Certification Problem
Input (TPDB SRS_Standard/Zantema_04/z086)
The rewrite relation of the following TRS is considered.
|
a(a(x1)) |
→ |
c(b(x1)) |
(1) |
|
b(b(x1)) |
→ |
c(a(x1)) |
(2) |
|
c(c(x1)) |
→ |
b(a(x1)) |
(3) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by ttt2 @ termCOMP 2023)
1 Dependency Pair Transformation
The following set of initial dependency pairs has been identified.
|
a#(a(x1)) |
→ |
b#(x1) |
(4) |
|
a#(a(x1)) |
→ |
c#(b(x1)) |
(5) |
|
b#(b(x1)) |
→ |
a#(x1) |
(6) |
|
b#(b(x1)) |
→ |
c#(a(x1)) |
(7) |
|
c#(c(x1)) |
→ |
a#(x1) |
(8) |
|
c#(c(x1)) |
→ |
b#(a(x1)) |
(9) |
1.1 Subterm Criterion Processor
We use the projection to multisets
| π(c#)
|
= |
{
1
}
|
| π(b#)
|
= |
{
1
}
|
| π(a#)
|
= |
{
1
}
|
| π(c)
|
= |
{
1, 1
}
|
| π(b)
|
= |
{
1, 1
}
|
| π(a)
|
= |
{
1, 1
}
|
to remove the pairs:
|
a#(a(x1)) |
→ |
b#(x1) |
(4) |
|
b#(b(x1)) |
→ |
a#(x1) |
(6) |
|
c#(c(x1)) |
→ |
a#(x1) |
(8) |
1.1.1 Dependency Graph Processor
The dependency pairs are split into 1
component.