Certification Problem
Input (TPDB TRS_Standard/Applicative_05/TypeEx5)
The rewrite relation of the following TRS is considered.
|
ap(ap(g,x),y) |
→ |
y |
(1) |
|
ap(f,x) |
→ |
ap(f,app(g,x)) |
(2) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
ap(f,x) |
|
→
|
ap(f,app(g,x)) |
|
= |
t1
|
where t1 =
t0σ
and
σ =
{x/app(g,x)}