Term Rewriting System R:
[X]
f(a, a) -> f(a, b)
f(a, b) -> f(s(a), c)
f(s(X), c) -> f(X, c)
f(c, c) -> f(a, a)

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

F(a, a) -> F(a, b)
F(a, b) -> F(s(a), c)
F(s(X), c) -> F(X, c)
F(c, c) -> F(a, a)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

F(c, c) -> F(a, a)
F(s(X), c) -> F(X, c)
F(a, b) -> F(s(a), c)
F(a, a) -> F(a, b)


Rules:


f(a, a) -> f(a, b)
f(a, b) -> f(s(a), c)
f(s(X), c) -> f(X, c)
f(c, c) -> f(a, a)




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