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