YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> stop(A,B,C,D,E,F,G,H,I,J,K,0,M,N) [1 >= A && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (?,1) 1. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1,E,F,G,0,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (?,1) 2. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1,E,F,G,1,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (?,1) 3. lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl13(A,L,C,D,E,F,G,H,I,J,K,1 + L,M,N) [D >= H && D >= 1 && 1 + H >= D && A >= 1 + D && N = A && 1 + L = D && J = A] (?,1) 4. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl91(A,B,C,D,E,O,G,H,I,J,K,L,M,N) [D >= H && D >= 1 && A >= 1 + D && 1 + H >= D && J = A && 1 + L = D && N = A] (?,1) 5. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,J,E,F,G,H,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] (?,1) 6. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,J,E,F,G,J,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] (?,1) 7. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> stop(A,B,C,D,E,F,G,H,I,J,K,L,M,N) [2 + H >= A && A >= 2 && A >= 1 + H && 1 + L = A && 2 + B = A && 1 + D = A && N = A && J = A] (?,1) 8. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1 + L,E,F,G,L,I,2 + L,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] (?,1) 9. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1 + L,E,F,G,1 + L,I,2 + L,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] (?,1) 10. start0(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> start(A,C,C,E,E,G,G,I,I,K,K,M,M,A) True (1,1) Signature: {(lbl13,14);(lbl53,14);(lbl91,14);(start,14);(start0,14);(stop,14)} Flow Graph: [0->{},1->{4,5,6},2->{4,5,6},3->{7,8,9},4->{3},5->{4,5,6},6->{4,5,6},7->{},8->{4,5,6},9->{4,5,6},10->{0,1 ,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(5,4),(5,5),(5,6),(6,4),(6,5),(6,6)] * Step 2: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> stop(A,B,C,D,E,F,G,H,I,J,K,0,M,N) [1 >= A && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (?,1) 1. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1,E,F,G,0,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (?,1) 2. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1,E,F,G,1,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (?,1) 3. lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl13(A,L,C,D,E,F,G,H,I,J,K,1 + L,M,N) [D >= H && D >= 1 && 1 + H >= D && A >= 1 + D && N = A && 1 + L = D && J = A] (?,1) 4. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl91(A,B,C,D,E,O,G,H,I,J,K,L,M,N) [D >= H && D >= 1 && A >= 1 + D && 1 + H >= D && J = A && 1 + L = D && N = A] (?,1) 5. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,J,E,F,G,H,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] (?,1) 6. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,J,E,F,G,J,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] (?,1) 7. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> stop(A,B,C,D,E,F,G,H,I,J,K,L,M,N) [2 + H >= A && A >= 2 && A >= 1 + H && 1 + L = A && 2 + B = A && 1 + D = A && N = A && J = A] (?,1) 8. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1 + L,E,F,G,L,I,2 + L,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] (?,1) 9. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1 + L,E,F,G,1 + L,I,2 + L,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] (?,1) 10. start0(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> start(A,C,C,E,E,G,G,I,I,K,K,M,M,A) True (1,1) Signature: {(lbl13,14);(lbl53,14);(lbl91,14);(start,14);(start0,14);(stop,14)} Flow Graph: [0->{},1->{4,5,6},2->{4,5,6},3->{7,8,9},4->{3},5->{},6->{},7->{},8->{4,5,6},9->{4,5,6},10->{0,1,2}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> stop(A,B,C,D,E,F,G,H,I,J,K,0,M,N) [1 >= A && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (1,1) 1. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1,E,F,G,0,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (1,1) 2. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1,E,F,G,1,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (1,1) 3. lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl13(A,L,C,D,E,F,G,H,I,J,K,1 + L,M,N) [D >= H && D >= 1 && 1 + H >= D && A >= 1 + D && N = A && 1 + L = D && J = A] (?,1) 4. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl91(A,B,C,D,E,O,G,H,I,J,K,L,M,N) [D >= H && D >= 1 && A >= 1 + D && 1 + H >= D && J = A && 1 + L = D && N = A] (?,1) 5. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,J,E,F,G,H,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] (1,1) 6. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,J,E,F,G,J,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] (1,1) 7. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> stop(A,B,C,D,E,F,G,H,I,J,K,L,M,N) [2 + H >= A && A >= 2 && A >= 1 + H && 1 + L = A && 2 + B = A && 1 + D = A && N = A && J = A] (1,1) 8. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1 + L,E,F,G,L,I,2 + L,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] (?,1) 9. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1 + L,E,F,G,1 + L,I,2 + L,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] (?,1) 10. start0(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> start(A,C,C,E,E,G,G,I,I,K,K,M,M,A) True (1,1) Signature: {(lbl13,14);(lbl53,14);(lbl91,14);(start,14);(start0,14);(stop,14)} Flow Graph: [0->{},1->{4,5,6},2->{4,5,6},3->{7,8,9},4->{3},5->{},6->{},7->{},8->{4,5,6},9->{4,5,6},10->{0,1,2}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl13) = -2 + x1 + -1*x2 p(lbl53) = -1 + -1*x4 + x10 p(lbl91) = -1 + x1 + -1*x4 p(start) = 0 p(start0) = 0 p(stop) = 0 Following rules are strictly oriented: [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] ==> lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -2 + A + -1*B > 0 = lbl53(A,B,C,1 + L,E,F,G,1 + L,I,2 + L,K,L,M,N) Following rules are weakly oriented: [1 >= A && B = C && D = E && F = G && H = I && J = K && L = M && N = A] ==> start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = 0 >= 0 = stop(A,B,C,D,E,F,G,H,I,J,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] ==> start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = 0 >= 0 = lbl53(A,B,C,1,E,F,G,0,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] ==> start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = 0 >= 0 = lbl53(A,B,C,1,E,F,G,1,I,2,K,0,M,N) [D >= H && D >= 1 && 1 + H >= D && A >= 1 + D && N = A && 1 + L = D && J = A] ==> lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -1 + A + -1*D >= -2 + A + -1*L = lbl13(A,L,C,D,E,F,G,H,I,J,K,1 + L,M,N) [D >= H && D >= 1 && A >= 1 + D && 1 + H >= D && J = A && 1 + L = D && N = A] ==> lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -1 + -1*D + J >= -1 + A + -1*D = lbl91(A,B,C,D,E,O,G,H,I,J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] ==> lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -1 + -1*D + J >= 0 = lbl53(A,B,C,J,E,F,G,H,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] ==> lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -1 + -1*D + J >= 0 = lbl53(A,B,C,J,E,F,G,J,I,1 + J,K,L,M,N) [2 + H >= A && A >= 2 && A >= 1 + H && 1 + L = A && 2 + B = A && 1 + D = A && N = A && J = A] ==> lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -2 + A + -1*B >= 0 = stop(A,B,C,D,E,F,G,H,I,J,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] ==> lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -2 + A + -1*B >= 0 = lbl53(A,B,C,1 + L,E,F,G,L,I,2 + L,K,L,M,N) True ==> start0(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = 0 >= 0 = start(A,C,C,E,E,G,G,I,I,K,K,M,M,A) * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> stop(A,B,C,D,E,F,G,H,I,J,K,0,M,N) [1 >= A && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (1,1) 1. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1,E,F,G,0,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (1,1) 2. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1,E,F,G,1,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (1,1) 3. lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl13(A,L,C,D,E,F,G,H,I,J,K,1 + L,M,N) [D >= H && D >= 1 && 1 + H >= D && A >= 1 + D && N = A && 1 + L = D && J = A] (?,1) 4. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl91(A,B,C,D,E,O,G,H,I,J,K,L,M,N) [D >= H && D >= 1 && A >= 1 + D && 1 + H >= D && J = A && 1 + L = D && N = A] (?,1) 5. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,J,E,F,G,H,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] (1,1) 6. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,J,E,F,G,J,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] (1,1) 7. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> stop(A,B,C,D,E,F,G,H,I,J,K,L,M,N) [2 + H >= A && A >= 2 && A >= 1 + H && 1 + L = A && 2 + B = A && 1 + D = A && N = A && J = A] (1,1) 8. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1 + L,E,F,G,L,I,2 + L,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] (?,1) 9. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1 + L,E,F,G,1 + L,I,2 + L,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] (0,1) 10. start0(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> start(A,C,C,E,E,G,G,I,I,K,K,M,M,A) True (1,1) Signature: {(lbl13,14);(lbl53,14);(lbl91,14);(start,14);(start0,14);(stop,14)} Flow Graph: [0->{},1->{4,5,6},2->{4,5,6},3->{7,8,9},4->{3},5->{},6->{},7->{},8->{4,5,6},9->{4,5,6},10->{0,1,2}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl13) = -1 + x1 + -1*x12 p(lbl53) = -2 + x1 + -1*x12 p(lbl91) = -2 + x1 + -1*x12 p(start) = -1 + x1 p(start0) = -1 + x1 p(stop) = -1 + x1 + -1*x12 Following rules are strictly oriented: [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] ==> start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -1 + A > -2 + A = lbl53(A,B,C,1,E,F,G,0,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] ==> start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -1 + A > -2 + A = lbl53(A,B,C,1,E,F,G,1,I,2,K,0,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] ==> lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -1 + A + -1*L > -2 + A + -1*L = lbl53(A,B,C,1 + L,E,F,G,L,I,2 + L,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] ==> lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -1 + A + -1*L > -2 + A + -1*L = lbl53(A,B,C,1 + L,E,F,G,1 + L,I,2 + L,K,L,M,N) Following rules are weakly oriented: [1 >= A && B = C && D = E && F = G && H = I && J = K && L = M && N = A] ==> start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -1 + A >= -1 + A = stop(A,B,C,D,E,F,G,H,I,J,K,0,M,N) [D >= H && D >= 1 && 1 + H >= D && A >= 1 + D && N = A && 1 + L = D && J = A] ==> lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -2 + A + -1*L >= -2 + A + -1*L = lbl13(A,L,C,D,E,F,G,H,I,J,K,1 + L,M,N) [D >= H && D >= 1 && A >= 1 + D && 1 + H >= D && J = A && 1 + L = D && N = A] ==> lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -2 + A + -1*L >= -2 + A + -1*L = lbl91(A,B,C,D,E,O,G,H,I,J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] ==> lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -2 + A + -1*L >= -2 + A + -1*L = lbl53(A,B,C,J,E,F,G,H,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] ==> lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -2 + A + -1*L >= -2 + A + -1*L = lbl53(A,B,C,J,E,F,G,J,I,1 + J,K,L,M,N) [2 + H >= A && A >= 2 && A >= 1 + H && 1 + L = A && 2 + B = A && 1 + D = A && N = A && J = A] ==> lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -1 + A + -1*L >= -1 + A + -1*L = stop(A,B,C,D,E,F,G,H,I,J,K,L,M,N) True ==> start0(A,B,C,D,E,F,G,H,I,J,K,L,M,N) = -1 + A >= -1 + A = start(A,C,C,E,E,G,G,I,I,K,K,M,M,A) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> stop(A,B,C,D,E,F,G,H,I,J,K,0,M,N) [1 >= A && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (1,1) 1. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1,E,F,G,0,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (1,1) 2. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1,E,F,G,1,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (1,1) 3. lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl13(A,L,C,D,E,F,G,H,I,J,K,1 + L,M,N) [D >= H && D >= 1 && 1 + H >= D && A >= 1 + D && N = A && 1 + L = D && J = A] (?,1) 4. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl91(A,B,C,D,E,O,G,H,I,J,K,L,M,N) [D >= H && D >= 1 && A >= 1 + D && 1 + H >= D && J = A && 1 + L = D && N = A] (?,1) 5. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,J,E,F,G,H,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] (1,1) 6. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,J,E,F,G,J,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] (1,1) 7. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> stop(A,B,C,D,E,F,G,H,I,J,K,L,M,N) [2 + H >= A && A >= 2 && A >= 1 + H && 1 + L = A && 2 + B = A && 1 + D = A && N = A && J = A] (1,1) 8. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1 + L,E,F,G,L,I,2 + L,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] (1 + A,1) 9. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1 + L,E,F,G,1 + L,I,2 + L,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] (0,1) 10. start0(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> start(A,C,C,E,E,G,G,I,I,K,K,M,M,A) True (1,1) Signature: {(lbl13,14);(lbl53,14);(lbl91,14);(start,14);(start0,14);(stop,14)} Flow Graph: [0->{},1->{4,5,6},2->{4,5,6},3->{7,8,9},4->{3},5->{},6->{},7->{},8->{4,5,6},9->{4,5,6},10->{0,1,2}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> stop(A,B,C,D,E,F,G,H,I,J,K,0,M,N) [1 >= A && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (1,1) 1. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1,E,F,G,0,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (1,1) 2. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1,E,F,G,1,I,2,K,0,M,N) [A >= 2 && B = C && D = E && F = G && H = I && J = K && L = M && N = A] (1,1) 3. lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl13(A,L,C,D,E,F,G,H,I,J,K,1 + L,M,N) [D >= H && D >= 1 && 1 + H >= D && A >= 1 + D && N = A && 1 + L = D && J = A] (3 + A,1) 4. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl91(A,B,C,D,E,O,G,H,I,J,K,L,M,N) [D >= H && D >= 1 && A >= 1 + D && 1 + H >= D && J = A && 1 + L = D && N = A] (3 + A,1) 5. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,J,E,F,G,H,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] (1,1) 6. lbl53(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,J,E,F,G,J,I,1 + J,K,L,M,N) [A >= 1 + J && D >= H && D >= 1 && A >= J && J >= 1 + D && 1 + H >= D && 1 + L = D && N = A] (1,1) 7. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> stop(A,B,C,D,E,F,G,H,I,J,K,L,M,N) [2 + H >= A && A >= 2 && A >= 1 + H && 1 + L = A && 2 + B = A && 1 + D = A && N = A && J = A] (1,1) 8. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1 + L,E,F,G,L,I,2 + L,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] (1 + A,1) 9. lbl13(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> lbl53(A,B,C,1 + L,E,F,G,1 + L,I,2 + L,K,L,M,N) [A >= 3 + B && A >= 2 + B && H >= B && B >= 0 && 1 + B >= H && L = 1 + B && D = 1 + B && N = A && J = A] (0,1) 10. start0(A,B,C,D,E,F,G,H,I,J,K,L,M,N) -> start(A,C,C,E,E,G,G,I,I,K,K,M,M,A) True (1,1) Signature: {(lbl13,14);(lbl53,14);(lbl91,14);(start,14);(start0,14);(stop,14)} Flow Graph: [0->{},1->{4,5,6},2->{4,5,6},3->{7,8,9},4->{3},5->{},6->{},7->{},8->{4,5,6},9->{4,5,6},10->{0,1,2}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))