YES(?,POLY) * Step 1: 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) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A && E = F && G = H] 1. start(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,2*D,F,-1 + 2*D,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && B = C && D = A && E = F && G = H] 2. start(A,B,C,D,E,F,G,H) -> lbl121(A,2*D,C,D,-1 + 2*D,F,-1 + 2*D,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && B = C && D = A && E = F && G = H] 3. lbl82(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [1 + G >= 0 (?,1) && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= A && 2*A >= E && D = A && 1 + G = A] 4. lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [1 + G >= 0 (?,1) && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] 5. lbl82(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [1 + G >= 0 (?,1) && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] 6. lbl121(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [1 + G >= 0 (?,1) && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 1 + E && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] 7. lbl121(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [1 + G >= 0 (?,1) && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] 8. lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [1 + G >= 0 (?,1) && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] 9. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(lbl121,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4,5},2->{6,7,8},3->{},4->{3,4,5},5->{6,7,8},6->{},7->{3,4,5},8->{6,7,8},9->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(5,6)] * Step 2: FromIts 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) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A && E = F && G = H] 1. start(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,2*D,F,-1 + 2*D,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && B = C && D = A && E = F && G = H] 2. start(A,B,C,D,E,F,G,H) -> lbl121(A,2*D,C,D,-1 + 2*D,F,-1 + 2*D,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && B = C && D = A && E = F && G = H] 3. lbl82(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [1 + G >= 0 (?,1) && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= A && 2*A >= E && D = A && 1 + G = A] 4. lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [1 + G >= 0 (?,1) && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] 5. lbl82(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [1 + G >= 0 (?,1) && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] 6. lbl121(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [1 + G >= 0 (?,1) && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 1 + E && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] 7. lbl121(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [1 + G >= 0 (?,1) && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] 8. lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [1 + G >= 0 (?,1) && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] 9. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(lbl121,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,4,5},2->{6,7,8},3->{},4->{3,4,5},5->{7,8},6->{},7->{3,4,5},8->{6,7,8},9->{0,1,2}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,2*D,F,-1 + 2*D,H) [G + -1*H >= 0 && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl121(A,2*D,C,D,-1 + 2*D,F,-1 + 2*D,H) [G + -1*H >= 0 && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && B = C && D = A && E = F && G = H] lbl82(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [1 + G >= 0 && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= A && 2*A >= E && D = A && 1 + G = A] lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [1 + G >= 0 && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] lbl82(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [1 + G >= 0 && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] lbl121(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [1 + G >= 0 && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 1 + E && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] lbl121(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [1 + G >= 0 && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [1 + G >= 0 && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True Signature: {(lbl121,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{3,4,5},2->{6,7,8},3->{},4->{3,4,5},5->{7,8},6->{},7->{3,4,5},8->{6,7,8},9->{0,1,2}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,2*D,F,-1 + 2*D,H) [G + -1*H >= 0 && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl121(A,2*D,C,D,-1 + 2*D,F,-1 + 2*D,H) [G + -1*H >= 0 && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && B = C && D = A && E = F && G = H] lbl82(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [1 + G >= 0 && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= A && 2*A >= E && D = A && 1 + G = A] lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [1 + G >= 0 && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] lbl82(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [1 + G >= 0 && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] lbl121(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [1 + G >= 0 && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 1 + E && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] lbl121(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [1 + G >= 0 && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [1 + G >= 0 && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,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 