Remove petri net examples; add population protocol examples

examples/broadcast.pp

+population protocol "Broadcast Protocol" {
+    states { true false}
+    transitions { x_false_true }
+    arcs {
+       { false, true } -> x_false_true -> { true, true }
+    }
+    initial { true false }
+    yes { true }
+    no { false }
+}

examples/dekkers.pnet

-/*
-
-    //flag[] is boolean array; and turn is an integer
-    flag[1] = false
-    flag[2] = false
-    turn    = 1   // or 2
-
-P1:
-p1:flag[1] = true;
-p2:while (flag[2] == true) {
-p3:   if (turn ≠ 1) {
-p4:      flag[1] = false;
-p5:      while (turn ≠ 1) {
-           // busy wait
-         }
-p6:      flag[1] = true;
-      }
-   }
-
-p7:// critical section
-   ...
-   turn    = 2;
-p8:flag[1] = false;
-   // remainder section
-
-
-
-P2:
-q1:flag[2] = true;
-q2:while (flag[1] == true) {
-q3:   if (turn ≠ 2) {
-q4:      flag[2] = false;
-q5:      while (turn ≠ 2) {
-           // busy wait
-         }
-q6:      flag[2] = true;
-      }
-   }
-
-q7:// critical section
-   ...
-   turn    = 1;
-q8:flag[2] = false;
-   // remainder section
-
-*/
-petri net "Dekker's algorithm" {
-    places {
-        p1 p2 p3 p4 p5 p6 p7 p8
-        q1 q2 q3 q4 q5 q6 q7 q8
-        flag1t flag1f flag2t flag2f turn1 turn2
-    }
-    transitions {
-        u1 u2 u3 u4 u5 u6 u7 u8 u9 u10 u11 u12
-        v1 v2 v3 v4 v5 v6 v7 v8 v9 v10 v11 v12
-    }
-    arcs {
-        { p1 flag1f } -> u1  -> { p2 flag1t }
-        { p2 flag2f } -> u2  -> { p7 flag2f }
-        { p2 flag2t } -> u3  -> { p3 flag2t }
-        { p3 turn1  } -> u4  -> { p2 turn1  }
-        { p3 turn2  } -> u5  -> { p4 turn2  }
-        { p4 flag1t } -> u6  -> { p5 flag1f }
-        { p5 turn1  } -> u7  -> { p6 turn1  }
-        { p5 turn2  } -> u8  -> { p5 turn2  }
-        { p6 flag1f } -> u9  -> { p2 flag1t }
-        { p7 turn1  } -> u10 -> { p8 turn2  }
-        { p7 turn2  } -> u11 -> { p8 turn2  }
-        { p8 flag1t } -> u12 -> { p1 flag1f }
-
-        { q1 flag2f } -> v1  -> { q2 flag2t }
-        { q2 flag1f } -> v2  -> { q7 flag1f }
-        { q2 flag1t } -> v3  -> { q3 flag1t }
-        { q3 turn1  } -> v4  -> { q4 turn1  }
-        { q3 turn2  } -> v5  -> { q2 turn2  }
-        { q4 flag2t } -> v6  -> { q5 flag2f }
-        { q5 turn1  } -> v7  -> { q5 turn1  }
-        { q5 turn2  } -> v8  -> { q6 turn2  }
-        { q6 flag2f } -> v9  -> { q2 flag2t }
-        { q7 turn1  } -> v10 -> { q8 turn1  }
-        { q7 turn2  } -> v11 -> { q8 turn1  }
-        { q8 flag2t } -> v12 -> { q1 flag2f }
-    }
-    initial {
-        p1 q1 flag1f flag2f turn1
-    }
-}
-liveness property "fairness for first process" {
-    u1 + u2 + u3 + u4 + u5 + u6 + u7 + u8 + u9 + u10 + u11 + u12 > 0 &&
-    v1 + v2 + v3 + v4 + v5 + v6 + v7 + v8 + v9 + v10 + v11 + v12 > 0 &&
-    u2 = 0
-}
-liveness property "fairness for second process" {
-    u1 + u2 + u3 + u4 + u5 + u6 + u7 + u8 + u9 + u10 + u11 + u12 > 0 &&
-    v1 + v2 + v3 + v4 + v5 + v6 + v7 + v8 + v9 + v10 + v11 + v12 > 0 &&
-    v2 = 0
-}
-safety property "mutual exclusion" {
-    p7 >= 1 && q7 >= 1
-}

