f(g(

R

↳Dependency Pair Analysis

F(g(x)) -> F(a(g(g(f(x))), g(f(x))))

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

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

f(g(x)) -> f(a(g(g(f(x))), g(f(x))))

The following dependency pair can be strictly oriented:

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

Additionally, the following rule can be oriented:

f(g(x)) -> f(a(g(g(f(x))), g(f(x))))

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(a(x)_{1}, x_{2})= 0 _{ }^{ }_{ }^{ }POL(f(x)_{1})= 0 _{ }^{ }_{ }^{ }POL(F(x)_{1})= x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Dependency Graph

f(g(x)) -> f(a(g(g(f(x))), g(f(x))))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes