a(f, a(g, a(f,

a(g, a(f, a(g,

R

↳Dependency Pair Analysis

A(f, a(g, a(f,x))) -> A(f, a(g, a(g, a(f,x))))

A(f, a(g, a(f,x))) -> A(g, a(g, a(f,x)))

A(g, a(f, a(g,x))) -> A(g, a(f, a(f, a(g,x))))

A(g, a(f, a(g,x))) -> A(f, a(f, a(g,x)))

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

**A(g, a(f, a(g, x))) -> A(f, a(f, a(g, x)))**

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

a(g, a(f, a(g,x))) -> a(g, a(f, a(f, a(g,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:

A(f, a(g, a(f,x))) -> A(f, a(g, a(g, a(f,x))))

A(f, a(g, a(f, a(g,x'')))) -> A(f, a(g, a(g, a(f, a(f, a(g,x''))))))

A(f, a(g, a(f, a(g, a(f,x''))))) -> A(f, a(g, a(g, a(f, a(g, a(g, a(f,x'')))))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Narrowing Transformation

**A(f, a(g, a(f, a(g, a(f, x''))))) -> A(f, a(g, a(g, a(f, a(g, a(g, a(f, x'')))))))**

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

a(g, a(f, a(g,x))) -> a(g, a(f, a(f, a(g,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:

A(f, a(g, a(f,x))) -> A(g, a(g, a(f,x)))

A(f, a(g, a(f, a(g,x'')))) -> A(g, a(g, a(f, a(f, a(g,x'')))))

A(f, a(g, a(f, a(g, a(f,x''))))) -> A(g, a(g, a(f, a(g, a(g, a(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

**A(f, a(g, a(f, a(g, a(f, x''))))) -> A(g, a(g, a(f, a(g, a(g, a(f, x''))))))**

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

a(g, a(f, a(g,x))) -> a(g, a(f, a(f, a(g,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:

A(g, a(f, a(g,x))) -> A(g, a(f, a(f, a(g,x))))

A(g, a(f, a(g, a(f,x'')))) -> A(g, a(f, a(f, a(g, a(g, a(f,x''))))))

A(g, a(f, a(g, a(f, a(g,x''))))) -> A(g, a(f, a(f, a(g, a(f, a(f, a(g,x'')))))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Nar

...

→DP Problem 4

↳Narrowing Transformation

**A(g, a(f, a(g, a(f, a(g, x''))))) -> A(g, a(f, a(f, a(g, a(f, a(f, a(g, x'')))))))**

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

a(g, a(f, a(g,x))) -> a(g, a(f, a(f, a(g,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:

A(g, a(f, a(g,x))) -> A(f, a(f, a(g,x)))

A(g, a(f, a(g, a(f,x'')))) -> A(f, a(f, a(g, a(g, a(f,x'')))))

A(g, a(f, a(g, a(f, a(g,x''))))) -> A(f, a(f, a(g, a(f, a(f, a(g,x''))))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Nar

...

→DP Problem 5

↳Remaining Obligation(s)

The following remains to be proven:

**A(f, a(g, a(f, a(g, a(f, x''))))) -> A(g, a(g, a(f, a(g, a(g, a(f, x''))))))**

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

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

Duration:

0:00 minutes