Certification Problem
Input (TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-100)
The rewrite relation of the following TRS is considered.
|
a(x1) |
→ |
x1 |
(1) |
|
a(a(a(x1))) |
→ |
b(x1) |
(2) |
|
b(c(x1)) |
→ |
c(a(c(b(x1)))) |
(3) |
|
c(x1) |
→ |
x1 |
(4) |
Property / Task
Prove or disprove termination.Answer / Result
No.Proof (by matchbox @ termCOMP 2023)
1 Loop
The following loop proves nontermination.
| t0
|
= |
a(b(b(c(c(x1))))) |
|
→
|
a(b(c(a(c(b(c(x1))))))) |
|
→
|
a(b(c(c(b(c(x1)))))) |
|
→
|
a(c(a(c(b(c(b(c(x1)))))))) |
|
→
|
a(c(a(b(c(b(c(x1))))))) |
|
→
|
a(a(b(c(b(c(x1)))))) |
|
→
|
a(a(c(a(c(b(b(c(x1)))))))) |
|
→
|
a(a(a(c(b(b(c(x1))))))) |
|
→
|
b(c(b(b(c(x1))))) |
|
→
|
c(a(c(b(b(b(c(x1))))))) |
|
→
|
c(a(b(b(b(c(x1)))))) |
|
→
|
a(b(b(b(c(x1))))) |
|
→
|
a(b(b(c(a(c(b(x1))))))) |
|
→
|
a(b(b(c(c(b(x1)))))) |
|
= |
t13
|
where t13 =
t0σ
and
σ =
{x1/b(x1)}