Term Rewriting System R:
[X, Y]
f(X, g(X), Y) -> f(Y, Y, Y)
g(b) -> c
b -> c

Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

F(X, g(X), Y) -> F(Y, Y, Y)

Furthermore, R contains one SCC.


   R
DPs
       →DP Problem 1
Non Termination


Dependency Pair:

F(X, g(X), Y) -> F(Y, Y, Y)


Rules:


f(X, g(X), Y) -> f(Y, Y, Y)
g(b) -> c
b -> c





Found an infinite P-chain over R:
P =

F(X, g(X), Y) -> F(Y, Y, Y)

R =

f(X, g(X), Y) -> f(Y, Y, Y)
g(b) -> c
b -> c

s = F(g(b), g(b), g(b))
evaluates to t =F(g(b), g(b), g(b))

Thus, s starts an infinite chain.

Non-Termination of R could be shown.
Duration:
0:00 minutes