f(f(a, f(a, a)),

R

↳Dependency Pair Analysis

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

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

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

The following dependency pair can be strictly oriented:

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

Additionally, the following usable rule using the Ce-refinement can be oriented:

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

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

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

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

Duration:

0:00 minutes