diff --git a/lib/relations/conformance.conf b/lib/relations/conformance.conf
index a2a88c9a..85d32f80 100644
--- a/lib/relations/conformance.conf
+++ b/lib/relations/conformance.conf
@@ -29,4 +29,5 @@ SUITES=(
   "fed:lib/relations/tests/fed.sx:(relations-fed-tests-run!)"
   "shape:lib/relations/tests/shape.sx:(relations-shape-tests-run!)"
   "tree:lib/relations/tests/tree.sx:(relations-tree-tests-run!)"
+  "routes:lib/relations/tests/routes.sx:(relations-routes-tests-run!)"
 )
diff --git a/lib/relations/explain.sx b/lib/relations/explain.sx
index 09369f8c..e7548f8c 100644
--- a/lib/relations/explain.sx
+++ b/lib/relations/explain.sx
@@ -69,6 +69,28 @@
 
 ;; --- current-db convenience layer ---
 
+(define
+  relations-ap-dfs
+  (fn
+    (db b kind path node)
+    (if
+      (= node b)
+      (list path)
+      (relations-concat-map
+        (fn
+          (nbr)
+          (if
+            (relations-eng-member? nbr path)
+            (list)
+            (relations-ap-dfs db b kind (append path (list nbr)) nbr)))
+        (relations-children-of db node kind)))))
+
+(define
+  relations-all-paths
+  (fn
+    (db a b kind)
+    (if (= a b) (list (list a)) (relations-ap-dfs db b kind (list a) a))))
+
 (define
   relations/path
   (fn (a b kind) (relations-path (relations-ensure-db!) a b kind)))
@@ -84,3 +106,7 @@
 (define
   relations/reachable-any?
   (fn (a b) (relations-reachable-any? (relations-ensure-db!) a b)))
+
+(define
+  relations/all-paths
+  (fn (a b kind) (relations-all-paths (relations-ensure-db!) a b kind)))
diff --git a/lib/relations/scoreboard.json b/lib/relations/scoreboard.json
index 08613c5b..413b177d 100644
--- a/lib/relations/scoreboard.json
+++ b/lib/relations/scoreboard.json
@@ -1,15 +1,16 @@
 {
   "lang": "relations",
-  "total_passed": 126,
+  "total_passed": 135,
   "total_failed": 0,
-  "total": 126,
+  "total": 135,
   "suites": [
     {"name":"direct","passed":22,"failed":0,"total":22},
     {"name":"reach","passed":24,"failed":0,"total":24},
     {"name":"path","passed":24,"failed":0,"total":24},
     {"name":"fed","passed":22,"failed":0,"total":22},
     {"name":"shape","passed":18,"failed":0,"total":18},
-    {"name":"tree","passed":16,"failed":0,"total":16}
+    {"name":"tree","passed":16,"failed":0,"total":16},
+    {"name":"routes","passed":9,"failed":0,"total":9}
   ],
-  "generated": "2026-06-07T13:07:14+00:00"
+  "generated": "2026-06-07T13:18:20+00:00"
 }
diff --git a/lib/relations/scoreboard.md b/lib/relations/scoreboard.md
index 8974ab10..44d75fd7 100644
--- a/lib/relations/scoreboard.md
+++ b/lib/relations/scoreboard.md
@@ -1,6 +1,6 @@
 # relations scoreboard
 
-**126 / 126 passing** (0 failure(s)).
+**135 / 135 passing** (0 failure(s)).
 
