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

↳Instantiation Transformation

**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))

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳FwdInst

...

→DP Problem 4

↳Forward Instantiation Transformation

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

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳FwdInst

...

→DP Problem 5

↳Instantiation Transformation

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

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Inst

→DP Problem 2

↳FwdInst

...

→DP Problem 6

↳Remaining Obligation(s)

The following remains to be proven:

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

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

Duration:

0:00 minutes