Term Rewriting System R:
[x]
f(h(x)) -> f(i(x))
f(i(x)) -> a
i(x) -> h(x)
Innermost Termination of R to be shown.
R
↳Removing Redundant Rules for Innermost Termination
Removing the following rules from R which left hand sides contain non normal subterms
f(i(x)) -> a
R
↳RRRI
→TRS2
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(h(x)) -> F(i(x))
F(h(x)) -> I(x)
Furthermore, R contains one SCC.
R
↳RRRI
→TRS2
↳DPs
→DP Problem 1
↳Non Termination
Dependency Pair:
F(h(x)) -> F(i(x))
Rules:
f(h(x)) -> f(i(x))
i(x) -> h(x)
Found an infinite P-chain over R:
P =
F(h(x)) -> F(i(x))
R =
f(h(x)) -> f(i(x))
i(x) -> h(x)
s = F(i(x'''))
evaluates to t =F(i(x'''))
Thus, s starts an infinite chain.
Innermost Non-Termination of R could be shown.
Duration:
0:07 minutes