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