YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + 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 && A >= 5 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,0,G,1 + 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 && 2 >= A && B = C && D = E && F = G && H = A] 2. start(A,B,C,D,E,F,G,H) -> lbl82(A,0,C,D,E,1,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 >= 3 && 4 >= A && B = C && D = E && F = G && H = A] 3. lbl92(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && D >= 4 && D >= A && 10 + F >= 5*D && H = 1 + D] 4. lbl92(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,0,G,1 + H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && 1 >= D && D >= A && 10 + F >= 5*D && H = 1 + D] 5. lbl92(A,B,C,D,E,F,G,H) -> lbl82(A,0,C,D,E,1,G,H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && D >= 2 && 3 >= D && D >= A && 10 + F >= 5*D && H = 1 + D] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,F,G,1 + H) [4 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 4 + B + -1*H >= 0 && 8 + -1*A + -1*H >= 0 && -3 + H >= 0 && -4 + F + H >= 0 && -3 + B + H >= 0 && -1*A + H >= 0 && 1 + B + -1*F >= 0 && -1 + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && 3 + -1*A + F >= 0 && B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && H >= A && H >= 3 && 4 >= H && F = 10 && B = 9] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,F,C,D,E,1 + F,G,H) [4 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 4 + B + -1*H >= 0 && 8 + -1*A + -1*H >= 0 && -3 + H >= 0 && -4 + F + H >= 0 && -3 + B + H >= 0 && -1*A + H >= 0 && 1 + B + -1*F >= 0 && -1 + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && 3 + -1*A + F >= 0 && B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && H >= 3 && 8 >= B && 9 >= B && H >= A && 4 >= H && F = 1 + B] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl82,8);(lbl92,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4,5},2->{6,7},3->{},4->{3,4,5},5->{6,7},6->{3,4,5},7->{6,7},8->{0,1,2}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + 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) && -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 >= 5 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,0,G,1 + H) [A + -1*H >= 0 (1,1) && -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 && 2 >= A && B = C && D = E && F = G && H = A] 2. start(A,B,C,D,E,F,G,H) -> lbl82(A,0,C,D,E,1,G,H) [A + -1*H >= 0 (1,1) && -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 >= 3 && 4 >= A && B = C && D = E && F = G && H = A] 3. lbl92(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [5 + -1*H >= 0 (1,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && D >= 4 && D >= A && 10 + F >= 5*D && H = 1 + D] 4. lbl92(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,0,G,1 + H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && 1 >= D && D >= A && 10 + F >= 5*D && H = 1 + D] 5. lbl92(A,B,C,D,E,F,G,H) -> lbl82(A,0,C,D,E,1,G,H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && D >= 2 && 3 >= D && D >= A && 10 + F >= 5*D && H = 1 + D] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,F,G,1 + H) [4 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 4 + B + -1*H >= 0 && 8 + -1*A + -1*H >= 0 && -3 + H >= 0 && -4 + F + H >= 0 && -3 + B + H >= 0 && -1*A + H >= 0 && 1 + B + -1*F >= 0 && -1 + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && 3 + -1*A + F >= 0 && B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && H >= A && H >= 3 && 4 >= H && F = 10 && B = 9] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,F,C,D,E,1 + F,G,H) [4 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 4 + B + -1*H >= 0 && 8 + -1*A + -1*H >= 0 && -3 + H >= 0 && -4 + F + H >= 0 && -3 + B + H >= 0 && -1*A + H >= 0 && 1 + B + -1*F >= 0 && -1 + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && 3 + -1*A + F >= 0 && B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && H >= 3 && 8 >= B && 9 >= B && H >= A && 4 >= H && F = 1 + B] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl82,8);(lbl92,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4,5},2->{6,7},3->{},4->{3,4,5},5->{6,7},6->{3,4,5},7->{6,7},8->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,3),(2,6),(4,3),(5,6),(6,4)] * Step 