f(f(

R

↳Dependency Pair Analysis

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

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

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

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

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

innermost

On this DP problem, a Narrowing SCC transformation can be performed.

As a result of transforming the rule

no new Dependency Pairs are created.

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

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

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

innermost

Duration:

0:00 minutes