Term Rewriting System R:
[x]
f(s(x)) -> f(g(x, x))
g(0, 1) -> s(0)
0 -> 1
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(s(x)) -> F(g(x, x))
F(s(x)) -> G(x, x)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Non Termination
Dependency Pair:
F(s(x)) -> F(g(x, x))
Rules:
f(s(x)) -> f(g(x, x))
g(0, 1) -> s(0)
0 -> 1
Found an infinite P-chain over R:
P =
F(s(x)) -> F(g(x, x))
R =
f(s(x)) -> f(g(x, x))
g(0, 1) -> s(0)
0 -> 1
s = F(g(0, 0))
evaluates to t =F(g(0, 0))
Thus, s starts an infinite chain.
Non-Termination of R could be shown.
Duration:
0:00 minutes