f(f(a,

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↳Dependency Pair Analysis

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

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

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

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

Furthermore,

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↳DPs

→DP Problem 1

↳Polynomial Ordering

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

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

The following dependency pair can be strictly oriented:

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

Additionally, the following usable rule w.r.t. to the implicit AFS can be oriented:

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

Used ordering: Polynomial ordering with Polynomial interpretation:

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

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

Duration:

0:00 minutes