Term Rewriting System R:
[y, x, z]
f(0, y) -> y
f(x, 0) -> x
f(i(x), y) -> i(x)
f(f(x, y), z) -> f(x, f(y, z))
f(g(x, y), z) -> g(f(x, z), f(y, z))
f(1, g(x, y)) -> x
f(2, g(x, y)) -> y

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

F(f(x, y), z) -> F(x, f(y, z))
F(f(x, y), z) -> F(y, z)
F(g(x, y), z) -> F(x, z)
F(g(x, y), z) -> F(y, z)

Furthermore, R contains one SCC. 


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




The following remains to be proven:
Dependency Pairs:

F(g(x, y), z) -> F(y, z)
F(g(x, y), z) -> F(x, z)
F(f(x, y), z) -> F(y, z)
F(f(x, y), z) -> F(x, f(y, z))


Rules:


f(0, y) -> y
f(x, 0) -> x
f(i(x), y) -> i(x)
f(f(x, y), z) -> f(x, f(y, z))
f(g(x, y), z) -> g(f(x, z), f(y, z))
f(1, g(x, y)) -> x
f(2, g(x, y)) -> y




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