Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/Ex15_Luc98_L)
The rewrite relation of the following TRS is considered.
|
and(true) |
→ |
X |
(1) |
|
if(true) |
→ |
X |
(2) |
|
if(false) |
→ |
Y |
(3) |
|
add(0) |
→ |
X |
(4) |
|
and(false) |
→ |
false |
(5) |
|
add(s) |
→ |
s |
(6) |
|
first(0,X) |
→ |
nil |
(7) |
|
first(s,cons) |
→ |
cons |
(8) |
| from |
→ |
cons |
(9) |
The evaluation strategy is outermostProperty / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
and(true) |
|
→
|
and(true) |
|
= |
t1
|
where t1 =
t0