diff --git a/demo.modal b/demo.modal
index aa62b1b..abf0af4 100644
--- a/demo.modal
+++ b/demo.modal
@@ -35,15 +35,6 @@
 <> (reverse' ?a ()) (?a)
 <> (reverse' ?a (?h ?t)) (reverse' (?h ?a) ?t)
 
--- ( normalize, remove trailing zeros )
--- ( currently zero is (0 ()) though arguably it could be () )
--- ( that change would require auditing our rules )
-<> (normalize (?h ?t)) ((?h normalize' () ?t))
-<> (normalize' ?s ()) (())
-<> (normalize' ?s (0 ?t)) (normalize' (0 ?s) ?t)
-<> (normalize' () (1 ?t)) ((1 normalize' () ?t))
-<> (normalize' (0 ?s) (1 ?t)) ((0 normalize' ?s (1 ?t)))
-
 -- ( to integer )
 <> ((int ?*)) ((sum f (one) g reverse (?*)))
 <> (g ()) (())
@@ -123,20 +114,21 @@
 <> (mulc ?t (1 ?x) ?y) (mulc (?y ?t) ?x (0 ?y))
 
 -- ( subtraction )
-<> ((sub ?x ?y)) (normalize subc 0 ?x ?y)
-<> (subc 0 () ()) (())
-<> (subc 1 () ()) (#err)
-<> (subc 0 ?x ()) (?x)
-<> (subc 1 ?x ()) (subc 1 ?x (0 ()))
-<> (subc ?c () ?y) (subc ?c (0 ()) ?y)
-<> (subc 0 (0 ?x) (0 ?y)) ((0 subc 0 ?x ?y))
-<> (subc 0 (0 ?x) (1 ?y)) ((1 subc 1 ?x ?y))
-<> (subc 0 (1 ?x) (0 ?y)) ((1 subc 0 ?x ?y))
-<> (subc 0 (1 ?x) (1 ?y)) ((0 subc 0 ?x ?y))
-<> (subc 1 (0 ?x) (0 ?y)) ((1 subc 1 ?x ?y))
-<> (subc 1 (0 ?x) (1 ?y)) ((0 subc 1 ?x ?y))
-<> (subc 1 (1 ?x) (0 ?y)) ((0 subc 0 ?x ?y))
-<> (subc 1 (1 ?x) (1 ?y)) ((1 subc 1 ?x ?y))
+<> ((sub ?x ?y)) (sub1 0 ?x ?y ())
+<> (sub1 0 () () ?s) (())
+<> (sub1 1 () () ?s) (#err)
+<> (sub1 ?c ?x () ?s) (sub1 ?c ?x (0 ()) ?s)
+<> (sub1 ?c () ?y ?s) (sub1 ?c (0 ()) ?y ?s)
+<> (sub1 0 (0 ?x) (0 ?y) ?s) (sub1 0 ?x ?y (0 ?s))
+<> (sub1 0 (0 ?x) (1 ?y) ?s) (sub2 1 ?x ?y ?s)
+<> (sub1 0 (1 ?x) (0 ?y) ?s) (sub2 0 ?x ?y ?s)
+<> (sub1 0 (1 ?x) (1 ?y) ?s) (sub1 0 ?x ?y (0 ?s))
+<> (sub1 1 (0 ?x) (0 ?y) ?s) (sub2 1 ?x ?y ?s)
+<> (sub1 1 (0 ?x) (1 ?y) ?s) (sub1 1 ?x ?y (0 ?s))
+<> (sub1 1 (1 ?x) (0 ?y) ?s) (sub1 0 ?x ?y (0 ?s))
+<> (sub1 1 (1 ?x) (1 ?y) ?s) (sub2 1 ?x ?y ?s)
+<> (sub2 ?c ?x ?y ()) ((1 sub1 ?c ?x ?y ()))
+<> (sub2 ?c ?x ?y (?h ?t)) ((0 sub2 ?c ?x ?y ?t))
 
 <> (dec (0 ())) (#err)
 <> (dec (1 ())) ((0 ()))
@@ -197,4 +189,4 @@
 <> ((mod' (?q ?r))) (?r)
 
 -- (bstr (mul (int 2399) (int 3499)))
-(str (int 1234567890))
+(str (int 1234567))