Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/Ex1_GL02a)
The rewrite relation of the following TRS is considered.
|
eq(0,0) |
→ |
true |
(1) |
|
eq(s(X),s(Y)) |
→ |
eq(X,Y) |
(2) |
|
eq(X,Y) |
→ |
false |
(3) |
|
inf(X) |
→ |
cons(X,inf(s(X))) |
(4) |
|
take(0,X) |
→ |
nil |
(5) |
|
take(s(X),cons(Y,L)) |
→ |
cons(Y,take(X,L)) |
(6) |
|
length(nil) |
→ |
0 |
(7) |
|
length(cons(X,L)) |
→ |
s(length(L)) |
(8) |
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
|
= |
inf(X) |
|
→
|
cons(X,inf(s(X))) |
|
= |
t1
|
where t1 =
C[t0σ]
and
σ =
{X/s(X)}
and
C = cons(X,☐)