YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A] (?,1) 1. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + C && B = C && D = A] (?,1) 2. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 (?,1) && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 2 + A >= C && C >= 0 && 2 + C >= A && B = C && D = A] 3. start(A,B,C,D) -> lbl81(A,B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && C >= 3 + A && B = C && D = A] (?,1) 4. start(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 3 + C && C >= 0 && B = C && D = A] (?,1) 5. lbl81(A,B,C,D) -> stop(A,B,C,D) [-2 + C + -1*D >= 0 (?,1) && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + A && 2 + D = C && B = C] 6. lbl81(A,B,C,D) -> lbl81(A,B,C,1 + D) [-2 + C + -1*D >= 0 (?,1) && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + D && D >= 1 + A && C >= 2 + D && B = C] 7. lbl91(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 (?,1) && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + C && 2 + B = A && D = A] 8. lbl91(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 (?,1) && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + B && A >= 2 + B && B >= 1 + C && D = A] 9. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(lbl81,4);(lbl91,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{},2->{},3->{5,6},4->{7,8},5->{},6->{5,6},7->{},8->{7,8},9->{0,1,2,3,4}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A] (1,1) 1. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + C && B = C && D = A] (1,1) 2. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 (1,1) && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 2 + A >= C && C >= 0 && 2 + C >= A && B = C && D = A] 3. start(A,B,C,D) -> lbl81(A,B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && C >= 3 + A && B = C && D = A] (1,1) 4. start(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 3 + C && C >= 0 && B = C && D = A] (1,1) 5. lbl81(A,B,C,D) -> stop(A,B,C,D) [-2 + C + -1*D >= 0 (1,1) && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + A && 2 + D = C && B = C] 6. lbl81(A,B,C,D) -> lbl81(A,B,C,1 + D) [-2 + C + -1*D >= 0 (?,1) && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + D && D >= 1 + A && C >= 2 + D && B = C] 7. lbl91(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 (1,1) && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + C && 2 + B = A && D = A] 8. lbl91(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 (?,1) && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + B && A >= 2 + B && B >= 1 + C && D = A] 9. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(lbl81,4);(lbl91,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{},2->{},3->{5,6},4->{7,8},5->{},6->{5,6},7->{},8->{7,8},9->{0,1,2,3,4}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl81) = x1 + -1*x2 p(lbl91) = 1 + x1 + -1*x2 p(start) = x1 + -1*x2 p(start0) = x1 + -1*x3 p(stop) = x1 + -1*x2 Following rules are strictly oriented: [A + -1*D >= 0 ==> && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + C && 2 + B = A && D = A] lbl91(A,B,C,D) = 1 + A + -1*B > A + -1*B = stop(A,B,C,D) [A + -1*D >= 0 ==> && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + B && A >= 2 + B && B >= 1 + C && D = A] lbl91(A,B,C,D) = 1 + A + -1*B > A + -1*B = lbl91(A,1 + B,C,D) Following rules are weakly oriented: [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A] ==> start(A,B,C,D) = A + -1*B >= A + -1*B = stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + C && B = C && D = A] ==> start(A,B,C,D) = A + -1*B >= A + -1*B = stop(A,B,C,D) [A + -1*D >= 0 ==> && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 2 + A >= C && C >= 0 && 2 + C >= A && B = C && D = A] start(A,B,C,D) = A + -1*B >= A + -1*B = stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && C >= 3 + A && B = C && D = A] ==> start(A,B,C,D) = A + -1*B >= A + -1*B = lbl81(A,B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 3 + C && C >= 0 && B = C && D = A] ==> start(A,B,C,D) = A + -1*B >= A + -1*B = lbl91(A,1 + B,C,D) [-2 + C + -1*D >= 0 ==> && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + A && 2 + D = C && B = C] lbl81(A,B,C,D) = A + -1*B >= A + -1*B = stop(A,B,C,D) [-2 + C + -1*D >= 0 ==> && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + D && D >= 1 + A && C >= 2 + D && B = C] lbl81(A,B,C,D) = A + -1*B >= A + -1*B = lbl81(A,B,C,1 + D) True ==> start0(A,B,C,D) = A + -1*C >= A + -1*C = start(A,C,C,A) * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A] (1,1) 1. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + C && B = C && D = A] (1,1) 2. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 (1,1) && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 2 + A >= C && C >= 0 && 2 + C >= A && B = C && D = A] 3. start(A,B,C,D) -> lbl81(A,B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && C >= 3 + A && B = C && D = A] (1,1) 4. start(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 3 + C && C >= 0 && B = C && D = A] (1,1) 5. lbl81(A,B,C,D) -> stop(A,B,C,D) [-2 + C + -1*D >= 0 (1,1) && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + A && 2 + D = C && B = C] 6. lbl81(A,B,C,D) -> lbl81(A,B,C,1 + D) [-2 + C + -1*D >= 0 (?,1) && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + D && D >= 1 + A && C >= 2 + D && B = C] 7. lbl91(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 (1,1) && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + C && 2 + B = A && D = A] 8. lbl91(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 (A + C,1) && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + B && A >= 2 + B && B >= 1 + C && D = A] 9. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(lbl81,4);(lbl91,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{},2->{},3->{5,6},4->{7,8},5->{},6->{5,6},7->{},8->{7,8},9->{0,1,2,3,4}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl81) = 1 + x2 + -1*x4 p(lbl91) = -2 + x3 + -1*x4 p(start) = x2 + -1*x4 p(start0) = -1*x1 + x3 p(stop) = -2 + x3 + -1*x4 Following rules are strictly oriented: [-2 + C + -1*D >= 0 ==> && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + A && 2 + D = C && B = C] lbl81(A,B,C,D) = 1 + B + -1*D > -2 + C + -1*D = stop(A,B,C,D) [-2 + C + -1*D >= 0 ==> && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + D && D >= 1 + A && C >= 2 + D && B = C] lbl81(A,B,C,D) = 1 + B + -1*D > B + -1*D = lbl81(A,B,C,1 + D) Following rules are weakly oriented: [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A] ==> start(A,B,C,D) = B + -1*D >= -2 + C + -1*D = stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + C && B = C && D = A] ==> start(A,B,C,D) = B + -1*D >= -2 + C + -1*D = stop(A,B,C,D) [A + -1*D >= 0 ==> && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 2 + A >= C && C >= 0 && 2 + C >= A && B = C && D = A] start(A,B,C,D) = B + -1*D >= -2 + C + -1*D = stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && C >= 3 + A && B = C && D = A] ==> start(A,B,C,D) = B + -1*D >= B + -1*D = lbl81(A,B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 3 + C && C >= 0 && B = C && D = A] ==> start(A,B,C,D) = B + -1*D >= -2 + C + -1*D = lbl91(A,1 + B,C,D) [A + -1*D >= 0 ==> && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + C && 2 + B = A && D = A] lbl91(A,B,C,D) = -2 + C + -1*D >= -2 + C + -1*D = stop(A,B,C,D) [A + -1*D >= 0 ==> && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + B && A >= 2 + B && B >= 1 + C && D = A] lbl91(A,B,C,D) = -2 + C + -1*D >= -2 + C + -1*D = lbl91(A,1 + B,C,D) True ==> start0(A,B,C,D) = -1*A + C >= -1*A + C = start(A,C,C,A) * Step 4: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A] (1,1) 1. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + C && B = C && D = A] (1,1) 2. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 (1,1) && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 2 + A >= C && C >= 0 && 2 + C >= A && B = C && D = A] 3. start(A,B,C,D) -> lbl81(A,B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && C >= 3 + A && B = C && D = A] (1,1) 4. start(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 3 + C && C >= 0 && B = C && D = A] (1,1) 5. lbl81(A,B,C,D) -> stop(A,B,C,D) [-2 + C + -1*D >= 0 (1,1) && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + A && 2 + D = C && B = C] 6. lbl81(A,B,C,D) -> lbl81(A,B,C,1 + D) [-2 + C + -1*D >= 0 (A + C,1) && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + D && D >= 1 + A && C >= 2 + D && B = C] 7. lbl91(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 (1,1) && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + C && 2 + B = A && D = A] 8. lbl91(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 (A + C,1) && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + B && A >= 2 + B && B >= 1 + C && D = A] 9. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(lbl81,4);(lbl91,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{},2->{},3->{5,6},4->{7,8},5->{},6->{5,6},7->{},8->{7,8},9->{0,1,2,3,4}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(n^1))