Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/#4.14)
The rewrite relation of the following TRS is considered.
|
f(g(x),s(0)) |
→ |
f(g(x),g(x)) |
(1) |
|
g(s(x)) |
→ |
s(g(x)) |
(2) |
|
g(0) |
→ |
0 |
(3) |
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(g(s(0)),g(s(0))) |
|
→
|
f(g(s(0)),s(g(0))) |
|
→
|
f(g(s(0)),s(0)) |
|
→
|
f(g(s(0)),g(s(0))) |
|
= |
t3
|
where t3 =
t0