3: AddSinks WORST_CASE(?,POLY) + 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) && -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 >= 5 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,0,G,1 + H) [A + -1*H >= 0 (1,1) && -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 && 2 >= A && B = C && D = E && F = G && H = A] 2. start(A,B,C,D,E,F,G,H) -> lbl82(A,0,C,D,E,1,G,H) [A + -1*H >= 0 (1,1) && -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 >= 3 && 4 >= A && B = C && D = E && F = G && H = A] 3. lbl92(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [5 + -1*H >= 0 (1,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && D >= 4 && D >= A && 10 + F >= 5*D && H = 1 + D] 4. lbl92(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,0,G,1 + H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && 1 >= D && D >= A && 10 + F >= 5*D && H = 1 + D] 5. lbl92(A,B,C,D,E,F,G,H) -> lbl82(A,0,C,D,E,1,G,H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && D >= 2 && 3 >= D && D >= A && 10 + F >= 5*D && H = 1 + D] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,F,G,1 + H) [4 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 4 + B + -1*H >= 0 && 8 + -1*A + -1*H >= 0 && -3 + H >= 0 && -4 + F + H >= 0 && -3 + B + H >= 0 && -1*A + H >= 0 && 1 + B + -1*F >= 0 && -1 + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && 3 + -1*A + F >= 0 && B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && H >= A && H >= 3 && 4 >= H && F = 10 && B = 9] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,F,C,D,E,1 + F,G,H) [4 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 4 + B + -1*H >= 0 && 8 + -1*A + -1*H >= 0 && -3 + H >= 0 && -4 + F + H >= 0 && -3 + B + H >= 0 && -1*A + H >= 0 && 1 + B + -1*F >= 0 && -1 + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && 3 + -1*A + F >= 0 && B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && H >= 3 && 8 >= B && 9 >= B && H >= A && 4 >= H && F = 1 + B] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl82,8);(lbl92,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{4,5},2->{7},3->{},4->{4,5},5->{7},6->{3,5},7->{6,7},8->{0,1,2}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + 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 && A >= 5 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,0,G,1 + 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 && 2 >= A && B = C && D = E && F = G && H = A] 2. start(A,B,C,D,E,F,G,H) -> lbl82(A,0,C,D,E,1,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 >= 3 && 4 >= A && B = C && D = E && F = G && H = A] 3. lbl92(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && D >= 4 && D >= A && 10 + F >= 5*D && H = 1 + D] 4. lbl92(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,0,G,1 + H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && 1 >= D && D >= A && 10 + F >= 5*D && H = 1 + D] 5. lbl92(A,B,C,D,E,F,G,H) -> lbl82(A,0,C,D,E,1,G,H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && D >= 2 && 3 >= D && D >= A && 10 + F >= 5*D && H = 1 + D] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,F,G,1 + H) [4 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 4 + B + -1*H >= 0 && 8 + -1*A + -1*H >= 0 && -3 + H >= 0 && -4 + F + H >= 0 && -3 + B + H >= 0 && -1*A + H >= 0 && 1 + B + -1*F >= 0 && -1 + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && 3 + -1*A + F >= 0 && B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && H >= A && H >= 3 && 4 >= H && F = 10 && B = 9] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,F,C,D,E,1 + F,G,H) [4 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 4 + B + -1*H >= 0 && 8 + -1*A + -1*H >= 0 && -3 + H >= 0 && -4 + F + H >= 0 && -3 + B + H >= 0 && -1*A + H >= 0 && 1 + B + -1*F >= 0 && -1 + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && 3 + -1*A + F >= 0 && B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && H >= 3 && 8 >= B && 9 >= B && H >= A && 4 >= H && F = 1 + B] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) 