*(

*(

*(

*(

R

↳Dependency Pair Analysis

*'(X, +(Y, 1)) -> *'(X, +(Y, *(1, 0)))

*'(X, +(Y, 1)) -> *'(1, 0)

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

***'( X, +(Y, 1)) -> *'(X, +(Y, *(1, 0)))**

*(X, +(Y, 1)) -> +(*(X, +(Y, *(1, 0))),X)

*(X, 1) ->X

*(X, 0) ->X

*(X, 0) -> 0

innermost

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

As a result of transforming the rule

two new Dependency Pairs are created:

*'(X, +(Y, 1)) -> *'(X, +(Y, *(1, 0)))

*'(X, +(Y, 1)) -> *'(X, +(Y, 1))

*'(X, +(Y, 1)) -> *'(X, +(Y, 0))

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:

***'( X, +(Y, 1)) -> *'(X, +(Y, 1))**

*(X, +(Y, 1)) -> +(*(X, +(Y, *(1, 0))),X)

*(X, 1) ->X

*(X, 0) ->X

*(X, 0) -> 0

innermost

Duration:

0:00 minutes