diff --git a/_CoqProject b/_CoqProject
index 705f33879afcca438575c20230182e71dbda58fb..dc9ec33770ae3d4d57e94526b20352919f5ddff6 100644
--- a/_CoqProject
+++ b/_CoqProject
@@ -45,4 +45,5 @@ theories/logrel/examples/rec_subtyping.v
 theories/logrel/examples/choice_subtyping.v
 theories/logrel/examples/mapper.v
 theories/logrel/examples/mapper_list.v
-theories/logrel/examples/compute_list_par.v
\ No newline at end of file
+theories/logrel/examples/compute_service.v
+theories/logrel/examples/compute_client_list.v
\ No newline at end of file
diff --git a/theories/logrel/examples/compute_list_par.v b/theories/logrel/examples/compute_client_list.v
similarity index 85%
rename from theories/logrel/examples/compute_list_par.v
rename to theories/logrel/examples/compute_client_list.v
index 78a5b794572aca0bab957e7540fd231ce2f3c902..eb02d4eab61d811956e7fb6f6062aa07f4647da9 100644
--- a/theories/logrel/examples/compute_list_par.v
+++ b/theories/logrel/examples/compute_client_list.v
@@ -5,16 +5,7 @@ From actris.channel Require Import proofmode proto channel.
 From actris.logrel Require Import term_typing_rules session_typing_rules
      subtyping_rules napp.
 From actris.logrel.lib Require Import par_start.
-
-Definition cont : Z := 1.
-Definition stop : Z := 2.
-
-Definition compute_service : val :=
-  rec: "go" "c":=
-    branch [cont;stop] "c"
-    (λ: "c", let: "v" := recv "c" in
-             send "c" ("v" #());; "go" "c")
-    (λ: "c", #()).
+From actris.logrel.examples Require Import compute_service.
 
 Definition send_all_par : val :=
   rec: "go" "c" "xs" "lk" "counter" :=
@@ -62,58 +53,6 @@ Section compute_example.
   Context `{heapG Σ, chanG Σ, lockG Σ, spawnG Σ}.
   Context `{!inG Σ fracR}.
 
-  Definition compute_type_service_aux (rec : lsty Σ) : lsty Σ :=
-    lty_branch $ <[cont := (<?? A> TY () ⊸ A; <!!> TY A ; rec)%lty]> $
-                 <[stop := END%lty]> $ ∅.
-  Instance mapper_type_rec_service_contractive :
-    Contractive (compute_type_service_aux).
-  Proof. solve_proto_contractive. Qed.
-  Definition compute_type_service : lsty Σ :=
-    lty_rec (compute_type_service_aux).
-
-  (** This judgement is checked only with the typing rules of the type system *)
-  Lemma ltyped_compute_service Γ :
-    ⊢ Γ ⊨ compute_service : lty_chan compute_type_service ⊸ () ⫤ Γ.
-  Proof.
-    iApply (ltyped_subsumption _ _ _ _ _ _
-              (lty_chan compute_type_service → ())%lty);
-      [ iApply env_le_refl | iApply lty_le_copy_elim | iApply env_le_refl | ].
-    iApply ltyped_val_ltyped.
-    iApply ltyped_val_rec.
-    iApply ltyped_post_nil.
-    iApply ltyped_app.
-    { iApply (ltyped_lam []). iApply ltyped_post_nil. iApply ltyped_unit. }
-    iApply (ltyped_app _ _ _ _ _
-              (chan (<?? A> TY () ⊸ A; <!!> TY A; compute_type_service) ⊸ ())%lty).
-    {
-      simpl.
-      iApply (ltyped_lam [EnvItem "go" _]).
-      iApply ltyped_post_nil.
-      iApply ltyped_recv_texist; [ done | apply _ | ].
-      iIntros (Ys).
-      pose proof (ltys_S_inv Ys) as [A [Ys' HYs]].
-      pose proof (ltys_O_inv Ys') as HYs'.
-      rewrite HYs HYs' /=.
-      iApply ltyped_seq.
-      { iApply (ltyped_send _ [EnvItem "v" _; EnvItem "c" _; EnvItem "go" _]);
-          [ done | ].
-        iApply ltyped_app; [ by iApply ltyped_unit | ]=> /=.
-        by iApply ltyped_var. }
-      simpl.
-      iApply ltyped_app; [ by iApply ltyped_var | ].
-      simpl. rewrite !(Permutation_swap (EnvItem "go" _)).
-      iApply ltyped_subsumption; [ | | iApply env_le_refl | ].
-      { iApply env_le_cons; [ iApply lty_le_refl | iApply env_le_nil ]. }
-      { iApply lty_le_copy_elim. }
-      by iApply ltyped_var. }
-    iApply ltyped_app; [ by iApply ltyped_var | ].
-    iApply ltyped_subsumption; [ iApply env_le_nil | | iApply env_le_refl | ].
-    { iApply lty_le_arr; [ | iApply lty_le_refl ]. iApply lty_le_chan.
-      iApply lty_le_l; [ iApply lty_le_rec_unfold | iApply lty_le_refl ]. }
-    rewrite /compute_type_service_aux.
-    iApply ltyped_branch. intros x. rewrite -elem_of_dom. set_solver.
-  Qed.
-
   Definition compute_type_client_aux (A : ltty Σ) (rec : lsty Σ) : lsty Σ :=
     lty_select $ <[cont := (<!!> TY () ⊸ A; <??> TY A ; rec)%lty]> $
                  <[stop := END%lty]>∅.
@@ -425,7 +364,7 @@ Section compute_example.
       iSplit=> //. iApply lty_le_l; [ iApply lty_le_dual_end | iApply lty_le_refl ].
   Qed.
 
