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

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

+'(s(x), s(y)) -> +'(s(x), +(y, 0))
+'(s(x), s(y)) -> +'(y, 0)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Remaining Obligation(s)




The following remains to be proven:
Dependency Pair:

+'(s(x), s(y)) -> +'(s(x), +(y, 0))


Rules:


+(0, y) -> y
+(s(x), 0) -> s(x)
+(s(x), s(y)) -> s(+(s(x), +(y, 0)))




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