Certification Problem
Input (TPDB TRS_Standard/Strategy_removed_CSR_05/Ex3_2_Luc97)
The rewrite relation of the following TRS is considered.
|
dbl(0) |
→ |
0 |
(1) |
|
dbl(s(X)) |
→ |
s(s(dbl(X))) |
(2) |
|
dbls(nil) |
→ |
nil |
(3) |
|
dbls(cons(X,Y)) |
→ |
cons(dbl(X),dbls(Y)) |
(4) |
|
sel(0,cons(X,Y)) |
→ |
X |
(5) |
|
sel(s(X),cons(Y,Z)) |
→ |
sel(X,Z) |
(6) |
|
indx(nil,X) |
→ |
nil |
(7) |
|
indx(cons(X,Y),Z) |
→ |
cons(sel(X,Z),indx(Y,Z)) |
(8) |
|
from(X) |
→ |
cons(X,from(s(X))) |
(9) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
from(X) |
|
→
|
cons(X,from(s(X))) |
|
= |
t1
|
where t1 =
C[t0σ]
and
σ =
{X/s(X)}
and
C = cons(X,☐)