-  Lemma ltyped_compute_prog A e Γ Γ' :
+  Lemma ltyped_compute_list_par A e Γ Γ' :
     (Γ ⊨ e : ref_uniq (lty_list (() ⊸ A)) ⫤ Γ') -∗
     Γ ⊨ par_start (compute_service) (compute_client e) :
       (() * (ref_uniq (lty_list A))) ⫤ Γ'.
diff --git a/theories/logrel/examples/compute_service.v b/theories/logrel/examples/compute_service.v
new file mode 100644
index 0000000000000000000000000000000000000000..8384ee91ce3262e7192e05a12aaebec16bc0bf13
--- /dev/null
+++ b/theories/logrel/examples/compute_service.v
@@ -0,0 +1,74 @@
+From iris.algebra Require Import frac.
+From iris.heap_lang Require Import metatheory.
+From actris.utils Require Import llist.
+From actris.channel Require Import proofmode proto channel.
+From actris.logrel Require Import term_typing_rules session_typing_rules
+     subtyping_rules napp.
+From actris.logrel.lib Require Import par_start.
+
+Definition cont : Z := 1.
+Definition stop : Z := 2.
+
+Definition compute_service : val :=
+  rec: "go" "c":=
+    branch [cont;stop] "c"
+    (λ: "c", let: "v" := recv "c" in
+             send "c" ("v" #());; "go" "c")
+    (λ: "c", #()).
+ 
+Section compute_example.
+  Context `{heapG Σ, chanG Σ, spawnG Σ}.
+
+  Definition compute_type_service_aux (rec : lsty Σ) : lsty Σ :=
+    lty_branch $ <[cont := (<?? A> TY () ⊸ A; <!!> TY A ; rec)%lty]> $
+                 <[stop := END%lty]> $ ∅.
+  Instance mapper_type_rec_service_contractive :
+    Contractive (compute_type_service_aux).
+  Proof. solve_proto_contractive. Qed.
+  Definition compute_type_service : lsty Σ :=
+    lty_rec (compute_type_service_aux).
+
+  (** This judgement is checked only with the typing rules of the type system *)
+  Lemma ltyped_compute_service Γ :
+    ⊢ Γ ⊨ compute_service : lty_chan compute_type_service ⊸ () ⫤ Γ.
+  Proof.
+    iApply (ltyped_subsumption _ _ _ _ _ _
+              (lty_chan compute_type_service → ())%lty);
+      [ iApply env_le_refl | iApply lty_le_copy_elim | iApply env_le_refl | ].
+    iApply ltyped_val_ltyped.
+    iApply ltyped_val_rec.
+    iApply ltyped_post_nil.
+    iApply ltyped_app.
+    { iApply (ltyped_lam []). iApply ltyped_post_nil. iApply ltyped_unit. }
+    iApply (ltyped_app _ _ _ _ _
+              (chan (<?? A> TY () ⊸ A; <!!> TY A; compute_type_service) ⊸ ())%lty).
+    {
+      simpl.
+      iApply (ltyped_lam [EnvItem "go" _]).
+      iApply ltyped_post_nil.
+      iApply ltyped_recv_texist; [ done | apply _ | ].
+      iIntros (Ys).
+      pose proof (ltys_S_inv Ys) as [A [Ys' HYs]].
+      pose proof (ltys_O_inv Ys') as HYs'.
+      rewrite HYs HYs' /=.
+      iApply ltyped_seq.
+      { iApply (ltyped_send _ [EnvItem "v" _; EnvItem "c" _; EnvItem "go" _]);
+          [ done | ].
+        iApply ltyped_app; [ by iApply ltyped_unit | ]=> /=.
+        by iApply ltyped_var. }
+      simpl.
+      iApply ltyped_app; [ by iApply ltyped_var | ].
+      simpl. rewrite !(Permutation_swap (EnvItem "go" _)).
+      iApply ltyped_subsumption; [ | | iApply env_le_refl | ].
+      { iApply env_le_cons; [ iApply lty_le_refl | iApply env_le_nil ]. }
+      { iApply lty_le_copy_elim. }
+      by iApply ltyped_var. }
+    iApply ltyped_app; [ by iApply ltyped_var | ].
+    iApply ltyped_subsumption; [ iApply env_le_nil | | iApply env_le_refl | ].
+    { iApply lty_le_arr; [ | iApply lty_le_refl ]. iApply lty_le_chan.
+      iApply lty_le_l; [ iApply lty_le_rec_unfold | iApply lty_le_refl ]. }
+    rewrite /compute_type_service_aux.
+    iApply ltyped_branch. intros x. rewrite -elem_of_dom. set_solver.
+  Qed.
+
+End compute_example.