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

↳Narrowing Transformation

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

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

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

On this DP problem, a Narrowing SCC transformation can be performed.

As a result of transforming the rule

one new Dependency Pair is created:

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Polynomial Ordering

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

↳Nar

→DP Problem 2

↳Polo

...

→DP Problem 3

↳Dependency Graph

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