Term Rewriting System R:
[x, y, z]
f(f(f(a, x), y), z) -> f(f(x, z), f(y, z))
f(f(b, x), y) -> x
f(c, y) -> y

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

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


Rules:


f(f(f(a, x), y), z) -> f(f(x, z), f(y, z))
f(f(b, x), y) -> x
f(c, y) -> y


Strategy:

innermost



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