f(g(

f(h(

R

↳Dependency Pair Analysis

F(g(X)) -> F(f(X))

F(g(X)) -> F(X)

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

**F(g( X)) -> F(X)**

f(g(X)) -> g(f(f(X)))

f(h(X)) -> h(g(X))

The following dependency pairs can be strictly oriented:

F(g(X)) -> F(X)

F(g(X)) -> F(f(X))

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

f(g(X)) -> g(f(f(X)))

f(h(X)) -> h(g(X))

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(h(x)_{1})= 0 _{ }^{ }_{ }^{ }POL(f(x)_{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

f(g(X)) -> g(f(f(X)))

f(h(X)) -> h(g(X))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes