Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/ExIntrod_GM99_L)
The rewrite relation of the following TRS is considered.
|
tail(cons(X)) |
→ |
Y |
(1) |
|
if(true) |
→ |
X |
(2) |
|
if(false) |
→ |
Y |
(3) |
| primes |
→ |
sieve(from(s(s(0)))) |
(4) |
|
from(X) |
→ |
cons(X) |
(5) |
|
head(cons(X)) |
→ |
X |
(6) |
|
filter(s(s(X)),cons(Y)) |
→ |
if(divides(s(s(X)),Y)) |
(7) |
|
sieve(cons(X)) |
→ |
cons(X) |
(8) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
tail(cons(X)) |
|
→
|
tail(cons(X)) |
|
= |
t1
|
where t1 =
t0σ
and
σ =
{Y/tail(cons(X))}