Term Rewriting System R:
[x, y]
f(g(x), x, y) -> f(y, y, g(y))
g(g(x)) -> g(x)
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(g(x), x, y) -> F(y, y, g(y))
F(g(x), x, y) -> G(y)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Non Termination
Dependency Pair:
F(g(x), x, y) -> F(y, y, g(y))
Rules:
f(g(x), x, y) -> f(y, y, g(y))
g(g(x)) -> g(x)
Found an infinite P-chain over R:
P =
F(g(x), x, y) -> F(y, y, g(y))
R =
f(g(x), x, y) -> f(y, y, g(y))
g(g(x)) -> g(x)
s = F(g(g(x''')), g(g(x''')), g(g(g(x'''))))
evaluates to t =F(g(g(x''')), g(g(x''')), g(g(g(x'''))))
Thus, s starts an infinite chain.
Non-Termination of R could be shown.
Duration:
0:00 minutes