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);(lbl121,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{14},1->{3,4,5},2->{6,7,8},3->{11,13},4->{3,4,5},5->{7,8},6->{10,12},7->{3,4,5},8->{6,7,8},9->{0,1,2}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14] | `- p:[4,7,5,8] c: [5,7,8] | `- p:[4] c: [4] * Step 5: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,2*D,F,-1 + 2*D,H) [G + -1*H >= 0 && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl121(A,2*D,C,D,-1 + 2*D,F,-1 + 2*D,H) [G + -1*H >= 0 && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && B = C && D = A && E = F && G = H] lbl82(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [1 + G >= 0 && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= A && 2*A >= E && D = A && 1 + G = A] lbl82(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [1 + G >= 0 && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] lbl82(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [1 + G >= 0 && 1 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && E >= 0 && D + E >= 0 && -1*D + E >= 0 && A + E >= 0 && -1*A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && G >= A && E >= 1 + G && 2*A >= E && 1 + G >= A && D = A] lbl121(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [1 + G >= 0 && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && A >= 1 + E && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] lbl121(A,B,C,D,E,F,G,H) -> lbl82(A,B,C,D,E,F,-1 + G,H) [1 + G >= 0 && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,G,C,D,-1 + E,F,-1 + E,H) [1 + G >= 0 && 2 + E + G >= 0 && 1 + D + G >= 0 && 1 + -1*D + G >= 0 && 1 + B + G >= 0 && 1 + A + G >= 0 && 1 + -1*A + G >= 0 && 1 + E >= 0 && 1 + D + E >= 0 && 1 + -1*D + E >= 0 && 1 + B + E >= 0 && 1 + A + E >= 0 && 1 + -1*A + E >= 0 && B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && B + D >= 0 && A + D >= 0 && -1*A + D >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && A >= 0 && E >= A && 2*A >= 1 + E && B >= A && 1 + E >= B && G = E && D = A] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,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 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);(lbl121,8);(lbl82,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{14},1->{3,4,5},2->{6,7,8},3->{11,13},4->{3,4,5},5->{7,8},6->{10,12},7->{3,4,5},8->{6,7,8},9->{0,1,2}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14] | `- p:[4,7,5,8] c: [5,7,8] | `- p:[4] c: [4]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow 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 ~> lbl82 [A <= A, B <= B, C <= C, D <= D, E <= A + D, F <= F, G <= K + A + D, H <= H] start ~> lbl121 [A <= A, B <= A + D, C <= C, D <= D, E <= K + A + D, F <= F, G <= K + A + D, H <= H] lbl82 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl82 ~> lbl82 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl82 ~> lbl121 [A <= A, B <= G, C <= C, D <= D, E <= E, F <= F, G <= E, H <= H] lbl121 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl121 ~> lbl82 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl121 ~> lbl121 [A <= A, B <= G, C <= C, D <= D, E <= G, F <= F, G <= G, H <= H] start0 ~> start [A <= A, B <= C, C <= C, D <= A, E <= F, F <= F, G <= H, 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] 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 <= K + E] lbl82 ~> lbl82 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl121 ~> lbl82 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl82 ~> lbl121 [A <= A, B <= G, C <= C, D <= D, E <= E, F <= F, G <= E, H <= H] lbl121 ~> lbl121 [A <= A, B <= G, C <= C, D <= D, E <= G, F <= F, G <= G, H <= H] + Loop: [0.0.0 <= K + D + G] lbl82 ~> lbl82 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare 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 ~> lbl82 [A ~+> E,A ~+> G,D ~+> E,D ~+> G,K ~+> G] start ~> lbl121 [A ~+> B,A ~+> E,A ~+> G,D ~+> B,D ~+> E,D ~+> G,K ~+> E,K ~+> G] lbl82 ~> stop [] lbl82 ~> lbl82 [] lbl82 ~> lbl121 [E ~=> G,G ~=> B] lbl121 ~> stop [] lbl121 ~> lbl82 [] lbl121 ~> lbl121 [G ~=> B,G ~=> E] start0 ~> start [A ~=> D,C ~=> B,F ~=> E,H ~=> G] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] + Loop: [E ~+> 0.0,K ~+> 0.0] lbl82 ~> lbl82 [] lbl121 ~> lbl82 [] lbl82 ~> lbl121 [E ~=> G,G ~=> B] lbl121 ~> lbl121 [G ~=> B,G ~=> E] + Loop: [D ~+> 0.0.0,G ~+> 0.0.0,K ~+> 0.0.0] lbl82 ~> lbl82 [] + Applied Processor: Lare + Details: start0 ~> exitus616 [A ~=> D ,C ~=> B ,F ~=> E ,H ~=> G ,A ~+> B ,A ~+> E ,A ~+> G ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> E ,K ~+> G ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> B ,A ~*> E ,A ~*> G ,A ~*> 0.0 ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] + lbl82> [E ~=> B ,E ~=> G ,G ~=> B ,D ~+> 0.0.0 ,D ~+> tick ,E ~+> 0.0 ,E ~+> tick ,G ~+> 0.0.0 ,G ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,E ~*> tick ,K ~*> tick] lbl121> [E ~=> B ,E ~=> G ,G ~=> B ,D ~+> 0.0.0 ,D ~+> tick ,E ~+> 0.0 ,E ~+> tick ,G ~+> 0.0.0 ,G ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,E ~*> tick ,K ~*> tick] lbl82> [E ~=> B ,E ~=> G ,G ~=> B ,G ~=> E ,D ~+> 0.0.0 ,D ~+> tick ,E ~+> 0.0 ,E ~+> tick ,G ~+> 0.0.0 ,G ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,E ~*> tick ,K ~*> tick] lbl121> [E ~=> B ,E ~=> G ,G ~=> B ,G ~=> E ,D ~+> 0.0.0 ,D ~+> tick ,E ~+> 0.0 ,E ~+> tick ,G ~+> 0.0.0 ,G ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,E ~*> tick ,K ~*> tick] + lbl82> [D ~+> 0.0.0,D ~+> tick,G ~+> 0.0.0,G ~+> tick,tick ~+> tick,K ~+> 0.0.0,K ~+> tick] YES(?,POLY)