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

↳Argument Filtering and Ordering

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

The following rules can be oriented:

a -> g(c)

g(a) -> b

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

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

Used Argument Filtering System:

F(x,_{1}x) -> F(_{2}x,_{1}x)_{2}

g(x) -> g(_{1}x)_{1}

a -> a

f(x,_{1}x) -> f(_{2}x,_{1}x)_{2}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳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