Term Rewriting System R:
[x]
f(a) -> f(b)
f(x) -> g(x)
g(b) -> g(a)
Termination of R to be shown.
TRS
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
f(x) -> g(x)
where the Polynomial interpretation:
| POL(g(x1)) | = x1 |
| POL(b) | = 0 |
| 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(a) -> F(b)
G(b) -> G(a)
R contains no SCCs.
Termination of R successfully shown.
Duration:
0:01 minutes