Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/#4.12a)
The rewrite relation of the following TRS is considered.
|
h(x,y) |
→ |
f(x,y,x) |
(1) |
|
f(0,1,x) |
→ |
h(x,x) |
(2) |
|
g(x,y) |
→ |
x |
(3) |
|
g(x,y) |
→ |
y |
(4) |
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(0,1),g(0,1),g(0,1)) |
|
→
|
f(g(0,1),1,g(0,1)) |
|
→
|
f(0,1,g(0,1)) |
|
→
|
h(g(0,1),g(0,1)) |
|
→
|
f(g(0,1),g(0,1),g(0,1)) |
|
= |
t4
|
where t4 =
t0