examples/free_choice.pnet

-petri net "Free Choice" {
-    places {
-        s r
-    }
-    transitions {
-        t u
-    }
-    arcs {
-        s -> t
-        r -> t
-        s -> u
-        r -> u
-    }
-    initial {
-        s r
-    }
-}

examples/h_fairly_terminates.pnet

-/*
-Consider the following asynchronous program:
-
-x = true;
-
-h() {
-  if (x) {
-    post h();
-    post g();
-  }
-}
-
-g() {
-  x = false;
-}
-
-init: h()
-
-The Petri net in this file emulates the execution of the program.
-*/
-petri net "asynchronous program" {
-    places {
-        // State
-        x not_x
-
-        // Scheduler
-        scheduler
-
-        // Handlers
-        h g
-
-        // Pending instances
-        pending_h pending_g
-    }
-    transitions {
-        dh dg ht hf gt gf
-    }
-    arcs {
-        // Dispatch h
-        { scheduler, pending_h } -> dh -> h
-
-        // Dispatch g
-        { scheduler, pending_g } -> dg -> g
-
-        // Exit h if x == true
-        { h, x } -> ht -> { x, pending_h, pending_g, scheduler }
-
-        // Exit h if x == false
-        { h, not_x } -> hf -> { not_x, scheduler }
-
-        // Exit g if x == true
-        { g, x } -> gt -> { not_x, scheduler }
-
-        // Exit g if x == false
-        { g, not_x } -> gf -> { not_x, scheduler }
-    }
-    initial {
-        // Initially, x is true, there's one pending instance of h(),
-        // and the scheduler has control.
-        x pending_h scheduler
-    }
-}
-safety property {
-    x >= 1 && not_x >= 1
-}
-liveness property "fair termination" {
-    dh >= 1 && dg >= 1
-}
-liveness property "h dispatched" {
-    dh = 0
-}

examples/h_fairly_terminates.pnet.terminating

-PLACE 'sigma,'m1,'m2,x,not_x,scheduler,h,g,pending_h,pending_g,'x,'not_x,'scheduler,'h,'g,'pending_h,'pending_g,dg_out,dh_out;
-
-MARKING 'm1:1,'pending_h:1,'scheduler:1,'x:1,pending_h:1,scheduler:1,x:1;
-
-TRANSITION 'switch
-CONSUME 'm1:1;
-PRODUCE 'm2:1;
-
-TRANSITION dh
-CONSUME 'scheduler:1,'pending_h:1,scheduler:1,pending_h:1,'m1:1;
-PRODUCE 'h:1,h:1,'m1:1;
-
-TRANSITION 'dh
-CONSUME 'scheduler:1,'pending_h:1,'m2:1;
-PRODUCE 'h:1,'sigma:1,'m2:1,dh_out:1;
-
-TRANSITION dg
-CONSUME 'scheduler:1,'pending_g:1,scheduler:1,pending_g:1,'m1:1;
-PRODUCE 'g:1,g:1,'m1:1;
-
-TRANSITION 'dg
-CONSUME 'scheduler:1,'pending_g:1,'m2:1;
-PRODUCE 'g:1,'sigma:1,'m2:1,dg_out:1;
-
-TRANSITION ht
-CONSUME 'h:1,'x:1,h:1,x:1,'m1:1;
-PRODUCE 'x:1,'pending_h:1,'pending_g:1,'scheduler:1,x:1,pending_h:1,pending_g:1,scheduler:1,'m1:1;
-
-TRANSITION 'ht
-CONSUME 'h:1,'x:1,'m2:1;
-PRODUCE 'x:1,'pending_h:1,'pending_g:1,'scheduler:1,'sigma:1,'m2:1;
-
-TRANSITION hf
-CONSUME 'h:1,'not_x:1,h:1,not_x:1,'m1:1;
-PRODUCE 'not_x:1,'scheduler:1,not_x:1,scheduler:1,'m1:1;
-
-TRANSITION 'hf
-CONSUME 'h:1,'not_x:1,'m2:1;
-PRODUCE 'not_x:1,'scheduler:1,'sigma:1,'m2:1;
-
-TRANSITION gt
-CONSUME 'g:1,'x:1,g:1,x:1,'m1:1;
-PRODUCE 'not_x:1,'scheduler:1,not_x:1,scheduler:1,'m1:1;
-
-TRANSITION 'gt
-CONSUME 'g:1,'x:1,'m2:1;
-PRODUCE 'not_x:1,'scheduler:1,'sigma:1,'m2:1;
-
-TRANSITION gf
-CONSUME 'g:1,'not_x:1,g:1,not_x:1,'m1:1;
-PRODUCE 'not_x:1,'scheduler:1,not_x:1,scheduler:1,'m1:1;
-
-TRANSITION 'gf
-CONSUME 'g:1,'not_x:1,'m2:1;
-PRODUCE 'not_x:1,'scheduler:1,'sigma:1,'m2:1;

examples/h_fairly_terminates.pnet.terminating.sara

-PROBLEM termination_by_reachability:
-GOAL REACHABILITY;
-FILE h_fairly_terminates.pnet.terminating TYPE LOLA;
-INITIAL 'm1:1,'pending_h:1,'scheduler:1,'x:1,pending_h:1,scheduler:1,x:1;
-FINAL COVER;
-CONSTRAINTS 'sigma>1,dh_out>1,dg_out>1,'x+-1x>0,'not_x+-1not_x>0,'scheduler+-1scheduler>0,'h+-1h>0,'g+-1g>0,'pending_h+-1pending_h>0,'pending_g+-1pending_g>0;

examples/h_fairly_terminates.pnet.terminating.task1

-EF ('sigma >= 1 AND dh_out >= 1 AND dg_out >= 1 AND ('x - x) >= 0 AND ('not_x - not_x) >= 0 AND ('scheduler - scheduler) >= 0 AND ('h - h) >= 0 AND ('g - g) >= 0 AND ('pending_h - pending_h) >= 0 AND ('pending_g - pending_g) >= 0)

examples/h_fairly_terminates_by_reachability.pnet

-petri net "asynchronous program" {
-    places {
-        // State
-        x not_x x_ not_x_
-
-        // Scheduler
-        scheduler scheduler_
-
-        // Handlers
-        h g h_ g_
-
-        // Pending instances
-        pending_h pending_g pending_h_ pending_g_
-
-        m1 m2 dh_out dg_out
-    }
-    transitions {
-        dh dg ht hf gt gf
-        dh_ dg_ ht_ hf_ gt_ gf_
-        switch
-    }
-    arcs {
-        // Dispatch h
-        { scheduler, pending_h, scheduler_, pending_h_, m1 } -> dh -> { h, h_, m1 }
-        { scheduler_, pending_h_, m2 } -> dh_ -> { h_, m2, dh_out }
-
-        // Dispatch g
-        { scheduler, pending_g, scheduler_, pending_g_, m1 } -> dg -> { g, g_, m1 }
-        { scheduler_, pending_g_, m2 } -> dg_ -> { g_, m2, dg_out }
-
-        // Exit h if x == true
-        { h, x, h_, x_, m1 } -> ht -> { x, pending_h, pending_g, scheduler, x_, pending_h_, pending_g_, scheduler_, m1 }
-        { h_, x_, m2 } -> ht_ -> { x_, pending_h_, pending_g_, scheduler_, m2 }
-
-        // Exit h if x == false
-        { h, not_x, h_, not_x_, m1 } -> hf -> { not_x, scheduler, not_x_, scheduler_, m1 }
-        { h_, not_x_, m2 } -> hf_ -> { not_x_, scheduler_, m2 }
-
-        // Exit g if x == true
-        { g, x, g_, x_, m1 } -> gt -> { not_x, scheduler, not_x_, scheduler_, m1 }
-        { g_, x_, m2 } -> gt_ -> { not_x_, scheduler_, m2 }
-
-        // Exit g if x == false
-        { g, not_x, g_, not_x_, m1 } -> gf -> { not_x, scheduler, not_x_, scheduler_, m1 }
-        { g_, not_x_, m2 } -> gf_ -> { not_x_, scheduler_, m2 }
-
-        m1 -> switch -> m2
-    }
-    initial {
-        // Initially, x is true, there's one pending instance of h(),
-        // and the scheduler has control.
-        x pending_h scheduler
-        x_ pending_h_ scheduler_
-        m1
-    }
-}
-safety property "terminating" {
-    dh_out >= 1 && dg_out >= 1 &&
-    x_ >= x && not_x_ >= not_x &&
-    scheduler_ >= scheduler &&
-    h_ >= h && g_ >= g &&
-    pending_h_ >= pending_h && pending_g_ >= pending_g
-}
-

examples/lamport.lola

-PLACE
-    p1, p2, p3,         b1, nb1,
-    q1, q2, q3, q4, q5, b2, nb2;
-
-MARKING
-    p1, q1, nb1, nb2;
-
-TRANSITION s1
-    CONSUME p1, nb1;
-    PRODUCE p2,  b1;
-
-TRANSITION s2
-    CONSUME p2,  b2;
-    PRODUCE p2,  b2;
-
-TRANSITION s3
-    CONSUME p2, nb2;
-    PRODUCE p3, nb2;
-
-TRANSITION s4
-    CONSUME p3,  b1;
-    PRODUCE p1, nb1;
-
-TRANSITION t1
-    CONSUME q1, nb2;
-    PRODUCE q2,  b2;
-
-TRANSITION t2
-    CONSUME q2,  b1;
-    PRODUCE q3,  b1;
-
-TRANSITION t3
-    CONSUME q3,  b2;
-    PRODUCE q4, nb2;
-
-TRANSITION t4
-    CONSUME q4, nb1;
-    PRODUCE q1, nb1;
-
-TRANSITION t5
-    CONSUME q4,  b1;
-    PRODUCE q4,  b1;
-
-TRANSITION t6
-    CONSUME q2, nb1;
-    PRODUCE q5, nb1;
-
-TRANSITION t7
-    CONSUME q5,  b2;
-    PRODUCE q1, nb2;

examples/lamport.pnet

-petri net "Lamport's algorithm" {
-    places {
-        p1 p2 p3       b1 nb1
-        q1 q2 q3 q4 q5 b2 nb2
-    }
-    transitions {
-        s1 s2 s3 s4
-        t1 t2 t3 t4 t5 t6 t7
-    }
-    arcs {
-        { p1, nb1 } -> s1 -> { p2,  b1 }
-        { p2, nb2 } -> s2 -> { p3, nb2 }
-        { p2,  b2 } -> s3 -> { p2,  b2 }
-        { p3,  b1 } -> s4 -> { p1, nb1 }
-
-        { q1, nb2 } -> t1 -> { q2,  b2 }
-        { q2,  b1 } -> t2 -> { q3,  b1 }
-        { q3,  b2 } -> t3 -> { q4, nb2 }
-        { q4, nb1 } -> t4 -> { q1, nb1 }
-        { q4,  b1 } -> t5 -> { q4,  b1 }
-        { q2, nb1 } -> t6 -> { q5, nb1 }
-        { q5,  b2 } -> t7 -> { q1, nb2 }
-    }
-    initial {
-        p1 q1 nb1 nb2
-    }
-}
-liveness property "fairness for first process" {
-    s1 + s2 + s3 + s4 > 0 && s2 = 0 && t1 + t2 + t3 + t4 + t5 + t6 + t7 > 0
-//    && (s3 + t1 = 0 || t5 = 0 || t3 + t4 + t7 > 1) // [b2], [q4] for X = [s3,t5]
-//    && (t4 + t6 = 0 || s3 = 0 || s1 + s2 + s4 > 0) // [nb1], [p2,p3] for X = [s3,t1(2),t2,t3,t4,t5,t6,t7]
-//    && (s4 + t4 + t6 = 0 || s3 = 0 || s1 + s2 > 0) // [nb1], [p2] for X = [s3,t1(2),t2,t3,t4,t5,t6,t7]
-}
-liveness property "fairness for second process" {
-    s1 + s2 + s3 + s4 > 0 && t6 = 0 && t1 + t2 + t3 + t4 + t5 + t6 + t7 > 0
-}
-safety property "mutual exclusion" {
-    p3 >= 1 && q5 >= 1
-}

examples/lamport.tpn

-place p1 init 1;
-place p2;
-place p3;
-place b1;
-place nb1 init 1;
-place q1 init 1;
-place q2;
-place q3;
-place q4;
-place q5;
-place b2;
-place nb2 init 1;
-
-trans s1 in p1 nb1 out p2  b1;
-trans s2 in p2  b2 out p2  b2;
-trans s3 in p2 nb2 out p3 nb2;
-trans s4 in p3  b1 out p1 nb1;
-
-trans t1 in q1 nb2 out q2  b2;
-trans t2 in q2  b1 out q3  b1;
-trans t3 in q3  b2 out q4 nb2;
-trans t4 in q4 nb1 out q1 nb1;
-trans t5 in q4  b1 out q4  b1;
-trans t6 in q2 nb1 out q5 nb1;
-trans t7 in q5  b2 out q1 nb2;

