Term Rewriting System R:
[x, y, z, u, v]
f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))
f(x, y, y) -> y
f(x, y, g(y)) -> x
f(x, x, y) -> x
f(g(x), x, y) -> y

Innermost Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

F(f(x, y, z), u, f(x, y, v)) -> F(x, y, f(z, u, v))
F(f(x, y, z), u, f(x, y, v)) -> F(z, u, v)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

F(f(x, y, z), u, f(x, y, v)) -> F(z, u, v)
F(f(x, y, z), u, f(x, y, v)) -> F(x, y, f(z, u, v))


Rules:


f(f(x, y, z), u, f(x, y, v)) -> f(x, y, f(z, u, v))
f(x, y, y) -> y
f(x, y, g(y)) -> x
f(x, x, y) -> x
f(g(x), x, y) -> y


Strategy:

innermost



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