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 && 1 >= A && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,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 >= 2 && B = C && D = E && F = G && H = A] 2. lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1 + -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1*F >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1 + -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] 3. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 4. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 5. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= F && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4,5},2->{},3->{3,4,5},4->{6,7},5->{6,7},6->{2},7->{3,4,5},8->{0,1}] + 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 && 1 >= A && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,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 >= 2 && B = C && D = E && F = G && H = A] 2. lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (1,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1 + -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1*F >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1 + -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] 3. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 4. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 5. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (1,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= F && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4,5},2->{},3->{3,4,5},4->{6,7},5->{6,7},6->{2},7->{3,4,5},8->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,5),(4,6),(7,5)] * 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 && 1 >= A && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,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 >= 2 && B = C && D = E && F = G && H = A] 2. lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (1,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1 + -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1*F >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1 + -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] 3. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 4. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 5. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (1,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= F && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4},2->{},3->{3,4,5},4->{7},5->{6,7},6->{2},7->{3,4},8->{0,1}] + 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 && 1 >= A && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,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 >= 2 && B = C && D = E && F = G && H = A] 2. lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1 + -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1*F >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1 + -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] 3. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 4. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 5. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= F && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) 9. lbl16(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);(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4,5},2->{},3->{3,4,5},4->{6,7},5->{6,7},6->{2,9},7->{3,4,5},8->{0,1,10},9->{},10->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,5),(4,6),(7,5)] * 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 && 1 >= A && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,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 >= 2 && B = C && D = E && F = G && H = A] 2. lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1 + -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1*F >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1 + -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] 3. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 4. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 5. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= F && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) 9. lbl16(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);(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4},2->{},3->{3,4,5},4->{7},5->{6,7},6->{2,9},7->{3,4},8->{0,1,10},9->{},10->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[3,7,4,5] c: [7] | `- p:[3] c: [3] * 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 && 1 >= A && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> lbl111(A,H,C,1,E,-1 + H,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 >= 2 && B = C && D = E && F = G && H = A] 2. lbl16(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1 + -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1*F >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1 + -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && -1 + A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= 1 + B && F = 0 && H = A && D = A] 3. lbl111(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= F && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 4. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 + D && D >= 1 && A >= 1 + F && A >= D + F && A >= B && F >= 1 && D >= 0 && H = A] 5. lbl111(A,B,C,D,E,F,G,H) -> lbl82(A,B + -1*F,C,H,E,-1 + F,G,H) [A + -1*H >= 0 (?,1) && -2 + H >= 0 && -3 + F + H >= 0 && -1 + -1*F + H >= 0 && -1 + -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -1 + A + -1*F >= 0 && -1 + F >= 0 && -3 + A + F >= 0 && -1 + A + -1*D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= 1 + F && A >= F && A >= B && D = 0 && H = A] 6. lbl82(A,B,C,D,E,F,G,H) -> lbl16(A,B,C,D,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && A >= 2 && A >= B && A >= 1 + B && F = 0 && H = A && D = A] 7. lbl82(A,B,C,D,E,F,G,H) -> lbl111(A,B,C,D + -1*F,E,F,G,H) [D + -1*H >= 0 (?,1) && A + -1*H >= 0 && -2 + H >= 0 && -2 + F + H >= 0 && -2 + -1*F + H >= 0 && -4 + D + H >= 0 && -1*D + H >= 0 && -1*B + H >= 0 && -4 + A + H >= 0 && -1*A + H >= 0 && -2 + D + -1*F >= 0 && -2 + A + -1*F >= 0 && F >= 0 && -2 + D + F >= 0 && -2 + A + F >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -1*B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && A + -1*B >= 0 && -2 + A >= 0 && F >= 1 && A >= F && A >= 2 + F && A >= B && A + F >= 1 + B && H = A && D = A] 8. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) 9. lbl16(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);(lbl111,8);(lbl16,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4},2->{},3->{3,4,5},4->{7},5->{6,7},6->{2,9},7->{3,4},8->{0,1,10},9->{},10->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[3,7,4,5] c: [7] | `- p:[3] c: [3]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,H,0.0,0.0.0] start ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] start ~> lbl111 [A <= A, B <= H, C <= C, D <= K, E <= E, F <= H, G <= G, H <= H] lbl16 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl111 ~> lbl111 [A <= A, B <= B, C <= C, D <= A, E <= E, F <= F, G <= G, H <= H] lbl111 ~> lbl82 [A <= A, B <= B, C <= C, D <= H, E <= E, F <= A, G <= G, H <= H] lbl111 ~> lbl82 [A <= A, B <= B + F, C <= C, D <= H, E <= E, F <= H, G <= G, H <= H] lbl82 ~> lbl16 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl82 ~> lbl111 [A <= A, B <= B, C <= C, D <= D, 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] lbl16 ~> 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 <= K + F] lbl111 ~> lbl111 [A <= A, B <= B, C <= C, D <= A, E <= E, F <= F, G <= G, H <= H] lbl82 ~> lbl111 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl111 ~> lbl82 [A <= A, B <= B, C <= C, D <= H, E <= E, F <= A, G <= G, H <= H] lbl111 ~> lbl82 [A <= A, B <= B + F, C <= C, D <= H, E <= E, F <= H, G <= G, H <= H] + Loop: [0.0.0 <= K + D] lbl111 ~> lbl111 [A <= A, B <= B, C <= C, D <= A, E <= E, F <= F, 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,0.0,0.0.0] start ~> stop [] start ~> lbl111 [H ~=> B,H ~=> F,K ~=> D] lbl16 ~> stop [] lbl111 ~> lbl111 [A ~=> D] lbl111 ~> lbl82 [A ~=> F,H ~=> D] lbl111 ~> lbl82 [H ~=> D,H ~=> F,B ~+> B,F ~+> B] lbl82 ~> lbl16 [] lbl82 ~> lbl111 [] start0 ~> start [A ~=> H,C ~=> B,E ~=> D,G ~=> F] lbl16 ~> exitus616 [] start ~> exitus616 [] + Loop: [F ~+> 0.0,K ~+> 0.0] lbl111 ~> lbl111 [A ~=> D] lbl82 ~> lbl111 [] lbl111 ~> lbl82 [A ~=> F,H ~=> D] lbl111 ~> lbl82 [H ~=> D,H ~=> F,B ~+> B,F ~+> B] + Loop: [D ~+> 0.0.0,K ~+> 0.0.0] lbl111 ~> lbl111 [A ~=> D] + Applied Processor: LareProcessor + Details: start0 ~> stop [A ~=> B ,A ~=> D ,A ~=> F ,A ~=> H ,C ~=> B ,E ~=> D ,G ~=> F ,K ~=> D ,A ~+> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> B ,A ~*> tick ,K ~*> B ,K ~*> 0.0.0 ,K ~*> tick] start0 ~> exitus616 [A ~=> B ,A ~=> D ,A ~=> F ,A ~=> H ,C ~=> B ,E ~=> D ,G ~=> F ,K ~=> D ,A ~+> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> B ,A ~*> tick ,K ~*> B ,K ~*> 0.0.0 ,K ~*> tick] + lbl82> [A ~=> F ,H ~=> D ,H ~=> F ,A ~+> B ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,D ~+> 0.0.0 ,D ~+> tick ,F ~+> B ,F ~+> 0.0 ,F ~+> tick ,H ~+> B ,H ~+> 0.0.0 ,H ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> B ,A ~*> tick ,D ~*> tick ,F ~*> B ,F ~*> tick ,H ~*> B ,H ~*> tick ,K ~*> B ,K ~*> tick] + lbl111> [A ~=> D,D ~+> 0.0.0,D ~+> tick,tick ~+> tick,K ~+> 0.0.0,K ~+> tick] YES(?,POLY)