examples/lamport_orig.pnet

-petri net "Lamport's algorithm" {
-    places {
-        p1 p2 p3       b1 nb1
-        q1 q2 q3 q4 q5    nb2
-    }
-    transitions {
-        s1 s2 s3
-        t1 t2 t3 t4 t5 t6
-    }
-    arcs {
-        { p1, nb1 } -> s1 -> { p2,  b1 }
-        { p2, nb2 } -> s2 -> { p3, nb2 }
-        { p3,  b1 } -> s3 -> { p1, nb1 }
-
-        { q1, nb2 } -> t1 -> { q2,     }
-        { q2,  b1 } -> t2 -> { q3,  b1 }
-        { q3,     } -> t3 -> { q4, nb2 }
-        { q4, nb1 } -> t4 -> { q1, nb1 }
-        { q2, nb1 } -> t5 -> { q5, nb1 }
-        { q5,     } -> t6 -> { q1, nb2 }
-    }
-    initial {
-        p1 q1 nb1 nb2
-    }
-}
-safety property "mutual exclusion" {
-    p3 >= 1 && q5 >= 1
-}
-

examples/leader_election.pnet

-petri net "leader election 2" {
-    places {
-        s1 s1m1 s1m2
-        s2 s2m1 s2m2
-        lead
-    }
-    transitions {
-        s1send1 s1pass2    s1accept1
-        s2send2 s2discard1 s2accept2
-        newleader
-    }
-    arcs {
-        s1   -> s1send1    -> s1m1
-        s2   -> s2send2    -> s2m2
-        s1m1 -> s2discard1
-        s1m2 -> s2accept2  -> lead
-        s2m1 -> s1accept1  -> lead
-        s2m2 -> s1pass2    -> s1m2
-        lead -> newleader  -> { s1 s2 }
-    }
-    initial { s1 s2 }
-}
-safety property {
-    lead >= 2
-}
-liveness property {
-    newleader = 0
-}