9. lbl92(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 10. start(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(exitus616,8);(lbl82,8);(lbl92,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4,5,9},2->{6,7},3->{},4->{3,4,5,9},5->{6,7},6->{3,4,5,9},7->{6,7},8->{0,1,2,10},9->{},10->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,3),(2,6),(4,3),(5,6),(6,4)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + 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 && A >= 5 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,0,G,1 + 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 && 2 >= A && B = C && D = E && F = G && H = A] 2. start(A,B,C,D,E,F,G,H) -> lbl82(A,0,C,D,E,1,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 >= 3 && 4 >= A && B = C && D = E && F = G && H = A] 3. lbl92(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && D >= 4 && D >= A && 10 + F >= 5*D && H = 1 + D] 4. lbl92(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,0,G,1 + H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && 1 >= D && D >= A && 10 + F >= 5*D && H = 1 + D] 5. lbl92(A,B,C,D,E,F,G,H) -> lbl82(A,0,C,D,E,1,G,H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && D >= 2 && 3 >= D && D >= A && 10 + F >= 5*D && H = 1 + D] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,F,G,1 + H) [4 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 4 + B + -1*H >= 0 && 8 + -1*A + -1*H >= 0 && -3 + H >= 0 && -4 + F + H >= 0 && -3 + B + H >= 0 && -1*A + H >= 0 && 1 + B + -1*F >= 0 && -1 + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && 3 + -1*A + F >= 0 && B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && H >= A && H >= 3 && 4 >= H && F = 10 && B = 9] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,F,C,D,E,1 + F,G,H) [4 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 4 + B + -1*H >= 0 && 8 + -1*A + -1*H >= 0 && -3 + H >= 0 && -4 + F + H >= 0 && -3 + B + H >= 0 && -1*A + H >= 0 && 1 + B + -1*F >= 0 && -1 + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && 3 + -1*A + F >= 0 && B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && H >= 3 && 8 >= B && 9 >= B && H >= A && 4 >= H && F = 1 + B] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) 9. lbl92(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 10. start(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(exitus616,8);(lbl82,8);(lbl92,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{4,5,9},2->{7},3->{},4->{4,5,9},5->{7},6->{3,5,9},7->{6,7},8->{0,1,2,10},9->{},10->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[4] c: [4] | `- p:[5,6,7] c: [7] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + 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 && A >= 5 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,0,G,1 + 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 && 2 >= A && B = C && D = E && F = G && H = A] 2. start(A,B,C,D,E,F,G,H) -> lbl82(A,0,C,D,E,1,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 >= 3 && 4 >= A && B = C && D = E && F = G && H = A] 3. lbl92(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && D >= 4 && D >= A && 10 + F >= 5*D && H = 1 + D] 4. lbl92(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,0,G,1 + H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && 1 >= D && D >= A && 10 + F >= 5*D && H = 1 + D] 5. lbl92(A,B,C,D,E,F,G,H) -> lbl82(A,0,C,D,E,1,G,H) [5 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 15 + -1*F + -1*H >= 0 && 1 + D + -1*H >= 0 && 9 + -1*D + -1*H >= 0 && 9 + -1*A + -1*H >= 0 && -1 + -1*D + H >= 0 && -1 + -1*A + H >= 0 && 10 + -1*F >= 0 && 14 + -1*D + -1*F >= 0 && 14 + -1*A + -1*F >= 0 && F >= 0 && 2 + -1*D + F >= 0 && 2 + -1*A + F >= 0 && 4 + -1*D >= 0 && 8 + -1*A + -1*D >= 0 && -1*A + D >= 0 && 4 + -1*A >= 0 && D >= 2 && 3 >= D && D >= A && 10 + F >= 5*D && H = 1 + D] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl92(A,B,C,H,E,F,G,1 + H) [4 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 4 + B + -1*H >= 0 && 8 + -1*A + -1*H >= 0 && -3 + H >= 0 && -4 + F + H >= 0 && -3 + B + H >= 0 && -1*A + H >= 0 && 1 + B + -1*F >= 0 && -1 + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && 3 + -1*A + F >= 0 && B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && H >= A && H >= 3 && 4 >= H && F = 10 && B = 9] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,F,C,D,E,1 + F,G,H) [4 + -1*H >= 0 (?,1) && 3 + F + -1*H >= 0 && 4 + B + -1*H >= 0 && 8 + -1*A + -1*H >= 0 && -3 + H >= 0 && -4 + F + H >= 0 && -3 + B + H >= 0 && -1*A + H >= 0 && 1 + B + -1*F >= 0 && -1 + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && 3 + -1*A + F >= 0 && B >= 0 && 4 + -1*A + B >= 0 && 4 + -1*A >= 0 && H >= 3 && 8 >= B && 9 >= B && H >= A && 4 >= H && F = 1 + B] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) 9. lbl92(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 10. start(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(exitus616,8);(lbl82,8);(lbl92,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{4,5,9},2->{7},3->{},4->{4,5,9},5->{7},6->{3,5,9},7->{6,7},8->{0,1,2,10},9->{},10->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[4] c: [4] | `- p:[5,6,7] c: [7]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,H,0.0,0.1] start ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] start ~> lbl92 [A <= A, B <= B, C <= C, D <= H, E <= E, F <= 0*K, G <= G, H <= K + H] start ~> lbl82 [A <= A, B <= 0*K, C <= C, D <= D, E <= E, F <= K, G <= G, H <= H] lbl92 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl92 ~> lbl92 [A <= A, B <= B, C <= C, D <= H, E <= E, F <= 0*K, G <= G, H <= K + H] lbl92 ~> lbl82 [A <= A, B <= 0*K, C <= C, D <= D, E <= E, F <= K, G <= G, H <= H] lbl82 ~> lbl92 [A <= A, B <= B, C <= C, D <= H, E <= E, F <= F, G <= G, H <= 5*K] lbl82 ~> lbl82 [A <= A, B <= F, C <= C, D <= D, E <= E, F <= 10*K, G <= G, H <= H] start0 ~> start [A <= A, B <= C, C <= C, D <= E, E <= E, F <= G, G <= G, H <= A] lbl92 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] start ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] + Loop: [0.0 <= 6*K + H] lbl92 ~> lbl92 [A <= A, B <= B, C <= C, D <= H, E <= E, F <= 0*K, G <= G, H <= K + H] + Loop: [0.1 <= 47*K + F + 9*H] lbl92 ~> lbl82 [A <= A, B <= 0*K, C <= C, D <= D, E <= E, F <= K, G <= G, H <= H] lbl82 ~> lbl92 [A <= A, B <= B, C <= C, D <= H, E <= E, F <= F, G <= G, H <= 5*K] lbl82 ~> lbl82 [A <= A, B <= F, C <= C, D <= D, E <= E, F <= 10*K, G <= G, H <= H] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,H,0.0,0.1] start ~> stop [] start ~> lbl92 [H ~=> D,K ~=> F,H ~+> H,K ~+> H] start ~> lbl82 [K ~=> B,K ~=> F] lbl92 ~> stop [] lbl92 ~> lbl92 [H ~=> D,K ~=> F,H ~+> H,K ~+> H] lbl92 ~> lbl82 [K ~=> B,K ~=> F] lbl82 ~> lbl92 [H ~=> D,K ~=> H] lbl82 ~> lbl82 [F ~=> B,K ~=> F] start0 ~> start [A ~=> H,C ~=> B,E ~=> D,G ~=> F] lbl92 ~> exitus616 [] start ~> exitus616 [] + Loop: [H ~+> 0.0,K ~*> 0.0] lbl92 ~> lbl92 [H ~=> D,K ~=> F,H ~+> H,K ~+> H] + Loop: [F ~+> 0.1,H ~*> 0.1,K ~*> 0.1] lbl92 ~> lbl82 [K ~=> B,K ~=> F] lbl82 ~> lbl92 [H ~=> D,K ~=> H] lbl82 ~> lbl82 [F ~=> B,K ~=> F] + Applied Processor: LareProcessor + Details: start0 ~> stop [A ~=> D ,A ~=> H ,C ~=> B ,E ~=> D ,G ~=> F ,K ~=> B ,K ~=> D ,K ~=> F ,K ~=> H ,A ~+> D ,A ~+> H ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> H ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,A ~*> H ,A ~*> 0.1 ,A ~*> tick ,K ~*> D ,K ~*> H ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] start0 ~> exitus616 [A ~=> D ,A ~=> H ,C ~=> B ,E ~=> D ,G ~=> F ,K ~=> B ,K ~=> D ,K ~=> F ,K ~=> H ,A ~+> D ,A ~+> H ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> H ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,A ~*> H ,A ~*> 0.1 ,A ~*> tick ,K ~*> D ,K ~*> H ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] + lbl92> [H ~=> D ,K ~=> F ,H ~+> D ,H ~+> H ,H ~+> 0.0 ,H ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> H ,H ~*> H ,K ~*> D ,K ~*> H ,K ~*> 0.0 ,K ~*> tick] + lbl92> [H ~=> D ,K ~=> B ,K ~=> D ,K ~=> F ,K ~=> H ,F ~+> 0.1 ,F ~+> tick ,tick ~+> tick ,H ~*> 0.1 ,H ~*> tick ,K ~*> 0.1 ,K ~*> tick] lbl92> [F ~=> B ,H ~=> D ,K ~=> B ,K ~=> D ,K ~=> F ,K ~=> H ,F ~+> 0.1 ,F ~+> tick ,tick ~+> tick ,H ~*> 0.1 ,H ~*> tick ,K ~*> 0.1 ,K ~*> tick] YES(?,POLY)