f(

f(g(

R

↳Dependency Pair Analysis

F(g(x),y) -> F(x,y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

f(x,x) -> a

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

The following dependency pair can be strictly oriented:

F(g(x),y) -> F(x,y)

The following rules can be oriented:

f(x,x) -> a

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(a)= 0 _{ }^{ }_{ }^{ }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}

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

f(x,x) -> a

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes