Many-to-many relationship types that do not have additional attributes

with keys as (select 
(select nspname from pg_namespace where oid=c.relnamespace) as key_schema,
c.relname as key_table, 
c.oid as key_table_oid,
o.conkey AS key_col
from pg_constraint o inner join pg_class c on c.oid = o.conrelid
where o.contype in ('u', 'p') and cardinality(o.conkey)=1),
keys_unnest as (select key_schema, key_table, key_table_oid, key_col, key_col_num, ordin
from keys, unnest(keys.key_col) with ordinality as k(key_col_num, ordin)),
keys_with_names AS (select key_schema AS table_schema, key_table AS table_name, a_key.attname AS column_name
from keys_unnest k inner join pg_attribute a_key on k.key_col_num = a_key.attnum and k.key_table_oid = a_key.attrelid and a_key.attisdropped = false
),
fk as (select 
(select nspname from pg_namespace where oid=c.relnamespace) as key_schema,
c.relname as key_table, 
c.oid as key_table_oid,
o.conkey AS key_col
from pg_constraint o inner join pg_class c on c.oid = o.conrelid
where o.contype='f'),
fk_unnest as (select key_schema, key_table, key_table_oid, key_col, key_col_num, ordin
from fk, unnest(fk.key_col) with ordinality as k(key_col_num, ordin)),
fk_with_names AS (select key_schema AS table_schema, key_table AS table_name, a_key.attname AS column_name
from fk_unnest k inner join pg_attribute a_key on k.key_col_num = a_key.attnum and k.key_table_oid = a_key.attrelid and a_key.attisdropped = false),
key_not_fk AS (select table_schema, table_name, column_name
from keys_with_names
except select table_schema, table_name, column_name
from fk_with_names),
surrogate_key AS (SELECT c.table_schema, c.table_name , c.column_name
FROM information_schema.columns c
LEFT JOIN information_schema.domains d USING (domain_schema, domain_name)
INNER JOIN information_schema.schemata s
ON c.table_schema=s.schema_name
WHERE  (coalesce (c.column_default, d.domain_default) ILIKE '%nextval%'  OR c.is_identity='YES')
AND c.data_type IN ('smallint','integer','bigint')
AND (c.table_schema = 'public'
OR s.schema_owner<>'postgres')
AND EXISTS (SELECT *
FROM key_not_fk AS k
WHERE k.table_schema=c.table_schema
AND k.table_name=c.table_name
AND k.column_name=c.column_name)),
allowed_cols AS (SELECT table_schema, table_name, column_name
FROM surrogate_key
UNION SELECT table_schema, table_name, column_name
FROM fk_with_names),
allowed_cols_grouped AS (SELECT table_schema, table_name, string_agg(column_name, ',' ORDER BY column_name) AS columns
FROM allowed_cols
GROUP BY table_schema, table_name),
at_least_two_fk as (select n.nspname as table_schema, c.relname as table_name
from pg_constraint o inner join pg_class c on c.oid = o.conrelid
inner join pg_namespace as n on n.oid=c.relnamespace
where o.contype = 'f'
group by n.nspname, c.relname
having count(*)>1),
potential_tables AS (SELECT table_schema, table_name, string_agg(column_name, ',' ORDER BY column_name) AS columns
FROM INFORMATION_SCHEMA.columns AS c
WHERE (table_schema, table_name) IN (SELECT table_schema, table_name
FROM INFORMATION_SCHEMA.tables
WHERE table_type='BASE TABLE')
AND table_schema NOT IN (SELECT schema_name
FROM INFORMATION_SCHEMA.schemata
WHERE schema_name<>'public' AND
schema_owner='postgres' AND schema_name IS NOT NULL)
AND (table_schema, table_name) IN (SELECT table_schema, table_name
FROM  at_least_two_fk)
GROUP BY table_schema, table_name)
SELECT potential_tables.* , EXISTS (SELECT * FROM INFORMATION_SCHEMA.table_constraints AS tc
WHERE tc.table_schema=potential_tables.table_schema 
AND tc.table_name=potential_tables.table_name
AND tc.constraint_type IN ('PRIMARY KEY','UNIQUE')) AS has_key 
FROM potential_tables INNER JOIN allowed_cols_grouped USING (table_schema, table_name, columns)
ORDER BY table_schema, table_name;