Term Rewriting System R:
[x]
f(x) -> g(f(x))
g(f(x)) -> x
g(x) -> a
Termination of R to be shown.
TRS
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
g(f(x)) -> x
where the Polynomial interpretation:
| POL(g(x1)) | = x1 |
| POL(a) | = 0 |
| POL(f(x1)) | = 1 + 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(x) -> G(f(x))
F(x) -> F(x)
Furthermore, R contains one SCC.
TRS
↳RRRPolo
→TRS2
↳DPs
→DP Problem 1
↳Non Termination
Dependency Pair:
F(x) -> F(x)
Rules:
g(x) -> a
f(x) -> g(f(x))
Found an infinite P-chain over R:
P =
F(x) -> F(x)
R =
g(x) -> a
f(x) -> g(f(x))
s = F(x')
evaluates to t =F(x')
Thus, s starts an infinite chain.
Non-Termination of R could be shown.
Duration:
0:00 minutes