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