Term Rewriting System R:
[X, Y, Z]
f(f(X, Y), Z) -> f(X, f(Y, Z))
f(X, f(Y, Z)) -> f(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(X, f(Y, Z)) -> F(Y, Y)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

F(X, f(Y, Z)) -> F(Y, Y)
F(f(X, Y), Z) -> F(Y, Z)
F(f(X, Y), Z) -> F(X, f(Y, Z))


Rules:


f(f(X, Y), Z) -> f(X, f(Y, Z))
f(X, f(Y, Z)) -> f(Y, Y)




Termination of R could not be shown.
Duration:
0:07 minutes