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

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

F(x, y) -> F(x, x)
F(s(x), y) -> F(y, x)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Non Termination


Dependency Pairs:

F(s(x), y) -> F(y, x)
F(x, y) -> F(x, x)


Rules:


f(x, y) -> f(x, x)
f(s(x), y) -> f(y, x)





Found an infinite P-chain over R:
P =

F(s(x), y) -> F(y, x)
F(x, y) -> F(x, x)

R =

f(x, y) -> f(x, x)
f(s(x), y) -> f(y, x)

s = F(x', x')
evaluates to t =F(x', x')

Thus, s starts an infinite chain.

Non-Termination of R could be shown.
Duration:
0:00 minutes