Certification Problem

Input (TPDB SRS_Relative/Waldmann_19/random-123)

The rewrite relation of the following TRS is considered.

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

{c(☐), b(☐), a(☐)}

1.1.1 Closure Under Flat Contexts

{c(☐), b(☐), a(☐)}

1.1.1.1 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 486 ruless (increase limit for explicit display).

1.1.1.1.1 Rule Removal

There are 405 ruless (increase limit for explicit display).

1.1.1.1.1.1 R is empty

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

1.2 Split

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

1.2.1 Closure Under Flat Contexts

{c(☐), b(☐), a(☐)}

1.2.1.1 Closure Under Flat Contexts

{c(☐), b(☐), a(☐)}

1.2.1.1.1 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 324 ruless (increase limit for explicit display).

1.2.1.1.1.1 Rule Removal

There are 243 ruless (increase limit for explicit display).

1.2.1.1.1.1.1 Rule Removal

1.2.1.1.1.1.1.1 R is empty

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

1.2.2 Closure Under Flat Contexts

{c(☐), b(☐), a(☐)}

1.2.2.1 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):

1.2.2.1.1 Rule Removal

1.2.2.1.1.1 Rule Removal

1.2.2.1.1.1.1 Rule Removal

1.2.2.1.1.1.1.1 R is empty

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