Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/Ex5_DLMMU04_L)
The rewrite relation of the following TRS is considered.
|
tail(cons(X)) |
→ |
XS |
(1) |
| pairNs |
→ |
cons(0) |
(2) |
| oddNs |
→ |
incr(pairNs) |
(3) |
|
incr(cons(X)) |
→ |
cons(s(X)) |
(4) |
|
take(0,XS) |
→ |
nil |
(5) |
|
take(s(N),cons(X)) |
→ |
cons(X) |
(6) |
|
zip(nil,XS) |
→ |
nil |
(7) |
|
zip(X,nil) |
→ |
nil |
(8) |
|
zip(cons(X),cons(Y)) |
→ |
cons(pair(X,Y)) |
(9) |
|
repItems(nil) |
→ |
nil |
(10) |
|
repItems(cons(X)) |
→ |
cons(X) |
(11) |
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 =
{XS/tail(cons(X))}