Certification Problem
Input (TPDB TRS_Standard/SK90/4.01)
The rewrite relation of the following TRS is considered.
|
minus(minus(x)) |
→ |
x |
(1) |
|
minux(+(x,y)) |
→ |
+(minus(y),minus(x)) |
(2) |
|
+(minus(x),+(x,y)) |
→ |
y |
(3) |
|
+(+(x,y),minus(y)) |
→ |
x |
(4) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Rule Removal
Using the
Knuth Bendix order with w0 = 1 and the following precedence and weight functions
| prec(minus) |
= |
0 |
|
weight(minus) |
= |
2 |
|
|
|
| prec(minux) |
= |
2 |
|
weight(minux) |
= |
4 |
|
|
|
| prec(+) |
= |
1 |
|
weight(+) |
= |
0 |
|
|
|
all of the following rules can be deleted.
|
minus(minus(x)) |
→ |
x |
(1) |
|
minux(+(x,y)) |
→ |
+(minus(y),minus(x)) |
(2) |
|
+(minus(x),+(x,y)) |
→ |
y |
(3) |
|
+(+(x,y),minus(y)) |
→ |
x |
(4) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.