Certification Problem
Input (TPDB TRS_Relative/INVY_15/#3.1_gen)
The relative rewrite relation R/S is considered where R is the following TRS
|
-(x,0) |
→ |
x |
(1) |
|
-(s(x),s(y)) |
→ |
-(x,y) |
(2) |
|
quot(0,s(y)) |
→ |
0 |
(3) |
|
quot(s(x),s(y)) |
→ |
s(quot(-(x,y),s(y))) |
(4) |
and S is the following TRS.
| gen |
→ |
0 |
(5) |
| gen |
→ |
s(gen) |
(6) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves that R/S is not relative terminating.
| t0
|
= |
quot(gen,s(0)) |
|
→S
|
quot(s(gen),s(0)) |
|
→R
|
s(quot(-(gen,0),s(0))) |
|
→R
|
s(quot(gen,s(0))) |
|
= |
t3
|
where t3 =
C[t0]
and
C = s(☐)