f(s(

f(0) -> 0

p(s(

R

↳Dependency Pair Analysis

F(s(x)) -> F(f(p(s(x))))

F(s(x)) -> F(p(s(x)))

F(s(x)) -> P(s(x))

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

**F(s( x)) -> F(p(s(x)))**

f(s(x)) -> s(f(f(p(s(x)))))

f(0) -> 0

p(s(x)) ->x

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

As a result of transforming the rule

one new Dependency Pair is created:

F(s(x)) -> F(f(p(s(x))))

F(s(x'')) -> F(f(x''))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Narrowing Transformation

**F(s( x'')) -> F(f(x''))**

f(s(x)) -> s(f(f(p(s(x)))))

f(0) -> 0

p(s(x)) ->x

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

As a result of transforming the rule

one new Dependency Pair is created:

F(s(x)) -> F(p(s(x)))

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

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Nar

...

→DP Problem 3

↳Narrowing Transformation

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

f(s(x)) -> s(f(f(p(s(x)))))

f(0) -> 0

p(s(x)) ->x

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

As a result of transforming the rule

two new Dependency Pairs are created:

F(s(x'')) -> F(f(x''))

F(s(s(x'))) -> F(s(f(f(p(s(x'))))))

F(s(0)) -> F(0)

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Nar

...

→DP Problem 4

↳Remaining Obligation(s)

The following remains to be proven:

**F(s(s( x'))) -> F(s(f(f(p(s(x'))))))**

f(s(x)) -> s(f(f(p(s(x)))))

f(0) -> 0

p(s(x)) ->x

Duration:

0:00 minutes