examples/leader_election_nlogn.pnet

-petri net "improved leader election 2" {
-    places {
-        s1a0 s1a1 s1a2 s1aH s1aP s1aD
-        s1max1 s1max2
-        s1left0 s1left1 s1left2
-        s1m1_n s1m1_1 s1m1_2
-        s1m2_n s1m2_1 s1m2_2
-
-        s2a0 s2a1 s2a2 s2aH s2aP s2aD
-        s2max1 s2max2
-        s2left0 s2left1 s2left2
-        s2m1_n s2m1_1 s2m1_2
-        s2m2_n s2m2_1 s2m2_2
-    }
-    transitions {
-        s1a0send1 s1a0send2
-
-        s1a1rec1max1 s1a1rec1max2left0 s1a1rec1max2left1 s1a1rec1max2left2
-        s1a1rec2max1left0 s1a1rec2max1left1 s1a1rec2max1left2 s1a1rec2max2
-
-        s1a2rec1left0 s1a2rec1left1 s1a2rec1max1left2 s1a2rec1max2left2
-        s1a2rec2left0 s1a2rec2left1 s1a2rec2left2
-
-        s1aPrec1_1 s1aPrec2_1 s1aPrec1_2 s1aPrec2_2
-
-        s1aDmax1left0 s1aDmax1left1 s1aDmax1left2 s1aDmax2left0 s1aDmax2left1 s1aDmax2left2
-
-        s2a0send1 s2a0send2
-
-        s2a1rec1max1 s2a1rec1max2left0 s2a1rec1max2left1 s2a1rec1max2left2
-        s2a1rec2max1left0 s2a1rec2max1left1 s2a1rec2max1left2 s2a1rec2max2
-
-        s2a2rec1left0 s2a2rec1left1 s2a2rec1max1left2 s2a2rec1max2left2
-        s2a2rec2left0 s2a2rec2left1 s2a2rec2left2
-
-        s2aPrec1_1 s2aPrec2_1 s2aPrec1_2 s2aPrec2_2
-
-        s2aDmax1left0 s2aDmax1left1 s2aDmax1left2 s2aDmax2left0 s2aDmax2left1 s2aDmax2left2
-
-        s1done s2done
-    }
-    arcs {
-        { s1a0 s1max1 s1m1_n } -> s1a0send1 -> { s1a1 s1max1 s1m1_1 }
-        { s1a0 s1max2 s1m1_n } -> s1a0send2 -> { s1a1 s1max2 s1m1_2 }
-
-        { s1a1 s1max1 s2m1_1 } -> s1a1rec1max1 -> { s1aH s1max1 s2m1_n }
-        { s1a1 s1max2 s1left0 s2m1_1 s1m2_n } -> s1a1rec1max2left0 -> { s1a2 s1max2 s1left1 s2m1_n s1m2_1 }
-        { s1a1 s1max2 s1left1 s2m1_1 s1m2_n } -> s1a1rec1max2left1 -> { s1a2 s1max2 s1left1 s2m1_n s1m2_1 }
-        { s1a1 s1max2 s1left2 s2m1_1 s1m2_n } -> s1a1rec1max2left2 -> { s1a2 s1max2 s1left1 s2m1_n s1m2_1 }
-        { s1a1 s1max1 s1left0 s2m1_2 s1m2_n } -> s1a1rec2max1left0 -> { s1a2 s1max1 s1left2 s2m1_n s1m2_2 }
-        { s1a1 s1max1 s1left1 s2m1_2 s1m2_n } -> s1a1rec2max1left1 -> { s1a2 s1max1 s1left2 s2m1_n s1m2_2 }
-        { s1a1 s1max1 s1left2 s2m1_2 s1m2_n } -> s1a1rec2max1left2 -> { s1a2 s1max1 s1left2 s2m1_n s1m2_2 }
-        { s1a1 s1max2 s2m1_2 } -> s1a1rec2max2 -> { s1aH s1max2 s2m1_n }
-
-        { s1a2 s1left0 s2m2_1 } -> s1a2rec1left0 -> { s1aP s1left0 s2m2_n }
-        { s1a2 s1left1 s2m2_1 } -> s1a2rec1left1 -> { s1aP s1left1 s2m2_n }
-        { s1a2 s1max1 s1left2 s2m2_1 s1m1_n } -> s1a2rec1max1left2 -> { s1a1 s1max2 s1left2 s2m2_n s1m1_2 }
-        { s1a2 s1max2 s1left2 s2m2_1 } -> s1a2rec1max2left2 -> { s1aP s1max2 s1left2 s2m2_n }
-        { s1a2 s1left0 s2m2_2 } -> s1a2rec2left0 -> { s1aP s1left0 s2m2_n }
-        { s1a2 s1left1 s2m2_2 } -> s1a2rec2left1 -> { s1aP s1left1 s2m2_n }
-        { s1a2 s1left2 s2m2_2 } -> s1a2rec2left2 -> { s1aP s1left2 s2m2_n }
-
-        { s1aP s2m1_1 s1m1_n } -> s1aPrec1_1 -> { s1aP s2m1_n s1m1_1 }
-        { s1aP s2m2_1 s1m2_n } -> s1aPrec2_1 -> { s1aP s2m2_n s1m2_1 }
-        { s1aP s2m1_2 s1m1_n } -> s1aPrec1_2 -> { s1aP s2m1_n s1m1_2 }
