Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/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) |
The evaluation strategy is outermostProperty / Task
Prove or disprove termination.Answer / Result
No.Proof (by AProVE @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
t0
|
= |
tail(cons(X)) |
|
→
|
tail(cons(X)) |
|
= |
t1
|
where t1 =
t0