Term Rewriting System R:
[x]
h(f(f(x))) -> h(f(g(f(x))))
f(g(f(x))) -> f(f(x))
Termination of R to be shown.
TRS
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
H(f(f(x))) -> H(f(g(f(x))))
H(f(f(x))) -> F(g(f(x)))
F(g(f(x))) -> F(f(x))
Furthermore, R contains one SCC.
TRS
↳DPs
→DP Problem 1
↳Non Termination
Dependency Pair:
H(f(f(x))) -> H(f(g(f(x))))
Rules:
h(f(f(x))) -> h(f(g(f(x))))
f(g(f(x))) -> f(f(x))
Found an infinite P-chain over R:
P =
H(f(f(x))) -> H(f(g(f(x))))
R =
h(f(f(x))) -> h(f(g(f(x))))
f(g(f(x))) -> f(f(x))
s = H(f(g(f(x'''))))
evaluates to t =H(f(g(f(x'''))))
Thus, s starts an infinite chain.
Non-Termination of R could be shown.
Duration:
0:01 minutes