Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/167391)

The rewrite relation of the following TRS is considered.

There are 110 ruless (increase limit for explicit display).

Property / Task

Answer / Result

Proof (by matchbox @ termCOMP 2023)

1 Split

We split R in the relative problem D/R-D and R-D, where the rules D

1.1 Closure Under Flat Contexts

{2(☐), 1(☐), 0(☐)}

There are 330 ruless (increase limit for explicit display).

1.1.1 Semantic Labeling

As carrier we take the set {0,1,2}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 3):

There are 990 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

There are 897 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.

1.2 Closure Under Flat Contexts

{2(☐), 1(☐), 0(☐)}

1.2.1 Closure Under Flat Contexts

{2(☐), 1(☐), 0(☐)}

There are 117 ruless (increase limit for explicit display).

1.2.1.1 Semantic Labeling

As carrier we take the set {0,...,8}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 9):

There are 1053 ruless (increase limit for explicit display).

1.2.1.1.1 Rule Removal

There are 1053 ruless (increase limit for explicit display).

1.2.1.1.1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.