*(

*(

*(

*(

R

↳Dependency Pair Analysis

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Usable Rules (Innermost)

***'( 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

As we are in the innermost case, we can delete all 2 non-usable-rules.

R

↳DPs

→DP Problem 1

↳UsableRules

→DP Problem 2

↳Non Termination

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

*(X, 0) -> 0

*(X, 0) ->X

innermost

Found an infinite P-chain over R:

P =

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

R =

*(X, 0) -> 0

*(X, 0) ->X

s = *'(

evaluates to t =*'(

Thus, s starts an infinite chain.

Duration:

0:03 minutes