f(f(a,

R

↳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,

R

↳DPs

→DP Problem 1

↳Argument Filtering and 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)

innermost

The following dependency pair can be strictly oriented:

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

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

f(f(a,x), a) -> f(f(x, f(a, f(a, 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) ->_{2}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(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)

innermost

Duration:

0:00 minutes