Termination Proof Script

Consider the TRS R consisting of the rewrite rules
1:    f(c(s(x),y))  → f(c(x,s(y)))
2:    f(c(s(x),s(y)))  → g(c(x,y))
3:    g(c(x,s(y)))  → g(c(s(x),y))
4:    g(c(s(x),s(y)))  → f(c(x,y))
There are 4 dependency pairs:
5:    F(c(s(x),y))  → F(c(x,s(y)))
6:    F(c(s(x),s(y)))  → G(c(x,y))
7:    G(c(x,s(y)))  → G(c(s(x),y))
8:    G(c(s(x),s(y)))  → F(c(x,y))
The approximated dependency graph contains one SCC: {5-8}.
Tyrolean Termination Tool  (0.03 seconds)   ---  May 3, 2006