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

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

F(g(x), g(y)) -> F(p(f(g(x), s(y))), g(s(p(x))))
F(g(x), g(y)) -> P(f(g(x), s(y)))
F(g(x), g(y)) -> F(g(x), s(y))
F(g(x), g(y)) -> G(s(p(x)))
F(g(x), g(y)) -> P(x)
P(0) -> G(0)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Remaining Obligation(s)




The following remains to be proven:
Dependency Pair:

F(g(x), g(y)) -> F(p(f(g(x), s(y))), g(s(p(x))))


Rules:


f(g(x), g(y)) -> f(p(f(g(x), s(y))), g(s(p(x))))
p(0) -> g(0)
g(s(p(x))) -> p(x)


Strategy:

innermost



Innermost Termination of R could not be shown.
Duration:
0:01 minutes