\set ECHO none
add_provenance

(1 row)
create_provenance_mapping

(1 row)
create_provenance_mapping

(1 row)
remove_provenance

(1 row)
src|dst|cost|path
a|a|4|{ac,ca}
a|c|3|{ab,bc}
b|a|2|{bc,ca}
c|b|1|{ca,ab}
c|c|4|{ca,ac}
(5 rows)
remove_provenance

(1 row)
n|cost|path
a|0|{}
b|1|{ab}
c|3|{ab,bc}
(3 rows)
remove_provenance

(1 row)
n|cost|path
a|0|{}
b|1|{ab}
c|3|{bc,ab}
(3 rows)
remove_provenance

(1 row)
n|cost|path
a|0|{}
b|1|{ca,ab}
c|4|{ca,ac}
(3 rows)
remove_provenance

(1 row)
remove_provenance

(1 row)
remove_provenance

(1 row)
n|cost|path
a|0|{}
b|1|{ab}
c|3|{ac}
d|1|{x1}
(4 rows)
remove_provenance

(1 row)
dst|cost|path
a|0|{ca}
b|1|{ab}
c|Infinity|
d|1|{x1}
(4 rows)
remove_provenance

(1 row)
l1|l2|cost|path
ab|bc|3|{ab,bc}
ab||1|{ab}
(2 rows)
remove_provenance

(1 row)
lbl|cost|path
ac|Infinity|
(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:  SQL function "sr_best_path" statement 1
ERROR:  ProvSQL: The wrapped sub-circuit only represents the absorptive quotient of a recursive query's provenance (fixpoint truncation or compiled reachability circuit), whose products are not in the order of the query, and the requested semiring is not commutative.  Re-run the query under the 'semiring' provenance class.
DETAIL:  provsql-reason: absorptive-noncommutative; scope: gap
CONTEXT:  SQL function "sr_best_path" statement 1
ERROR:  ProvSQL: sr_best_path requires nonnegative costs: with a negative one, the empty derivation is no longer the best, and a cycle may improve a derivation without end.
DETAIL:  provsql-reason: semiring-negative-cost; scope: deliberate
CONTEXT:  SQL function "sr_best_path" statement 1
remove_provenance

(1 row)