f(a, f(

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↳Dependency Pair Analysis

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

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

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

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

Furthermore,

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↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

The following dependency pair can be strictly oriented:

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

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

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(a)= 1 _{ }^{ }_{ }^{ }POL(f)= 0 _{ }^{ }

resulting in one new DP problem.

Used Argument Filtering System:

F(x,_{1}x) ->_{2}x_{1}

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

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↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

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

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

Duration:

0:00 minutes