Certification Problem
Input (TPDB TRS_Standard/Transformed_CSR_04/ExIntrod_Zan97_L)
The rewrite relation of the following TRS is considered.
|
if(true) |
→ |
X |
(1) |
|
if(false) |
→ |
Y |
(2) |
|
fact(X) |
→ |
if(zero(X)) |
(3) |
|
add(0,X) |
→ |
X |
(4) |
|
add(s(X),Y) |
→ |
s(add(X,Y)) |
(5) |
|
prod(0,X) |
→ |
0 |
(6) |
|
prod(s(X),Y) |
→ |
add(Y,prod(X,Y)) |
(7) |
|
zero(0) |
→ |
true |
(8) |
|
zero(s(X)) |
→ |
false |
(9) |
|
p(s(X)) |
→ |
X |
(10) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by ttt2 @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
if(true) |
|
→
|
if(true) |
|
= |
t1
|
where t1 =
t0σ
and
σ =
{X/if(true)}