f(g(

R

↳Dependency Pair Analysis

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

innermost

The following dependency pair can be strictly oriented:

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

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes