Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/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) |
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
|
= |
zeros |
|
→
|
cons(0,zeros) |
|
= |
t1
|
where t1 =
C[t0]
and
C = cons(0,☐)