f(s(

R

↳Dependency Pair Analysis

F(s(x),y,y) -> F(y,x, s(x))

Furthermore,

R

↳DPs

→DP Problem 1

↳Instantiation Transformation

**F(s( x), y, y) -> F(y, x, s(x))**

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

On this DP problem, an Instantiation SCC transformation can be performed.

As a result of transforming the rule

one new Dependency Pair is created:

F(s(x),y,y) -> F(y,x, s(x))

F(s(x0), s(x'''), s(x''')) -> F(s(x'''),x0, s(x0))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳Forward Instantiation Transformation

**F(s( x0), s(x'''), s(x''')) -> F(s(x'''), x0, s(x0))**

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

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

As a result of transforming the rule

one new Dependency Pair is created:

F(s(x0), s(x'''), s(x''')) -> F(s(x'''),x0, s(x0))

F(s(s(x'''''')), s(x'''0), s(x'''0)) -> F(s(x'''0), s(x''''''), s(s(x'''''')))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳FwdInst

...

→DP Problem 3

↳Remaining Obligation(s)

The following remains to be proven:

**F(s(s( x'''''')), s(x'''0), s(x'''0)) -> F(s(x'''0), s(x''''''), s(s(x'''''')))**

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

Duration:

0:00 minutes