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) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + G && B = C && D = E && F = G && H = A] 2. start(A,B,C,D,E,F,G,H) -> stop(A,0,C,F,E,F,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && F = 0 && B = C && D = E && G = 0 && H = A] 3. start(A,B,C,D,E,F,G,H) -> lM1(A,1,C,-1 + F,E,F,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && G >= 1 && B = C && D = E && F = G && H = A] 4. lM1(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 (?,1) && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= B && G >= B && B >= 1 && D = 0 && H = A && F = G] 5. lM1(A,B,C,D,E,F,G,H) -> lZZ1(A,0,C,D,E,F,G,H) [A + -1*H >= 0 (?,1) && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && D >= 1 && G >= A + D && A >= 1 && B = A && H = A && F = G] 6. lM1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A + -1*H >= 0 (?,1) && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B && D >= 1 && A >= B && G >= B + D && B >= 1 && H = A && F = G] 7. lZZ1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [-1 + G + -1*H >= 0 (?,1) && -1 + F + -1*H >= 0 && A + -1*H >= 0 && -1 + H >= 0 && -3 + G + H >= 0 && -3 + F + H >= 0 && -2 + D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -2 + G >= 0 && -4 + F + G >= 0 && -1*F + G >= 0 && -3 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -2 + -1*B + G >= 0 && -3 + A + G >= 0 && -1 + -1*A + G >= 0 && -2 + F >= 0 && -3 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -2 + -1*B + F >= 0 && -3 + A + F >= 0 && -1 + -1*A + F >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D >= 1 && G >= A + D && A >= 2 && B = 0 && H = A && F = G] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lM1,8);(lZZ1,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{},2->{},3->{4,5,6},4->{},5->{7},6->{4,5,6},7->{4,5,6},8->{0,1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(7,5)] * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + G && B = C && D = E && F = G && H = A] 2. start(A,B,C,D,E,F,G,H) -> stop(A,0,C,F,E,F,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && F = 0 && B = C && D = E && G = 0 && H = A] 3. start(A,B,C,D,E,F,G,H) -> lM1(A,1,C,-1 + F,E,F,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && G >= 1 && B = C && D = E && F = G && H = A] 4. lM1(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 (?,1) && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= B && G >= B && B >= 1 && D = 0 && H = A && F = G] 5. lM1(A,B,C,D,E,F,G,H) -> lZZ1(A,0,C,D,E,F,G,H) [A + -1*H >= 0 (?,1) && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && D >= 1 && G >= A + D && A >= 1 && B = A && H = A && F = G] 6. lM1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A + -1*H >= 0 (?,1) && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B && D >= 1 && A >= B && G >= B + D && B >= 1 && H = A && F = G] 7. lZZ1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [-1 + G + -1*H >= 0 (?,1) && -1 + F + -1*H >= 0 && A + -1*H >= 0 && -1 + H >= 0 && -3 + G + H >= 0 && -3 + F + H >= 0 && -2 + D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -2 + G >= 0 && -4 + F + G >= 0 && -1*F + G >= 0 && -3 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -2 + -1*B + G >= 0 && -3 + A + G >= 0 && -1 + -1*A + G >= 0 && -2 + F >= 0 && -3 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -2 + -1*B + F >= 0 && -3 + A + F >= 0 && -1 + -1*A + F >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D >= 1 && G >= A + D && A >= 2 && B = 0 && H = A && F = G] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lM1,8);(lZZ1,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{},2->{},3->{4,5,6},4->{},5->{7},6->{4,5,6},7->{4,6},8->{0,1,2,3}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + G && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> stop(A,0,C,F,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && F = 0 && B = C && D = E && G = 0 && H = A] start(A,B,C,D,E,F,G,H) -> lM1(A,1,C,-1 + F,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && G >= 1 && B = C && D = E && F = G && H = A] lM1(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= B && G >= B && B >= 1 && D = 0 && H = A && F = G] lM1(A,B,C,D,E,F,G,H) -> lZZ1(A,0,C,D,E,F,G,H) [A + -1*H >= 0 && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && D >= 1 && G >= A + D && A >= 1 && B = A && H = A && F = G] lM1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A + -1*H >= 0 && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B && D >= 1 && A >= B && G >= B + D && B >= 1 && H = A && F = G] lZZ1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [-1 + G + -1*H >= 0 && -1 + F + -1*H >= 0 && A + -1*H >= 0 && -1 + H >= 0 && -3 + G + H >= 0 && -3 + F + H >= 0 && -2 + D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -2 + G >= 0 && -4 + F + G >= 0 && -1*F + G >= 0 && -3 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -2 + -1*B + G >= 0 && -3 + A + G >= 0 && -1 + -1*A + G >= 0 && -2 + F >= 0 && -3 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -2 + -1*B + F >= 0 && -3 + A + F >= 0 && -1 + -1*A + F >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D >= 1 && G >= A + D && A >= 2 && B = 0 && H = A && F = G] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True Signature: {(lM1,8);(lZZ1,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{},2->{},3->{4,5,6},4->{},5->{7},6->{4,5,6},7->{4,6},8->{0,1,2,3}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + G && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> stop(A,0,C,F,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && F = 0 && B = C && D = E && G = 0 && H = A] start(A,B,C,D,E,F,G,H) -> lM1(A,1,C,-1 + F,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && G >= 1 && B = C && D = E && F = G && H = A] lM1(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= B && G >= B && B >= 1 && D = 0 && H = A && F = G] lM1(A,B,C,D,E,F,G,H) -> lZZ1(A,0,C,D,E,F,G,H) [A + -1*H >= 0 && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && D >= 1 && G >= A + D && A >= 1 && B = A && H = A && F = G] lM1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A + -1*H >= 0 && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B && D >= 1 && A >= B && G >= B + D && B >= 1 && H = A && F = G] lZZ1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [-1 + G + -1*H >= 0 && -1 + F + -1*H >= 0 && A + -1*H >= 0 && -1 + H >= 0 && -3 + G + H >= 0 && -3 + F + H >= 0 && -2 + D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -2 + G >= 0 && -4 + F + G >= 0 && -1*F + G >= 0 && -3 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -2 + -1*B + G >= 0 && -3 + A + G >= 0 && -1 + -1*A + G >= 0 && -2 + F >= 0 && -3 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -2 + -1*B + F >= 0 && -3 + A + F >= 0 && -1 + -1*A + F >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D >= 1 && G >= A + D && A >= 2 && B = 0 && H = A && F = G] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True Signature: {(exitus616,8);(lM1,8);(lZZ1,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{12},1->{11},2->{10},3->{4,5,6},4->{9},5->{7},6->{4,5,6},7->{4,6},8->{0,1,2,3}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[5,6,7] c: [5,6,7] * Step 5: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + G && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> stop(A,0,C,F,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && F = 0 && B = C && D = E && G = 0 && H = A] start(A,B,C,D,E,F,G,H) -> lM1(A,1,C,-1 + F,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && G >= 1 && B = C && D = E && F = G && H = A] lM1(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= B && G >= B && B >= 1 && D = 0 && H = A && F = G] lM1(A,B,C,D,E,F,G,H) -> lZZ1(A,0,C,D,E,F,G,H) [A + -1*H >= 0 && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && D >= 1 && G >= A + D && A >= 1 && B = A && H = A && F = G] lM1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [A + -1*H >= 0 && -1 + H >= 0 && -2 + G + H >= 0 && -2 + F + H >= 0 && -1 + D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1 + G >= 0 && -2 + F + G >= 0 && -1*F + G >= 0 && -1 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -1*B + G >= 0 && -2 + A + G >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -1*B + F >= 0 && -2 + A + F >= 0 && D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && A + -1*B >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B && D >= 1 && A >= B && G >= B + D && B >= 1 && H = A && F = G] lZZ1(A,B,C,D,E,F,G,H) -> lM1(A,1 + B,C,-1 + D,E,F,G,H) [-1 + G + -1*H >= 0 && -1 + F + -1*H >= 0 && A + -1*H >= 0 && -1 + H >= 0 && -3 + G + H >= 0 && -3 + F + H >= 0 && -2 + D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + A + H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -2 + G >= 0 && -4 + F + G >= 0 && -1*F + G >= 0 && -3 + D + G >= 0 && -1 + -1*D + G >= 0 && -2 + B + G >= 0 && -2 + -1*B + G >= 0 && -3 + A + G >= 0 && -1 + -1*A + G >= 0 && -2 + F >= 0 && -3 + D + F >= 0 && -1 + -1*D + F >= 0 && -2 + B + F >= 0 && -2 + -1*B + F >= 0 && -3 + A + F >= 0 && -1 + -1*A + F >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D >= 1 && G >= A + D && A >= 2 && B = 0 && H = A && F = G] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True Signature: {(exitus616,8);(lM1,8);(lZZ1,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{12},1->{11},2->{10},3->{4,5,6},4->{9},5->{7},6->{4,5,6},7->{4,6},8->{0,1,2,3}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[5,6,7] c: [5,6,7]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,H,0.0] start ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] start ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] start ~> stop [A <= A, B <= 0*K, C <= C, D <= F, E <= E, F <= F, G <= G, H <= H] start ~> lM1 [A <= A, B <= K, C <= C, D <= G, E <= E, F <= F, G <= G, H <= H] lM1 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lM1 ~> lZZ1 [A <= A, B <= 0*K, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lM1 ~> lM1 [A <= A, B <= H, C <= C, D <= F, E <= E, F <= F, G <= G, H <= H] lZZ1 ~> lM1 [A <= A, B <= K, C <= C, D <= F, E <= E, F <= F, G <= G, H <= H] start0 ~> start [A <= A, B <= C, C <= C, D <= E, E <= E, F <= G, G <= G, H <= A] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] + Loop: [0.0 <= A + B + D] lM1 ~> lZZ1 [A <= A, B <= 0*K, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lM1 ~> lM1 [A <= A, B <= H, C <= C, D <= F, E <= E, F <= F, G <= G, H <= H] lZZ1 ~> lM1 [A <= A, B <= K, C <= C, D <= F, E <= E, F <= F, G <= G, H <= H] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,H,0.0] start ~> stop [] start ~> stop [] start ~> stop [F ~=> D,K ~=> B] start ~> lM1 [G ~=> D,K ~=> B] lM1 ~> stop [] lM1 ~> lZZ1 [K ~=> B] lM1 ~> lM1 [F ~=> D,H ~=> B] lZZ1 ~> lM1 [F ~=> D,K ~=> B] start0 ~> start [A ~=> H,C ~=> B,E ~=> D,G ~=> F] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,D ~+> 0.0] lM1 ~> lZZ1 [K ~=> B] lM1 ~> lM1 [F ~=> D,H ~=> B] lZZ1 ~> lM1 [F ~=> D,K ~=> B] + Applied Processor: Lare + Details: start0 ~> exitus616 [A ~=> B ,A ~=> H ,C ~=> B ,E ~=> D ,G ~=> D ,G ~=> F ,K ~=> B ,A ~+> 0.0 ,A ~+> tick ,G ~+> 0.0 ,G ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick] + lM1> [F ~=> D ,H ~=> B ,K ~=> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick] YES(?,O(n^1))