YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && A = B && C = D && E = F] 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && A = B && C = D && E = F] 3. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0 && B = 0 && C = D && E = F] 4. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 (?,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] 5. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 (?,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] 6. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [-1 + E >= 0 (?,1) && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && 39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [-2 + E >= 0 (?,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] 8. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [-1 + E >= 0 (?,1) && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && E = 40 && C = 100 && A = 0 && B = 0] Signature: {(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{1,2,3},1->{4,5,7},2->{4,5,7},3->{6,8},4->{4,5,7},5->{4,5,7},6->{6,8},7->{},8->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && A = B && C = D && E = F] 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && A = B && C = D && E = F] 3. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0 && B = 0 && C = D && E = F] 4. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 (?,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] 5. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 (?,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] 6. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [-1 + E >= 0 (?,1) && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && 39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [-2 + E >= 0 (1,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] 8. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [-1 + E >= 0 (1,1) && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && E = 40 && C = 100 && A = 0 && B = 0] Signature: {(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{1,2,3},1->{4,5,7},2->{4,5,7},3->{6,8},4->{4,5,7},5->{4,5,7},6->{6,8},7->{},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,5),(1,7),(2,4),(2,7),(3,8),(4,5),(5,4)] * Step 3: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && A = B && C = D && E = F] 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && A = B && C = D && E = F] 3. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0 && B = 0 && C = D && E = F] 4. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 (?,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] 5. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 (?,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] 6. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [-1 + E >= 0 (?,1) && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && 39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [-2 + E >= 0 (1,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] 8. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [-1 + E >= 0 (1,1) && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && E = 40 && C = 100 && A = 0 && B = 0] Signature: {(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{1,2,3},1->{4},2->{5},3->{6},4->{4,7},5->{5,7},6->{6,8},7->{},8->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl111) = 38 p(lbl91) = 40 + -1*x5 p(start) = 39 p(start0) = 39 p(stop) = 40 + -1*x5 Following rules are strictly oriented: [E + -1*F >= 0 ==> && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && A = B && C = D && E = F] start(A,B,C,D,E,F) = 39 > 38 = lbl111(A,B,100,D,2,F) [E + -1*F >= 0 ==> && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && A = B && C = D && E = F] start(A,B,C,D,E,F) = 39 > 38 = lbl111(A,B,100,D,2,F) [-1 + E >= 0 ==> && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && 39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] lbl91(A,B,C,D,E,F) = 40 + -1*E > 39 + -1*E = lbl91(A,B,C,D,1 + E,F) Following rules are weakly oriented: True ==> start0(A,B,C,D,E,F) = 39 >= 39 = start(B,B,D,D,F,F) [E + -1*F >= 0 ==> && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0 && B = 0 && C = D && E = F] start(A,B,C,D,E,F) = 39 >= 39 = lbl91(A,B,100,D,1,F) [-2 + E >= 0 ==> && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] lbl111(A,B,C,D,E,F) = 38 >= 38 = lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 ==> && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] lbl111(A,B,C,D,E,F) = 38 >= 38 = lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 ==> && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] lbl111(A,B,C,D,E,F) = 38 >= 40 + -1*E = stop(A,B,C,D,E,F) [-1 + E >= 0 ==> && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && E = 40 && C = 100 && A = 0 && B = 0] lbl91(A,B,C,D,E,F) = 40 + -1*E >= 40 + -1*E = stop(A,B,C,D,E,F) * Step 4: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && A = B && C = D && E = F] 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && A = B && C = D && E = F] 3. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0 && B = 0 && C = D && E = F] 4. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 (?,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] 5. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 (?,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] 6. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [-1 + E >= 0 (39,1) && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && 39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [-2 + E >= 0 (1,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] 8. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [-1 + E >= 0 (1,1) && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && E = 40 && C = 100 && A = 0 && B = 0] Signature: {(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{1,2,3},1->{4},2->{5},3->{6},4->{4,7},5->{5,7},6->{6,8},7->{},8->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl111) = 384 + -1*x5 p(lbl91) = 381 p(start) = 382 p(start0) = 382 p(stop) = 355 + -6*x5 Following rules are strictly oriented: [E + -1*F >= 0 ==> && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0 && B = 0 && C = D && E = F] start(A,B,C,D,E,F) = 382 > 381 = lbl91(A,B,100,D,1,F) [-2 + E >= 0 ==> && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] lbl111(A,B,C,D,E,F) = 384 + -1*E > 382 + -1*E = lbl111(A,B,C,D,2 + E,F) [-1 + E >= 0 ==> && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && E = 40 && C = 100 && A = 0 && B = 0] lbl91(A,B,C,D,E,F) = 381 > 355 + -6*E = stop(A,B,C,D,E,F) Following rules are weakly oriented: True ==> start0(A,B,C,D,E,F) = 382 >= 382 = start(B,B,D,D,F,F) [E + -1*F >= 0 ==> && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && A = B && C = D && E = F] start(A,B,C,D,E,F) = 382 >= 382 = lbl111(A,B,100,D,2,F) [E + -1*F >= 0 ==> && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && A = B && C = D && E = F] start(A,B,C,D,E,F) = 382 >= 382 = lbl111(A,B,100,D,2,F) [-2 + E >= 0 ==> && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] lbl111(A,B,C,D,E,F) = 384 + -1*E >= 382 + -1*E = lbl111(A,B,C,D,2 + E,F) [-1 + E >= 0 ==> && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && 39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] lbl91(A,B,C,D,E,F) = 381 >= 381 = lbl91(A,B,C,D,1 + E,F) [-2 + E >= 0 ==> && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] lbl111(A,B,C,D,E,F) = 384 + -1*E >= 355 + -6*E = stop(A,B,C,D,E,F) * Step 5: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && A = B && C = D && E = F] 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && A = B && C = D && E = F] 3. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0 && B = 0 && C = D && E = F] 4. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 (?,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] 5. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 (382,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] 6. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [-1 + E >= 0 (39,1) && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && 39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [-2 + E >= 0 (1,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] 8. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [-1 + E >= 0 (1,1) && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && E = 40 && C = 100 && A = 0 && B = 0] Signature: {(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{1,2,3},1->{4},2->{5},3->{6},4->{4,7},5->{5,7},6->{6,8},7->{},8->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl111) = 716 + 3*x3 + -1*x5 p(lbl91) = 1715 + -38*x5 p(start) = 1678 p(start0) = 1678 p(stop) = 1604 + -1*x3 + -231*x5 Following rules are strictly oriented: [E + -1*F >= 0 ==> && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0 && B = 0 && C = D && E = F] start(A,B,C,D,E,F) = 1678 > 1677 = lbl91(A,B,100,D,1,F) [-2 + E >= 0 ==> && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] lbl111(A,B,C,D,E,F) = 716 + 3*C + -1*E > 714 + 3*C + -1*E = lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 ==> && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] lbl111(A,B,C,D,E,F) = 716 + 3*C + -1*E > 714 + 3*C + -1*E = lbl111(A,B,C,D,2 + E,F) [-1 + E >= 0 ==> && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && E = 40 && C = 100 && A = 0 && B = 0] lbl91(A,B,C,D,E,F) = 1715 + -38*E > 1604 + -1*C + -231*E = stop(A,B,C,D,E,F) Following rules are weakly oriented: True ==> start0(A,B,C,D,E,F) = 1678 >= 1678 = start(B,B,D,D,F,F) [E + -1*F >= 0 ==> && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && A = B && C = D && E = F] start(A,B,C,D,E,F) = 1678 >= 1014 = lbl111(A,B,100,D,2,F) [E + -1*F >= 0 ==> && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && A = B && C = D && E = F] start(A,B,C,D,E,F) = 1678 >= 1014 = lbl111(A,B,100,D,2,F) [-1 + E >= 0 ==> && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && 39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] lbl91(A,B,C,D,E,F) = 1715 + -38*E >= 1677 + -38*E = lbl91(A,B,C,D,1 + E,F) [-2 + E >= 0 ==> && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] lbl111(A,B,C,D,E,F) = 716 + 3*C + -1*E >= 1604 + -1*C + -231*E = stop(A,B,C,D,E,F) * Step 6: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && A = B && C = D && E = F] 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && A = B && C = D && E = F] 3. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [E + -1*F >= 0 (1,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0 && B = 0 && C = D && E = F] 4. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 (1678,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] 5. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [-2 + E >= 0 (382,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] 6. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [-1 + E >= 0 (39,1) && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && 39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [-2 + E >= 0 (1,1) && -102 + C + E >= 0 && 98 + -1*C + E >= 0 && 100 + -1*C >= 0 && -100 + C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] 8. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [-1 + E >= 0 (1,1) && -101 + C + E >= 0 && 99 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + -1*B + E >= 0 && -1 + A + E >= 0 && -1 + -1*A + E >= 0 && 100 + -1*C >= 0 && 100 + B + -1*C >= 0 && 100 + -1*B + -1*C >= 0 && 100 + A + -1*C >= 0 && 100 + -1*A + -1*C >= 0 && -100 + C >= 0 && -100 + B + C >= 0 && -100 + -1*B + C >= 0 && -100 + A + C >= 0 && -100 + -1*A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && -1*A >= 0 && A >= 0 && E = 40 && C = 100 && A = 0 && B = 0] Signature: {(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{1,2,3},1->{4},2->{5},3->{6},4->{4,7},5->{5,7},6->{6,8},7->{},8->{}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(1))