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) [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 >= A && B = C && D = A && E = F && G = H] 1. start(A,B,C,D,E,F,G,H) -> lbl6(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 && A >= 1 && A >= C && B = C && D = A && E = F && G = H] 2. start(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1,F,0,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 >= 1 && C >= 1 + A && B = C && D = A && E = F && G = H] 3. lbl6(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 + D >= 0 && -1*C + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1*B + C >= 0 && A + -1*B >= 0 && -1 + A >= 0 && A >= 1 && A >= C && G = H && E = F && D = A && B = C] 4. lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1 + E,F,G,H) [G >= 0 (?,1) && -1 + E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -1 + A + G >= 0 && D + -1*E >= 0 && -1 + C + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + E && C >= 1 + G && A + C >= 3 + G && A >= E && E >= 1 && C >= 1 + A && D = A && B = C] 5. lbl121(A,B,C,D,E,F,G,H) -> lbl141(A,B,C,D,0,F,1 + G,H) [G >= 0 (?,1) && -1 + E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -1 + A + G >= 0 && D + -1*E >= 0 && -1 + C + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + G && A + C >= 3 + G && A >= 1 && C >= 1 + A && E = A && D = A && B = C] 6. lbl141(A,B,C,D,E,F,G,H) -> cut(A,B,C,D,E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && -2 + A + G >= 0 && -1*E >= 0 && -1 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 2 && C >= 1 + A && C >= 1 && G = C && E = 0 && D = A && B = C] 7. lbl141(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1 + E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && -2 + A + G >= 0 && -1*E >= 0 && -1 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 && C >= 1 + G && A >= 2 && C >= 1 + A && G >= 1 && C >= G && E = 0 && D = A && B = C] 8. cut(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -3 + G >= 0 && -3 + E + G >= 0 && -3 + -1*E + G >= 0 && -5 + D + G >= 0 && -1 + -1*D + G >= 0 && -6 + C + G >= 0 && -1*C + G >= 0 && -6 + B + G >= 0 && -1*B + G >= 0 && -5 + A + G >= 0 && -1 + -1*A + G >= 0 && -1*E >= 0 && -2 + D + -1*E >= 0 && -3 + C + -1*E >= 0 && -3 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -5 + C + D >= 0 && -5 + B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -5 + A + C >= 0 && -1 + -1*A + C >= 0 && -3 + B >= 0 && -5 + A + B >= 0 && -1 + -1*A + B >= 0 && -2 + A >= 0 && C >= 1 + A && A >= 2 && E = 0 && G = C && D = A && B = C] 9. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(cut,8);(lbl121,8);(lbl141,8);(lbl6,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3},2->{4,5},3->{},4->{4,5},5->{6,7},6->{8},7->{4,5},8->{},9->{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) [G + -1*H >= 0 (1,1) && -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 >= A && B = C && D = A && E = F && G = H] 1. start(A,B,C,D,E,F,G,H) -> lbl6(A,B,C,D,E,F,G,H) [G + -1*H >= 0 (1,1) && -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 >= 1 && A >= C && B = C && D = A && E = F && G = H] 2. start(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1,F,0,H) [G + -1*H >= 0 (1,1) && -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 >= 1 && C >= 1 + A && B = C && D = A && E = F && G = H] 3. lbl6(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 (1,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1*C + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1*B + C >= 0 && A + -1*B >= 0 && -1 + A >= 0 && A >= 1 && A >= C && G = H && E = F && D = A && B = C] 4. lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1 + E,F,G,H) [G >= 0 (?,1) && -1 + E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -1 + A + G >= 0 && D + -1*E >= 0 && -1 + C + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + E && C >= 1 + G && A + C >= 3 + G && A >= E && E >= 1 && C >= 1 + A && D = A && B = C] 5. lbl121(A,B,C,D,E,F,G,H) -> lbl141(A,B,C,D,0,F,1 + G,H) [G >= 0 (?,1) && -1 + E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -1 + A + G >= 0 && D + -1*E >= 0 && -1 + C + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + G && A + C >= 3 + G && A >= 1 && C >= 1 + A && E = A && D = A && B = C] 6. lbl141(A,B,C,D,E,F,G,H) -> cut(A,B,C,D,E,F,G,H) [C + -1*G >= 0 (1,1) && B + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && -2 + A + G >= 0 && -1*E >= 0 && -1 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 2 && C >= 1 + A && C >= 1 && G = C && E = 0 && D = A && B = C] 7. lbl141(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1 + E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && -2 + A + G >= 0 && -1*E >= 0 && -1 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 && C >= 1 + G && A >= 2 && C >= 1 + A && G >= 1 && C >= G && E = 0 && D = A && B = C] 8. cut(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [C + -1*G >= 0 (1,1) && B + -1*G >= 0 && -3 + G >= 0 && -3 + E + G >= 0 && -3 + -1*E + G >= 0 && -5 + D + G >= 0 && -1 + -1*D + G >= 0 && -6 + C + G >= 0 && -1*C + G >= 0 && -6 + B + G >= 0 && -1*B + G >= 0 && -5 + A + G >= 0 && -1 + -1*A + G >= 0 && -1*E >= 0 && -2 + D + -1*E >= 0 && -3 + C + -1*E >= 0 && -3 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -5 + C + D >= 0 && -5 + B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -5 + A + C >= 0 && -1 + -1*A + C >= 0 && -3 + B >= 0 && -5 + A + B >= 0 && -1 + -1*A + B >= 0 && -2 + A >= 0 && C >= 1 + A && A >= 2 && E = 0 && G = C && D = A && B = C] 9. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(cut,8);(lbl121,8);(lbl141,8);(lbl6,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3},2->{4,5},3->{},4->{4,5},5->{6,7},6->{8},7->{4,5},8->{},9->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(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) [G + -1*H >= 0 (1,1) && -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 >= A && B = C && D = A && E = F && G = H] 1. start(A,B,C,D,E,F,G,H) -> lbl6(A,B,C,D,E,F,G,H) [G + -1*H >= 0 (1,1) && -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 >= 1 && A >= C && B = C && D = A && E = F && G = H] 2. start(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1,F,0,H) [G + -1*H >= 0 (1,1) && -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 >= 1 && C >= 1 + A && B = C && D = A && E = F && G = H] 3. lbl6(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 (1,1) && -1*G + H >= 0 && E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1*C + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1*B + C >= 0 && A + -1*B >= 0 && -1 + A >= 0 && A >= 1 && A >= C && G = H && E = F && D = A && B = C] 4. lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1 + E,F,G,H) [G >= 0 (?,1) && -1 + E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -1 + A + G >= 0 && D + -1*E >= 0 && -1 + C + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + E && C >= 1 + G && A + C >= 3 + G && A >= E && E >= 1 && C >= 1 + A && D = A && B = C] 5. lbl121(A,B,C,D,E,F,G,H) -> lbl141(A,B,C,D,0,F,1 + G,H) [G >= 0 (?,1) && -1 + E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -1 + A + G >= 0 && D + -1*E >= 0 && -1 + C + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + G && A + C >= 3 + G && A >= 1 && C >= 1 + A && E = A && D = A && B = C] 6. lbl141(A,B,C,D,E,F,G,H) -> cut(A,B,C,D,E,F,G,H) [C + -1*G >= 0 (1,1) && B + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && -2 + A + G >= 0 && -1*E >= 0 && -1 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 2 && C >= 1 + A && C >= 1 && G = C && E = 0 && D = A && B = C] 7. lbl141(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1 + E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && -2 + A + G >= 0 && -1*E >= 0 && -1 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 && C >= 1 + G && A >= 2 && C >= 1 + A && G >= 1 && C >= G && E = 0 && D = A && B = C] 8. cut(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [C + -1*G >= 0 (1,1) && B + -1*G >= 0 && -3 + G >= 0 && -3 + E + G >= 0 && -3 + -1*E + G >= 0 && -5 + D + G >= 0 && -1 + -1*D + G >= 0 && -6 + C + G >= 0 && -1*C + G >= 0 && -6 + B + G >= 0 && -1*B + G >= 0 && -5 + A + G >= 0 && -1 + -1*A + G >= 0 && -1*E >= 0 && -2 + D + -1*E >= 0 && -3 + C + -1*E >= 0 && -3 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -5 + C + D >= 0 && -5 + B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -5 + A + C >= 0 && -1 + -1*A + C >= 0 && -3 + B >= 0 && -5 + A + B >= 0 && -1 + -1*A + B >= 0 && -2 + A >= 0 && C >= 1 + A && A >= 2 && E = 0 && G = C && D = A && B = C] 9. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(cut,8);(lbl121,8);(lbl141,8);(lbl6,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3},2->{4,5},3->{},4->{4,5},5->{6,7},6->{8},7->{4},8->{},9->{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) [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 >= A && B = C && D = A && E = F && G = H] 1. start(A,B,C,D,E,F,G,H) -> lbl6(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 && A >= 1 && A >= C && B = C && D = A && E = F && G = H] 2. start(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1,F,0,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 >= 1 && C >= 1 + A && B = C && D = A && E = F && G = H] 3. lbl6(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 + D >= 0 && -1*C + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1*B + C >= 0 && A + -1*B >= 0 && -1 + A >= 0 && A >= 1 && A >= C && G = H && E = F && D = A && B = C] 4. lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1 + E,F,G,H) [G >= 0 (?,1) && -1 + E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -1 + A + G >= 0 && D + -1*E >= 0 && -1 + C + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + E && C >= 1 + G && A + C >= 3 + G && A >= E && E >= 1 && C >= 1 + A && D = A && B = C] 5. lbl121(A,B,C,D,E,F,G,H) -> lbl141(A,B,C,D,0,F,1 + G,H) [G >= 0 (?,1) && -1 + E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -1 + A + G >= 0 && D + -1*E >= 0 && -1 + C + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + G && A + C >= 3 + G && A >= 1 && C >= 1 + A && E = A && D = A && B = C] 6. lbl141(A,B,C,D,E,F,G,H) -> cut(A,B,C,D,E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && -2 + A + G >= 0 && -1*E >= 0 && -1 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 2 && C >= 1 + A && C >= 1 && G = C && E = 0 && D = A && B = C] 7. lbl141(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1 + E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && -2 + A + G >= 0 && -1*E >= 0 && -1 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 && C >= 1 + G && A >= 2 && C >= 1 + A && G >= 1 && C >= G && E = 0 && D = A && B = C] 8. cut(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -3 + G >= 0 && -3 + E + G >= 0 && -3 + -1*E + G >= 0 && -5 + D + G >= 0 && -1 + -1*D + G >= 0 && -6 + C + G >= 0 && -1*C + G >= 0 && -6 + B + G >= 0 && -1*B + G >= 0 && -5 + A + G >= 0 && -1 + -1*A + G >= 0 && -1*E >= 0 && -2 + D + -1*E >= 0 && -3 + C + -1*E >= 0 && -3 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -5 + C + D >= 0 && -5 + B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -5 + A + C >= 0 && -1 + -1*A + C >= 0 && -3 + B >= 0 && -5 + A + B >= 0 && -1 + -1*A + B >= 0 && -2 + A >= 0 && C >= 1 + A && A >= 2 && E = 0 && G = C && D = A && B = C] 9. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) 10. cut(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 11. lbl6(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 12. start(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(cut,8);(exitus616,8);(lbl121,8);(lbl141,8);(lbl6,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,11},2->{4,5},3->{},4->{4,5},5->{6,7},6->{8,10},7->{4,5},8->{},9->{0,1,2,12},10->{},11->{} ,12->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(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) [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 >= A && B = C && D = A && E = F && G = H] 1. start(A,B,C,D,E,F,G,H) -> lbl6(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 && A >= 1 && A >= C && B = C && D = A && E = F && G = H] 2. start(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1,F,0,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 >= 1 && C >= 1 + A && B = C && D = A && E = F && G = H] 3. lbl6(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 + D >= 0 && -1*C + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1*B + C >= 0 && A + -1*B >= 0 && -1 + A >= 0 && A >= 1 && A >= C && G = H && E = F && D = A && B = C] 4. lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1 + E,F,G,H) [G >= 0 (?,1) && -1 + E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -1 + A + G >= 0 && D + -1*E >= 0 && -1 + C + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + E && C >= 1 + G && A + C >= 3 + G && A >= E && E >= 1 && C >= 1 + A && D = A && B = C] 5. lbl121(A,B,C,D,E,F,G,H) -> lbl141(A,B,C,D,0,F,1 + G,H) [G >= 0 (?,1) && -1 + E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -1 + A + G >= 0 && D + -1*E >= 0 && -1 + C + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + G && A + C >= 3 + G && A >= 1 && C >= 1 + A && E = A && D = A && B = C] 6. lbl141(A,B,C,D,E,F,G,H) -> cut(A,B,C,D,E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && -2 + A + G >= 0 && -1*E >= 0 && -1 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 2 && C >= 1 + A && C >= 1 && G = C && E = 0 && D = A && B = C] 7. lbl141(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1 + E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && -2 + A + G >= 0 && -1*E >= 0 && -1 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 && C >= 1 + G && A >= 2 && C >= 1 + A && G >= 1 && C >= G && E = 0 && D = A && B = C] 8. cut(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -3 + G >= 0 && -3 + E + G >= 0 && -3 + -1*E + G >= 0 && -5 + D + G >= 0 && -1 + -1*D + G >= 0 && -6 + C + G >= 0 && -1*C + G >= 0 && -6 + B + G >= 0 && -1*B + G >= 0 && -5 + A + G >= 0 && -1 + -1*A + G >= 0 && -1*E >= 0 && -2 + D + -1*E >= 0 && -3 + C + -1*E >= 0 && -3 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -5 + C + D >= 0 && -5 + B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -5 + A + C >= 0 && -1 + -1*A + C >= 0 && -3 + B >= 0 && -5 + A + B >= 0 && -1 + -1*A + B >= 0 && -2 + A >= 0 && C >= 1 + A && A >= 2 && E = 0 && G = C && D = A && B = C] 9. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) 10. cut(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 11. lbl6(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 12. start(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(cut,8);(exitus616,8);(lbl121,8);(lbl141,8);(lbl6,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,11},2->{4,5},3->{},4->{4,5},5->{6,7},6->{8,10},7->{4},8->{},9->{0,1,2,12},10->{},11->{} ,12->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[4,7,5] c: [7] | `- p:[4] c: [4] * 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) [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 >= A && B = C && D = A && E = F && G = H] 1. start(A,B,C,D,E,F,G,H) -> lbl6(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 && A >= 1 && A >= C && B = C && D = A && E = F && G = H] 2. start(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1,F,0,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 >= 1 && C >= 1 + A && B = C && D = A && E = F && G = H] 3. lbl6(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 + D >= 0 && -1*C + D >= 0 && -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1*B + C >= 0 && A + -1*B >= 0 && -1 + A >= 0 && A >= 1 && A >= C && G = H && E = F && D = A && B = C] 4. lbl121(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1 + E,F,G,H) [G >= 0 (?,1) && -1 + E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -1 + A + G >= 0 && D + -1*E >= 0 && -1 + C + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + E && C >= 1 + G && A + C >= 3 + G && A >= E && E >= 1 && C >= 1 + A && D = A && B = C] 5. lbl121(A,B,C,D,E,F,G,H) -> lbl141(A,B,C,D,0,F,1 + G,H) [G >= 0 (?,1) && -1 + E + G >= 0 && -1 + D + G >= 0 && -2 + C + G >= 0 && -2 + B + G >= 0 && -1 + A + G >= 0 && D + -1*E >= 0 && -1 + C + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + G && A + C >= 3 + G && A >= 1 && C >= 1 + A && E = A && D = A && B = C] 6. lbl141(A,B,C,D,E,F,G,H) -> cut(A,B,C,D,E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && -2 + A + G >= 0 && -1*E >= 0 && -1 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 2 && C >= 1 + A && C >= 1 && G = C && E = 0 && D = A && B = C] 7. lbl141(A,B,C,D,E,F,G,H) -> lbl121(A,B,C,D,1 + E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -3 + C + G >= 0 && -3 + B + G >= 0 && -2 + A + G >= 0 && -1*E >= 0 && -1 + D + -1*E >= 0 && -2 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + C + D >= 0 && -3 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 && C >= 1 + G && A >= 2 && C >= 1 + A && G >= 1 && C >= G && E = 0 && D = A && B = C] 8. cut(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [C + -1*G >= 0 (?,1) && B + -1*G >= 0 && -3 + G >= 0 && -3 + E + G >= 0 && -3 + -1*E + G >= 0 && -5 + D + G >= 0 && -1 + -1*D + G >= 0 && -6 + C + G >= 0 && -1*C + G >= 0 && -6 + B + G >= 0 && -1*B + G >= 0 && -5 + A + G >= 0 && -1 + -1*A + G >= 0 && -1*E >= 0 && -2 + D + -1*E >= 0 && -3 + C + -1*E >= 0 && -3 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -2 + D + E >= 0 && -3 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && -1 + C + -1*D >= 0 && -1 + B + -1*D >= 0 && A + -1*D >= 0 && -2 + D >= 0 && -5 + C + D >= 0 && -5 + B + D >= 0 && -4 + A + D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -5 + A + C >= 0 && -1 + -1*A + C >= 0 && -3 + B >= 0 && -5 + A + B >= 0 && -1 + -1*A + B >= 0 && -2 + A >= 0 && C >= 1 + A && A >= 2 && E = 0 && G = C && D = A && B = C] 9. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) 10. cut(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 11. lbl6(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) 12. start(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True (?,1) Signature: {(cut,8);(exitus616,8);(lbl121,8);(lbl141,8);(lbl6,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{3,11},2->{4,5},3->{},4->{4,5},5->{6,7},6->{8,10},7->{4},8->{},9->{0,1,2,12},10->{},11->{} ,12->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[4,7,5] c: [7] | `- p:[4] c: [4]) + 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 ~> lbl6 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] start ~> lbl121 [A <= A, B <= B, C <= C, D <= D, E <= K, F <= F, G <= 0*K, H <= H] lbl6 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl121 ~> lbl121 [A <= A, B <= B, C <= C, D <= D, E <= D, F <= F, G <= G, H <= H] lbl121 ~> lbl141 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= C, H <= H] lbl141 ~> cut [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl141 ~> lbl121 [A <= A, B <= B, C <= C, D <= D, E <= K, F <= F, G <= G, H <= H] cut ~> stop [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 <= A, E <= F, F <= F, G <= H, H <= H] cut ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl6 ~> 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 + C + G] lbl121 ~> lbl121 [A <= A, B <= B, C <= C, D <= D, E <= D, F <= F, G <= G, H <= H] lbl141 ~> lbl121 [A <= A, B <= B, C <= C, D <= D, E <= K, F <= F, G <= G, H <= H] lbl121 ~> lbl141 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= C, H <= H] + Loop: [0.0.0 <= K + A + E] lbl121 ~> lbl121 [A <= A, B <= B, C <= C, D <= D, E <= D, 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 ~> lbl6 [] start ~> lbl121 [K ~=> E,K ~=> G] lbl6 ~> stop [] lbl121 ~> lbl121 [D ~=> E] lbl121 ~> lbl141 [C ~=> G,K ~=> E] lbl141 ~> cut [] lbl141 ~> lbl121 [K ~=> E] cut ~> stop [] start0 ~> start [A ~=> D,C ~=> B,F ~=> E,H ~=> G] cut ~> exitus616 [] lbl6 ~> exitus616 [] start ~> exitus616 [] + Loop: [C ~+> 0.0,G ~+> 0.0,K ~+> 0.0] lbl121 ~> lbl121 [D ~=> E] lbl141 ~> lbl121 [K ~=> E] lbl121 ~> lbl141 [C ~=> G,K ~=> E] + Loop: [A ~+> 0.0.0,E ~+> 0.0.0,K ~+> 0.0.0] lbl121 ~> lbl121 [D ~=> E] + Applied Processor: LareProcessor + Details: start0 ~> exitus616 [A ~=> D ,C ~=> B ,C ~=> G ,F ~=> E ,H ~=> G ,K ~=> E ,K ~=> G ,A ~+> 0.0.0 ,A ~+> tick ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,C ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] start0 ~> stop [A ~=> D ,C ~=> B ,C ~=> G ,F ~=> E ,H ~=> G ,K ~=> E ,K ~=> G ,A ~+> 0.0.0 ,A ~+> tick ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,C ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] + lbl141> [C ~=> G ,K ~=> E ,A ~+> 0.0.0 ,A ~+> tick ,C ~+> 0.0 ,C ~+> tick ,D ~+> 0.0.0 ,D ~+> tick ,E ~+> 0.0.0 ,E ~+> tick ,G ~+> 0.0 ,G ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,C ~*> tick ,D ~*> tick ,E ~*> tick ,G ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + lbl121> [D ~=> E ,A ~+> 0.0.0 ,A ~+> tick ,E ~+> 0.0.0 ,E ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] YES(?,POLY)