f(

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↳Dependency Pair Analysis

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

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

Furthermore,

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↳DPs

→DP Problem 1

↳Polynomial Ordering

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

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

The following dependency pair can be strictly oriented:

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

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

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

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.

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↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

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

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

Duration:

0:00 minutes