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