a -> g(c)

g(a) -> b

f(g(

R

↳Dependency Pair Analysis

A -> G(c)

F(g(X), b) -> F(a,X)

F(g(X), b) -> A

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

**F(g( X), b) -> F(a, X)**

a -> g(c)

g(a) -> b

f(g(X), b) -> f(a,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(g(X), b) -> F(a,X)

F(g(X), b) -> F(g(c),X)

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Polynomial Ordering

**F(g( X), b) -> F(g(c), X)**

a -> g(c)

g(a) -> b

f(g(X), b) -> f(a,X)

The following dependency pair can be strictly oriented:

F(g(X), b) -> F(g(c),X)

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

g(a) -> b

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Polo

...

→DP Problem 3

↳Dependency Graph

a -> g(c)

g(a) -> b

f(g(X), b) -> f(a,X)

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes