(g(

g(g(

h(h(

R

↳Dependency Pair Analysis

G(g(x)) -> G(h(g(x)))

G(g(x)) -> H(g(x))

H(h(x)) -> H(f(h(x),x))

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

**G(g( x)) -> G(h(g(x)))**

g(h(g(x))) -> g(x)

g(g(x)) -> g(h(g(x)))

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

The following dependency pair can be strictly oriented:

G(g(x)) -> G(h(g(x)))

Additionally, the following usable rule w.r.t. to the implicit AFS can be oriented:

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1})= 1 _{ }^{ }_{ }^{ }POL(G(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(h(x)_{1})= 0 _{ }^{ }_{ }^{ }POL(f(x)_{1}, x_{2})= 0 _{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Dependency Graph

g(h(g(x))) -> g(x)

g(g(x)) -> g(h(g(x)))

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes