Term Rewriting System R:
[X]
f(X) -> g(h(f(X)))
Innermost Termination of R to be shown.
TRS
↳Reversing
↳Rev
↳DPs
Rule(s) before reversing:
f(X) -> g(h(f(X)))
Rule(s) after reversing:
f'(x) -> f'(h'(g'(x)))
Trying another alternative:
TRS
↳Rev
↳Reversing
↳DPs
Rule(s) before reversing:
f(X) -> g(h(f(X)))
Rule(s) after reversing:
f'(x) -> f'(h'(g'(x)))
Trying another alternative:
TRS
↳Rev
↳Rev
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(X) -> F(X)
Furthermore, R contains one SCC.
TRS
↳Rev
↳Rev
↳DPs
→DP Problem 1
↳Non Termination
Dependency Pair:
F(X) -> F(X)
Rule:
f(X) -> g(h(f(X)))
Strategy:
innermost
Found an infinite P-chain over R:
P =
F(X) -> F(X)
R =
f(X) -> g(h(f(X)))
s = F(X')
evaluates to t =F(X')
Thus, s starts an infinite chain.
Innermost Non-Termination of R could be shown.
Duration:
0:03 minutes