f(f(

R

↳Dependency Pair Analysis

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

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

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

Furthermore,

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↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

The following dependency pair can be strictly oriented:

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

The following rule can be oriented:

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

Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:

a > f

resulting in one new DP problem.

Used Argument Filtering System:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

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

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

Duration:

0:00 minutes