\set ECHO none
add_provenance

(1 row)
create_provenance_mapping

(1 row)
create_provenance_mapping

(1 row)
remove_provenance

(1 row)
src|dst|word
a|a|ac · ca
a|c|ab · bc
b|a|bc · ca
c|b|ca · ab
c|c|ca · ac
(5 rows)
remove_provenance

(1 row)
n|equations|paths
a|x₃ where x₁ = x₃ ⊗ ab, x₂ = (x₃ ⊗ ac) ⊕ (x₁ ⊗ bc), x₃ = 𝟙 ⊕ (x₂ ⊗ ca)|((ac | ab · bc) · ca)*
b|x₁ where x₁ = x₃ ⊗ ab, x₂ = (x₃ ⊗ ac) ⊕ (x₁ ⊗ bc), x₃ = 𝟙 ⊕ (x₂ ⊗ ca)|((ac | ab · bc) · ca)* · ab
c|x₂ where x₁ = x₃ ⊗ ab, x₂ = (x₃ ⊗ ac) ⊕ (x₁ ⊗ bc), x₃ = 𝟙 ⊕ (x₂ ⊗ ca)|((ac | ab · bc) · ca)* · (ac | ab · bc)
(3 rows)
remove_provenance

(1 row)
n|equations|paths
a|x₃ where x₁ = ab ⊗ x₃, x₂ = (ac ⊗ x₃) ⊕ (bc ⊗ x₁), x₃ = 𝟙 ⊕ (ca ⊗ x₂)|(ca · (ac | bc · ab))*
b|x₁ where x₁ = ab ⊗ x₃, x₂ = (ac ⊗ x₃) ⊕ (bc ⊗ x₁), x₃ = 𝟙 ⊕ (ca ⊗ x₂)|ab · (ca · (ac | bc · ab))*
c|x₂ where x₁ = ab ⊗ x₃, x₂ = (ac ⊗ x₃) ⊕ (bc ⊗ x₁), x₃ = 𝟙 ⊕ (ca ⊗ x₂)|(ac | bc · ab) · (ca · (ac | bc · ab))*
(3 rows)
remove_provenance

(1 row)
n|cost|paths
a|0|ε
b|1|ab
c|3|ac | ab · bc
(3 rows)
remove_provenance

(1 row)
n|cost|paths
a|0|((ac | ab · bc) · ca)*
b|0|((ac | ab · bc) · ca)* · ab
c|0|((ac | ab · bc) · ca)* · (ac | ab · bc)
(3 rows)
ERROR:  ProvSQL: A cycle of negative cost makes the least cost unbounded, with no shortest derivation.
DETAIL:  provsql-reason: recursion-cycle-no-value; scope: deliberate
CONTEXT:  SQL function "sr_tropical_paths" statement 1
ERROR:  ProvSQL: This recursion's equations put the recursive relation between factors, or on both sides of them, and the requested semiring is not commutative: its least solution is not given by the star of a value.  Write the recursive relation at the same place of every recursive FROM clause (first, or last).
DETAIL:  provsql-reason: recursion-two-sided; scope: gap
CONTEXT:  PL/pgSQL function sr_regex(anyelement,regclass) line 3 at RETURN
remove_provenance

(1 row)
n|equations
b|x₂ where x₁ = (ca ⊗ x₃ ⊗ ac) ⊕ (ab ⊗ x₂ ⊗ bc), x₂ = ca ⊗ x₃ ⊗ ab, x₃ = 𝟙 ⊕ (ac ⊗ x₁ ⊗ ca) ⊕ (bc ⊗ x₁ ⊗ ca)
(1 row)
ERROR:  ProvSQL: A HAVING condition's provenance is a product over the worlds of its group, in no order of the query: it has no value in a semiring whose multiplication does not commute.
DETAIL:  provsql-reason: having-noncommutative; scope: gap
CONTEXT:  PL/pgSQL function sr_regex(anyelement,regclass) line 3 at RETURN
remove_provenance

(1 row)