f(a, f(f(a,

R

↳Dependency Pair Analysis

F(a, f(f(a,x), a)) -> F(f(a, f(a,x)), a)

F(a, f(f(a,x), a)) -> F(a, f(a,x))

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

**F(a, f(f(a, x), a)) -> F(a, f(a, x))**

f(a, f(f(a,x), a)) -> f(f(a, f(a,x)), a)

The following dependency pair can be strictly oriented:

F(a, f(f(a,x), a)) -> F(a, f(a,x))

The following usable rule w.r.t. to the AFS can be oriented:

f(a, f(f(a,x), a)) -> f(f(a, f(a,x)), a)

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(a)= 0 _{ }^{ }_{ }^{ }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}

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

f(a, f(f(a,x), a)) -> f(f(a, f(a,x)), a)

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes