Term Rewriting System R:

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

Termination of R to be shown.


This program has no overlaps, so it is sufficient to show innermost termination. 


R contains the following Dependency Pairs: 


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

Furthermore, R contains one SCC.


SCC1:

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

Found an infinite P-chain over R:
P = +'(1, x) -> +'(+(0, 1), x)
R = [+(0, x) -> x, +(1, x) -> +(+(0, 1), x)]
s = +'(1, x') evaluates to t = +'(1, x')
Thus, s starts an infinite reduction.


Non-Termination of R could be shown.

Duration: 0.543 seconds.