Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/4.06)
The rewrite relation of the following TRS is considered.
|
*(*(x,y),z) |
→ |
*(x,*(y,z)) |
(1) |
|
*(+(x,y),z) |
→ |
+(*(x,z),*(y,z)) |
(2) |
|
*(x,+(y,f(z))) |
→ |
*(g(x,z),+(y,y)) |
(3) |
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
|
= |
*(x,+(f(z'),f(z))) |
|
→
|
*(g(x,z),+(f(z'),f(z'))) |
|
= |
t1
|
where t1 =
t0σ
and
σ =
{z/z', x/g(x,z)}