Term Rewriting System R:

   [X, Y, X1, X2]
   f(g(X), Y) -> f(X, n__f(g(X), activate(Y)))
   f(X1, X2) -> n__f(X1, X2)
   activate(n__f(X1, X2)) -> f(X1, X2)
   activate(X) -> X

Termination of R to be shown.


R contains the following Dependency Pairs: 


   ACTIVATE(n__f(X1, X2)) -> F(X1, X2)
   F(g(X), Y) -> F(X, n__f(g(X), activate(Y)))
   F(g(X), Y) -> ACTIVATE(Y)

Furthermore, R contains one SCC.


SCC1:

F(g(X), Y) -> ACTIVATE(Y)
F(g(X), Y) -> F(X, n__f(g(X), activate(Y)))
ACTIVATE(n__f(X1, X2)) -> F(X1, X2)

Found an infinite P-chain over R:
P = F(g(X), Y) -> ACTIVATE(Y)
F(g(X), Y) -> F(X, n__f(g(X), activate(Y)))
ACTIVATE(n__f(X1, X2)) -> F(X1, X2)
R = [activate(n__f(X1, X2)) -> f(X1, X2), activate(X) -> X, f(g(X), Y) -> f(X, n__f(g(X), activate(Y))), f(X1, X2) -> n__f(X1, X2)]
s = F(g(g(X''')), Y''') evaluates to t = F(g(g(X''')), activate(Y'''))
Thus, s starts an infinite reduction as s matches t.


Non-Termination of R could be shown.

Duration: 0.690 seconds.