Term Rewriting System R:
[x]
f(g(a)) -> f(s(g(b)))
f(f(x)) -> b
g(x) -> f(g(x))
Termination of R to be shown.
TRS
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
f(g(a)) -> f(s(g(b)))
where the Polynomial interpretation:
| POL(g(x1)) | = x1 |
| POL(b) | = 0 |
| POL(s(x1)) | = x1 |
| 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:
G(x) -> F(g(x))
G(x) -> G(x)
Furthermore, R contains one SCC.
TRS
↳RRRPolo
→TRS2
↳DPs
→DP Problem 1
↳Non Termination
Dependency Pair:
G(x) -> G(x)
Rules:
g(x) -> f(g(x))
f(f(x)) -> b
Found an infinite P-chain over R:
P =
G(x) -> G(x)
R =
g(x) -> f(g(x))
f(f(x)) -> b
s = G(x')
evaluates to t =G(x')
Thus, s starts an infinite chain.
Non-Termination of R could be shown.
Duration:
0:01 minutes