Certification Problem
Input (TPDB TRS_Outermost/Strategy_outermost_added_08/test10)
The rewrite relation of the following TRS is considered.
|
h(X,Z) |
→ |
f(X,s(X),Z) |
(1) |
|
f(X,Y,g(X,Y)) |
→ |
h(0,g(X,Y)) |
(2) |
|
g(0,Y) |
→ |
0 |
(3) |
|
g(X,s(Y)) |
→ |
g(X,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(0,s(0),g(0,s(0))) |
|
→
|
h(0,g(0,s(0))) |
|
→
|
f(0,s(0),g(0,s(0))) |
|
= |
t2
|
where t2 =
t0