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+(* This example, checks the efficiency of the abstract machine used by ring *)
+(* Expected time < 1.00s *)
+
+Require Import BinInt.
+
+Definition Zplus x y :=
+match x with
+| 0%Z => y
+| Zpos x' =>
+    match y with
+    | 0%Z => x
+    | Zpos y' => Zpos (x' + y')
+    | Zneg y' =>
+        match (x' ?= y')%positive Eq with
+        | Eq => 0%Z
+        | Lt => Zneg (y' - x')
+        | Gt => Zpos (x' - y')
+        end
+    end
+| Zneg x' =>
+    match y with
+    | 0%Z => x
+    | Zpos y' =>
+        match (x' ?= y')%positive Eq with
+        | Eq => 0%Z
+        | Lt => Zpos (y' - x')
+        | Gt => Zneg (x' - y')
+        end
+    | Zneg y' => Zneg (x' + y')
+    end
+end.
+
+Require Import Ring.
+
+Lemma Zth : ring_theory Z0 (Zpos xH) Zplus Zmult Zminus Zopp (@eq Z).
+Admitted.
+
+Ltac Zcst t :=
+  match isZcst t with
+    true => t
+  | _ => constr:NotConstant
+  end.
+
+Add Ring Zr : Zth
+  (decidable Zeqb_ok, constants [Zcst]).
+
+Open Scope Z_scope.
+Infix "+" := Zplus : Z_scope.
+
+Goal forall a, a+a+a+a+a+a+a+a+a+a+a+a+a = a*13.
+Time intro; ring.