Term Rewriting System R:
[x]
f(x) -> g(f(x))
g(f(x)) -> x
g(x) -> a
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
g(f(x)) -> x
R
↳RRRI
→TRS2
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(x) -> G(f(x))
F(x) -> F(x)
Furthermore, R contains one SCC.
R
↳RRRI
→TRS2
↳DPs
→DP Problem 1
↳Non Termination
Dependency Pair:
F(x) -> F(x)
Rules:
f(x) -> g(f(x))
g(x) -> a
Found an infinite P-chain over R:
P =
F(x) -> F(x)
R =
f(x) -> g(f(x))
g(x) -> a
s = F(x')
evaluates to t =F(x')
Thus, s starts an infinite chain.
Innermost Non-Termination of R could be shown.
Duration:
0:00 minutes