Certification Problem
Input (TPDB TRS_Relative/Relative_05/rt3-8)
The relative rewrite relation R/S is considered where R is the following TRS
|
f(s(x),y) |
→ |
f(-(s(x),y),y) |
(1) |
and S is the following TRS.
|
+(0,y) |
→ |
y |
(2) |
|
+(s(x),y) |
→ |
s(+(x,y)) |
(3) |
|
-(x,0) |
→ |
x |
(4) |
|
-(0,y) |
→ |
0 |
(5) |
|
-(s(x),s(y)) |
→ |
-(x,y) |
(6) |
|
f(x,y) |
→ |
f(x,+(x,y)) |
(7) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves that R/S is not relative terminating.
| t0
|
= |
f(s(x),0) |
|
→R
|
f(-(s(x),0),0) |
|
→S
|
f(s(x),0) |
|
= |
t2
|
where t2 =
t0σ
and
σ =
{x/x}