Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/round_nonterm)
The rewrite relation of the following TRS is considered.
f(s(x),x) |
→ |
f(s(x),round(x)) |
(1) |
round(0) |
→ |
0 |
(2) |
round(0) |
→ |
s(0) |
(3) |
round(s(0)) |
→ |
s(0) |
(4) |
round(s(s(x))) |
→ |
s(s(round(x))) |
(5) |
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
|
= |
f(s(0),round(0)) |
|
→
|
f(s(0),0) |
|
→
|
f(s(0),round(0)) |
|
= |
t2
|
where t2 =
t0