Certification Problem
Input (TPDB SRS_Standard/ICFP_2010/162016)
The rewrite relation of the following TRS is considered.
There are 110 ruless (increase limit for explicit display).
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by matchbox @ termCOMP 2023)
1 Closure Under Flat Contexts
Using the flat contexts
{2(☐), 1(☐), 0(☐)}
We obtain the transformed TRS
There are 330 ruless (increase limit for explicit display).
1.1 Closure Under Flat Contexts
Using the flat contexts
{2(☐), 1(☐), 0(☐)}
We obtain the transformed TRS
There are 990 ruless (increase limit for explicit display).
1.1.1 Semantic Labeling
The following interpretations form a
model
of the rules.
As carrier we take the set
{0,...,8}.
Symbols are labeled by the interpretation of their arguments using the interpretations
(modulo 9):
| [2(x1)] |
= |
3x1 + 0 |
| [1(x1)] |
= |
3x1 + 1 |
| [0(x1)] |
= |
3x1 + 2 |
We obtain the labeled TRS
There are 8910 ruless (increase limit for explicit display).
1.1.1.1 Rule Removal
Using the
matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
| [20(x1)] |
= |
x1 +
|
| [23(x1)] |
= |
x1 +
|
| [26(x1)] |
= |
x1 +
|
| [21(x1)] |
= |
x1 +
|
| [24(x1)] |
= |
x1 +
|
| [27(x1)] |
= |
x1 +
|
| [22(x1)] |
= |
x1 +
|
| [25(x1)] |
= |
x1 +
|
| [28(x1)] |
= |
x1 +
|
| [10(x1)] |
= |
x1 +
|
| [13(x1)] |
= |
x1 +
|
| [16(x1)] |
= |
x1 +
|
| [11(x1)] |
= |
x1 +
|
| [14(x1)] |
= |
x1 +
|
| [17(x1)] |
= |
x1 +
|
| [12(x1)] |
= |
x1 +
|
| [15(x1)] |
= |
x1 +
|
| [18(x1)] |
= |
x1 +
|
| [00(x1)] |
= |
x1 +
|
| [03(x1)] |
= |
x1 +
|
| [06(x1)] |
= |
x1 +
|
| [01(x1)] |
= |
x1 +
|
| [04(x1)] |
= |
x1 +
|
| [07(x1)] |
= |
x1 +
|
| [02(x1)] |
= |
x1 +
|
| [05(x1)] |
= |
x1 +
|
| [08(x1)] |
= |
x1 +
|
all of the following rules can be deleted.
There are 8910 ruless (increase limit for explicit display).
1.1.1.1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.