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

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↳Dependency Pair Analysis

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

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

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

Furthermore,

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↳DPs

→DP Problem 1

↳Polynomial Ordering

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

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

The following dependency pair can be strictly oriented:

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

Additionally, the following rule can be oriented:

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

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

Duration:

0:00 minutes