 | Suite | Passed | Total | Status |
 |-------|--------|-------|--------|
@@ -10,3 +10,4 @@
 | fed | 22 | 22 | ok |
 | shape | 18 | 18 | ok |
 | tree | 16 | 16 | ok |
+| routes | 9 | 9 | ok |
diff --git a/lib/relations/tests/routes.sx b/lib/relations/tests/routes.sx
new file mode 100644
index 00000000..47b31381
--- /dev/null
+++ b/lib/relations/tests/routes.sx
@@ -0,0 +1,130 @@
+;; lib/relations/tests/routes.sx — extension: all simple paths (route enumeration).
+
+(define relations-ro-pass 0)
+(define relations-ro-fail 0)
+(define relations-ro-failures (list))
+
+(define
+  relations-ro-check!
+  (fn
+    (name got expected)
+    (if
+      (= got expected)
+      (set! relations-ro-pass (+ relations-ro-pass 1))
+      (do
+        (set! relations-ro-fail (+ relations-ro-fail 1))
+        (append!
+          relations-ro-failures
+          (str name "\n    expected: " expected "\n    got:      " got))))))
+
+(define
+  relations-ro-subset?
+  (fn
+    (xs ys)
+    (cond
+      ((= (len xs) 0) true)
+      ((relations-member? (first xs) ys)
+        (relations-ro-subset? (rest xs) ys))
+      (else false))))
+
+;; Order-insensitive set equality; elements compared structurally (works for
+;; lists-of-paths since `=` is structural).
+(define
+  relations-ro-set=?
+  (fn
+    (xs ys)
+    (and
+      (= (len xs) (len ys))
+      (relations-ro-subset? xs ys)
+      (relations-ro-subset? ys xs))))
+
+;; Diamond + branch + a cycle with an exit.
+;;   parent: a->b, a->c, b->d, c->d, b->e
+;;   member: a->z (a different kind, to test isolation)
+;;   parent cycle: g->h, h->g, h->out
+(define
+  relations-ro-fixture
+  (fn
+    ()
+    (relations-build-db
+      (list
+        (relations-rel (quote a) (quote b) (quote parent))
+        (relations-rel (quote a) (quote c) (quote parent))
+        (relations-rel (quote b) (quote d) (quote parent))
+        (relations-rel (quote c) (quote d) (quote parent))
+        (relations-rel (quote b) (quote e) (quote parent))
+        (relations-rel (quote a) (quote z) (quote member))
+        (relations-rel (quote g) (quote h) (quote parent))
+        (relations-rel (quote h) (quote g) (quote parent))
+        (relations-rel (quote h) (quote out) (quote parent))))))
+
+(define
+  relations-ro-run-all!
+  (fn
+    ()
+    (let
+      ((db (relations-ro-fixture)))
+      (do
+        (relations-ro-check!
+          "two routes a->d"
+          (relations-ro-set=?
+            (relations-all-paths db (quote a) (quote d) (quote parent))
+            (list
+              (list (quote a) (quote b) (quote d))
+              (list (quote a) (quote c) (quote d))))
+          true)
+        (relations-ro-check!
+          "single route a->e"
+          (relations-all-paths db (quote a) (quote e) (quote parent))
+          (list (list (quote a) (quote b) (quote e))))
+        (relations-ro-check!
+          "no route -> empty"
+          (relations-all-paths db (quote a) (quote zzz) (quote parent))
+          (list))
+        (relations-ro-check!
+          "self route is the singleton path"
+          (relations-all-paths db (quote a) (quote a) (quote parent))
+          (list (list (quote a))))
+        (relations-ro-check!
+          "route through a cycle terminates"
+          (relations-all-paths db (quote g) (quote out) (quote parent))
+          (list (list (quote g) (quote h) (quote out))))
+        (relations-ro-check!
+          "route count a->d is 2"
+          (len (relations-all-paths db (quote a) (quote d) (quote parent)))
+          2)
+        (relations-ro-check!
+          "kind isolation: no parent route to member target"
+          (relations-all-paths db (quote a) (quote z) (quote parent))
+          (list))
+        (relations-ro-check!
+          "member route a->z"
+          (relations-all-paths db (quote a) (quote z) (quote member))
+          (list (list (quote a) (quote z))))
+        (do
+          (relations/load!
+            (list
+              (relations-rel (quote p) (quote q) (quote parent))
+              (relations-rel (quote p) (quote r) (quote parent))
+              (relations-rel (quote q) (quote s) (quote parent))
+              (relations-rel (quote r) (quote s) (quote parent))))
+          (relations-ro-check!
+            "api all-paths two routes p->s"
+            (relations-ro-set=?
+              (relations/all-paths (quote p) (quote s) (quote parent))
+              (list
+                (list (quote p) (quote q) (quote s))
+                (list (quote p) (quote r) (quote s))))
+            true)
+          (relations/load! (list)))))))
+
+(define
+  relations-routes-tests-run!
+  (fn
+    ()
+    (do
+      (set! relations-ro-pass 0)
+      (set! relations-ro-fail 0)
+      (set! relations-ro-failures (list))
+      (relations-ro-run-all!)
+      {:failures relations-ro-failures :total (+ relations-ro-pass relations-ro-fail) :passed relations-ro-pass :failed relations-ro-fail})))
diff --git a/plans/relations-on-sx.md b/plans/relations-on-sx.md
index 768a69bc..c73e2363 100644
--- a/plans/relations-on-sx.md
+++ b/plans/relations-on-sx.md
@@ -18,7 +18,7 @@ links. Reuses `lib/datalog/` — does not reimplement the engine.
 
 ## Status (rolling)
 
-`bash lib/relations/conformance.sh` → **126/126** (Phases 1–4 complete + extensions)
+`bash lib/relations/conformance.sh` → **135/135** (Phases 1–4 complete + extensions)
 
 ## Ground rules
 
@@ -108,9 +108,18 @@ lib/relations/federation.sx
   (lowest common ancestors — a set; tree → singleton, DAG → may be several),
   `topo-order` (Kahn-style; nil for cyclic kinds). New `lib/relations/tree.sx`,
   computed in SX over `reach`/`ancestors`/`rnode`. `lib/relations/tests/tree.sx`.
+- [x] **route enumeration** — `all-paths` (all simple directed paths a→b, not just
+  the shortest; cycle-safe DFS) in explain.sx. `lib/relations/tests/routes.sx`.
 
 ## Progress log
 
+- **Extension: route enumeration** (135/135). `relations-all-paths(db,a,b,kind)`
+  in explain.sx — every simple (no repeated node) directed path a→b, not just the
+  shortest one `relations-path` returns; DFS that skips nodes already on the
+  current path so cyclic data terminates; a=b → `((a))`, no route → `()`. Reuses
+  engine's `relations-concat-map`/`-eng-member?`/`children-of`. + `relations/all-paths`
+  wrapper, `lib/relations/tests/routes.sx` (9 tests: two-route diamond, single
+  route, no route, self, route-through-cycle, route count, kind isolation).
 - **Extension: tree/DAG queries** (126/126). New `lib/relations/tree.sx`:
   `relations-common-ancestors` (intersection of the two ancestor sets),
   `relations-lca` (common ancestors with no other common ancestor reachable below