-        { s1aP s2m2_2 s1m2_n } -> s1aPrec2_2 -> { s1aP s2m2_n s1m2_2 }
-
-        { s1aD s1max1 s1left0 } -> s1aDmax1left0 -> { s1a0 s1max1 s1left0 }
-        { s1aD s1max1 s1left1 } -> s1aDmax1left1 -> { s1a0 s1max1 s1left0 }
-        { s1aD s1max1 s1left2 } -> s1aDmax1left2 -> { s1a0 s1max1 s1left0 }
-        { s1aD s1max2 s1left0 } -> s1aDmax2left0 -> { s1a0 s1max1 s1left0 }
-        { s1aD s1max2 s1left1 } -> s1aDmax2left1 -> { s1a0 s1max1 s1left0 }
-        { s1aD s1max2 s1left2 } -> s1aDmax2left2 -> { s1a0 s1max1 s1left0 }
-
-
-        { s2a0 s2max1 s2m1_n } -> s2a0send1 -> { s2a1 s2max1 s2m1_1 }
-        { s2a0 s2max2 s2m1_n } -> s2a0send2 -> { s2a1 s2max2 s2m1_2 }
-
-        { s2a1 s2max1 s1m1_1 } -> s2a1rec1max1 -> { s2aH s2max1 s1m1_n }
-        { s2a1 s2max2 s2left0 s1m1_1 s2m2_n } -> s2a1rec1max2left0 -> { s2a2 s2max2 s2left1 s1m1_n s2m2_1 }
-        { s2a1 s2max2 s2left1 s1m1_1 s2m2_n } -> s2a1rec1max2left1 -> { s2a2 s2max2 s2left1 s1m1_n s2m2_1 }
-        { s2a1 s2max2 s2left2 s1m1_1 s2m2_n } -> s2a1rec1max2left2 -> { s2a2 s2max2 s2left1 s1m1_n s2m2_1 }
-        { s2a1 s2max1 s2left0 s1m1_2 s2m2_n } -> s2a1rec2max1left0 -> { s2a2 s2max1 s2left2 s1m1_n s2m2_2 }
-        { s2a1 s2max1 s2left1 s1m1_2 s2m2_n } -> s2a1rec2max1left1 -> { s2a2 s2max1 s2left2 s1m1_n s2m2_2 }
-        { s2a1 s2max1 s2left2 s1m1_2 s2m2_n } -> s2a1rec2max1left2 -> { s2a2 s2max1 s2left2 s1m1_n s2m2_2 }
-        { s2a1 s2max2 s1m1_2 } -> s2a1rec2max2 -> { s2aH s2max2 s1m1_n }
-
-        { s2a2 s2left0 s1m2_1 } -> s2a2rec1left0 -> { s2aP s2left0 s1m2_n }
-        { s2a2 s2left1 s1m2_1 } -> s2a2rec1left1 -> { s2aP s2left1 s1m2_n }
-        { s2a2 s2max1 s2left2 s1m2_1 s2m1_n } -> s2a2rec1max1left2 -> { s2a1 s2max2 s2left2 s1m2_n s2m1_2 }
-        { s2a2 s2max2 s2left2 s1m2_1 } -> s2a2rec1max2left2 -> { s2aP s2max2 s2left2 s1m2_n }
-        { s2a2 s2left0 s1m2_2 } -> s2a2rec2left0 -> { s2aP s2left0 s1m2_n }
-        { s2a2 s2left1 s1m2_2 } -> s2a2rec2left1 -> { s2aP s2left1 s1m2_n }
-        { s2a2 s2left2 s1m2_2 } -> s2a2rec2left2 -> { s2aP s2left2 s1m2_n }
-
-        { s2aP s1m1_1 s2m1_n } -> s2aPrec1_1 -> { s2aP s1m1_n s2m1_1 }
-        { s2aP s1m2_1 s2m2_n } -> s2aPrec2_1 -> { s2aP s1m2_n s2m2_1 }
-        { s2aP s1m1_2 s2m1_n } -> s2aPrec1_2 -> { s2aP s1m1_n s2m1_2 }
-        { s2aP s1m2_2 s2m2_n } -> s2aPrec2_2 -> { s2aP s1m2_n s2m2_2 }
-
-        { s2aD s2max1 s2left0 } -> s2aDmax1left0 -> { s2a0 s2max2 s2left0 }
-        { s2aD s2max1 s2left1 } -> s2aDmax1left1 -> { s2a0 s2max2 s2left0 }
-        { s2aD s2max1 s2left2 } -> s2aDmax1left2 -> { s2a0 s2max2 s2left0 }
-        { s2aD s2max2 s2left0 } -> s2aDmax2left0 -> { s2a0 s2max2 s2left0 }
-        { s2aD s2max2 s2left1 } -> s2aDmax2left1 -> { s2a0 s2max2 s2left0 }
-        { s2aD s2max2 s2left2 } -> s2aDmax2left2 -> { s2a0 s2max2 s2left0 }
-
-
-        { s1aH s2aP } -> s1done -> { s1aD s2aD }
-        { s1aP s2aH } -> s2done -> { s1aD s2aD }
-    }
-    initial {
-        s1a0 s1max1 s1left0 s1m1_n s1m2_n
-        s2a0 s2max2 s2left0 s2m1_n s2m2_n
-    }
-}
-safety property "passive" {
-    s1aP >= 1 && s2aP >= 1
-}
-liveness property {
-    s1done = 0 && s2done = 0
-}