f(

f(

R

↳Dependency Pair Analysis

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

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

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

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

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Remaining Obligation(s)

The following remains to be proven:

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

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

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

innermost

Duration:

0:00 minutes