f(f(

g(g(

R

↳Dependency Pair Analysis

F(f(x)) -> G(f(x))

G(g(x)) -> F(x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

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

f(f(x)) -> g(f(x))

g(g(x)) -> f(x)

The following dependency pair can be strictly oriented:

G(g(x)) -> F(x)

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

g(g(x)) -> f(x)

f(f(x)) -> g(f(x))

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(G(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(f(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(F(x)_{1})= x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Dependency Graph

**F(f( x)) -> G(f(x))**

f(f(x)) -> g(f(x))

g(g(x)) -> f(x)

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes