Term Rewriting System R:
[x]
+(1, x) -> +(+(0, 1), x)
+(0, x) -> x

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

+'(1, x) -> +'(+(0, 1), x)
+'(1, x) -> +'(0, 1)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Narrowing Transformation


Dependency Pair:

+'(1, x) -> +'(+(0, 1), x)


Rules:


+(1, x) -> +(+(0, 1), x)
+(0, x) -> x





On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

+'(1, x) -> +'(+(0, 1), x)
one new Dependency Pair is created:

+'(1, x) -> +'(1, x)

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:
Dependency Pair:

+'(1, x) -> +'(1, x)


Rules:


+(1, x) -> +(+(0, 1), x)
+(0, x) -> x




Termination of R could not be shown.
Duration:
0:00 minutes