Term Rewriting System R:
[X]
f(a) -> f(c(a))
f(c(X)) -> X
f(c(a)) -> f(d(b))
f(a) -> f(d(a))
f(d(X)) -> X
f(c(b)) -> f(d(a))
e(g(X)) -> e(X)
Termination of R to be shown.
TRS
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
f(c(X)) -> X
f(d(X)) -> X
where the Polynomial interpretation:
| POL(c(x1)) | = x1 |
| POL(g(x1)) | = x1 |
| POL(e(x1)) | = x1 |
| POL(b) | = 0 |
| POL(d(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
↳Removing Redundant Rules
Removing the following rules from R which fullfill a polynomial ordering:
e(g(X)) -> e(X)
where the Polynomial interpretation:
| POL(c(x1)) | = x1 |
| POL(g(x1)) | = 1 + x1 |
| POL(e(x1)) | = x1 |
| POL(b) | = 0 |
| POL(d(x1)) | = x1 |
| POL(a) | = 0 |
| 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
↳RRRPolo
→TRS3
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
F(c(b)) -> F(d(a))
F(a) -> F(d(a))
F(c(a)) -> F(d(b))
F(a) -> F(c(a))
R contains no SCCs.
Termination of R successfully shown.
Duration:
0:00 minutes