f(a, f(

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↳Dependency Pair Analysis

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

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

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

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

Furthermore,

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↳DPs

→DP Problem 1

↳Polynomial Ordering

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

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

The following dependency pair can be strictly oriented:

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

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

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

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

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↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

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

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

Duration:

0:00 minutes