Term Rewriting System R:
[]
f(a) -> f(a)
a -> b
Termination of R to be shown.
TRS
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
a -> b
where the Polynomial interpretation:
| POL(b) | = 0 |
| POL(a) | = 1 |
| POL(f(x1)) | = x1 |
was used.
Not all Rules of R can be deleted, so we still have to regard a part of R.
TRS
↳RRRPolo
→TRS2
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(a) -> F(a)
Furthermore, R contains one SCC.
TRS
↳RRRPolo
→TRS2
↳DPs
→DP Problem 1
↳Non Termination
Dependency Pair:
F(a) -> F(a)
Rule:
f(a) -> f(a)
Found an infinite P-chain over R:
P =
F(a) -> F(a)
R =
f(a) -> f(a)
s = F(a)
evaluates to t =F(a)
Thus, s starts an infinite chain.
Non-Termination of R could be shown.
Duration:
0:00 minutes