Certification Problem
Input (TPDB TRS_Standard/Strategy_removed_mixed_05/ex6)
The rewrite relation of the following TRS is considered.
|
f(x,x) |
→ |
f(i(x),g(g(x))) |
(1) |
|
f(x,y) |
→ |
x |
(2) |
|
g(x) |
→ |
i(x) |
(3) |
|
f(x,i(x)) |
→ |
f(x,x) |
(4) |
|
f(i(x),i(g(x))) |
→ |
a |
(5) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
f(x306,x306) |
|
→
|
f(i(x306),g(g(x306))) |
|
→
|
f(i(x306),i(g(x306))) |
|
→
|
f(i(x306),i(i(x306))) |
|
→
|
f(i(x306),i(x306)) |
|
= |
t4
|
where t4 =
t0σ
and
σ =
{x306/i(x306)}