Certification Problem
Input (TPDB TRS_Standard/Strategy_removed_CSR_05/ExIntrod_GM04)
The rewrite relation of the following TRS is considered.
| nats |
→ |
adx(zeros) |
(1) |
| zeros |
→ |
cons(0,zeros) |
(2) |
|
incr(cons(X,Y)) |
→ |
cons(s(X),incr(Y)) |
(3) |
|
adx(cons(X,Y)) |
→ |
incr(cons(X,adx(Y))) |
(4) |
|
hd(cons(X,Y)) |
→ |
X |
(5) |
|
tl(cons(X,Y)) |
→ |
Y |
(6) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
zeros |
|
→
|
cons(0,zeros) |
|
= |
t1
|
where t1 =
C[t0]
and
C = cons(0,☐)