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,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 && 0 >= 1 + A && B = C && D = A && E = F && G = H] 1. start(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + 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 && D = 0 && B = C && A = 0 && E = F && G = H] 2. start(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,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 >= 1 && B = C && D = A && E = F && G = H] 3. start(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,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 >= 1 && B = C && D = A && E = F && G = H] 4. lbl142(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [-1 + E + -1*G >= 0 (?,1) && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && 1 + G = 0 && E = 0 && D = A] 5. lbl142(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + G,H) [-1 + E + -1*G >= 0 (?,1) && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && A >= 1 && G = 0 && E = 1 && D = A] 6. lbl142(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,G,H) [-1 + E + -1*G >= 0 (?,1) && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= 2 && A >= E && 1 + G = E && D = A] 7. lbl142(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,G,H) [-1 + E + -1*G >= 0 (?,1) && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= 2 && A >= E && 1 + G = E && D = A] 8. lbl131(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,E,F,-1 + G,H) [D + -1*G >= 0 (?,1) && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 && A >= G && E = G && D = A] 9. lbl131(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,E,F,G,H) [D + -1*G >= 0 (?,1) && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] 10. lbl131(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [D + -1*G >= 0 (?,1) && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] 11. lbl91(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [D + -1*G >= 0 (?,1) && A + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && -1 + D + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -1 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && A >= G && D = A] 12. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(lbl131,8);(lbl142,8);(lbl91,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{4,5,6,7},2->{11},3->{8,9,10},4->{},5->{4,5,6,7},6->{11},7->{8,9,10},8->{4,5,6,7},9->{11},10->{8 ,9,10},11->{8,9,10},12->{0,1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,5),(1,6),(1,7),(5,5),(5,6),(5,7),(8,4)] * 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,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 && 0 >= 1 + A && B = C && D = A && E = F && G = H] 1. start(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + 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 && D = 0 && B = C && A = 0 && E = F && G = H] 2. start(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,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 >= 1 && B = C && D = A && E = F && G = H] 3. start(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,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 >= 1 && B = C && D = A && E = F && G = H] 4. lbl142(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [-1 + E + -1*G >= 0 (?,1) && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && 1 + G = 0 && E = 0 && D = A] 5. lbl142(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + G,H) [-1 + E + -1*G >= 0 (?,1) && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && A >= 1 && G = 0 && E = 1 && D = A] 6. lbl142(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,G,H) [-1 + E + -1*G >= 0 (?,1) && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= 2 && A >= E && 1 + G = E && D = A] 7. lbl142(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,G,H) [-1 + E + -1*G >= 0 (?,1) && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= 2 && A >= E && 1 + G = E && D = A] 8. lbl131(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,E,F,-1 + G,H) [D + -1*G >= 0 (?,1) && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 && A >= G && E = G && D = A] 9. lbl131(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,E,F,G,H) [D + -1*G >= 0 (?,1) && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] 10. lbl131(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [D + -1*G >= 0 (?,1) && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] 11. lbl91(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [D + -1*G >= 0 (?,1) && A + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && -1 + D + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -1 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && A >= G && D = A] 12. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True (1,1) Signature: {(lbl131,8);(lbl142,8);(lbl91,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{4},2->{11},3->{8,9,10},4->{},5->{4},6->{11},7->{8,9,10},8->{5,6,7},9->{11},10->{8,9,10},11->{8 ,9,10},12->{0,1,2,3}] + 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,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 && 0 >= 1 + A && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + 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 && D = 0 && B = C && A = 0 && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,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 >= 1 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,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 >= 1 && B = C && D = A && E = F && G = H] lbl142(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [-1 + E + -1*G >= 0 && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && 1 + G = 0 && E = 0 && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + G,H) [-1 + E + -1*G >= 0 && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && A >= 1 && G = 0 && E = 1 && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,G,H) [-1 + E + -1*G >= 0 && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= 2 && A >= E && 1 + G = E && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,G,H) [-1 + E + -1*G >= 0 && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= 2 && A >= E && 1 + G = E && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,E,F,-1 + G,H) [D + -1*G >= 0 && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 && A >= G && E = G && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,E,F,G,H) [D + -1*G >= 0 && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [D + -1*G >= 0 && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] lbl91(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [D + -1*G >= 0 && A + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && -1 + D + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -1 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && A >= G && D = A] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,A,F,F,H,H) True Signature: {(lbl131,8);(lbl142,8);(lbl91,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{4},2->{11},3->{8,9,10},4->{},5->{4},6->{11},7->{8,9,10},8->{5,6,7},9->{11},10->{8,9,10},11->{8 ,9,10},12->{0,1,2,3}] + 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,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 && 0 >= 1 + A && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + 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 && D = 0 && B = C && A = 0 && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,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 >= 1 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,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 >= 1 && B = C && D = A && E = F && G = H] lbl142(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [-1 + E + -1*G >= 0 && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && 1 + G = 0 && E = 0 && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + G,H) [-1 + E + -1*G >= 0 && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && A >= 1 && G = 0 && E = 1 && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,G,H) [-1 + E + -1*G >= 0 && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= 2 && A >= E && 1 + G = E && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,G,H) [-1 + E + -1*G >= 0 && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= 2 && A >= E && 1 + G = E && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,E,F,-1 + G,H) [D + -1*G >= 0 && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 && A >= G && E = G && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,E,F,G,H) [D + -1*G >= 0 && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [D + -1*G >= 0 && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] lbl91(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [D + -1*G >= 0 && A + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && -1 + D + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -1 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && A >= G && 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 Signature: {(exitus616,8);(lbl131,8);(lbl142,8);(lbl91,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{16},1->{4},2->{11},3->{8,9,10},4->{13,14,15},5->{4},6->{11},7->{8,9,10},8->{5,6,7},9->{11},10->{8,9 ,10},11->{8,9,10},12->{0,1,2,3}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[11,6,8,7,10,9] c: [6,7,8] | `- p:[9,10,11] c: [9,10,11] * 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,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 && 0 >= 1 + A && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + 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 && D = 0 && B = C && A = 0 && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,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 >= 1 && B = C && D = A && E = F && G = H] start(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,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 >= 1 && B = C && D = A && E = F && G = H] lbl142(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [-1 + E + -1*G >= 0 && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && 1 + G = 0 && E = 0 && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,0,F,-1 + G,H) [-1 + E + -1*G >= 0 && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && A >= 1 && G = 0 && E = 1 && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,0,F,G,H) [-1 + E + -1*G >= 0 && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= 2 && A >= E && 1 + G = E && D = A] lbl142(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1,F,G,H) [-1 + E + -1*G >= 0 && -1 + D + -1*G >= 0 && -1 + A + -1*G >= 0 && 1 + G >= 0 && 1 + E + G >= 0 && 1 + -1*E + G >= 0 && 1 + D + G >= 0 && 1 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && E >= 0 && D + E >= 0 && A + E >= 0 && A + -1*D >= 0 && D >= 0 && A + D >= 0 && -1*A + D >= 0 && A >= 0 && E >= 2 && A >= E && 1 + G = E && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl142(A,B,C,D,E,F,-1 + G,H) [D + -1*G >= 0 && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 && A >= G && E = G && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl91(A,I,C,D,E,F,G,H) [D + -1*G >= 0 && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] lbl131(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [D + -1*G >= 0 && A + -1*G >= 0 && -1 + G >= 0 && -2 + E + G >= 0 && -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && D + -1*E >= 0 && A + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -2 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && G >= E && E >= 1 && A >= G && D = A] lbl91(A,B,C,D,E,F,G,H) -> lbl131(A,B,C,D,1 + E,F,G,H) [D + -1*G >= 0 && A + -1*G >= 0 && -1 + G >= 0 && -1 + E + G >= 0 && -1 + -1*E + G >= 0 && -2 + D + G >= 0 && -2 + A + G >= 0 && -1 + D + -1*E >= 0 && -1 + A + -1*E >= 0 && E >= 0 && -1 + D + E >= 0 && -1 + A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && -1 + A >= 0 && G >= 1 + E && A >= G && 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 Signature: {(exitus616,8);(lbl131,8);(lbl142,8);(lbl91,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{16},1->{4},2->{11},3->{8,9,10},4->{13,14,15},5->{4},6->{11},7->{8,9,10},8->{5,6,7},9->{11},10->{8,9 ,10},11->{8,9,10},12->{0,1,2,3}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[11,6,8,7,10,9] c: [6,7,8] | `- p:[9,10,11] c: [9,10,11]) + 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 <= D, H <= H] start ~> lbl142 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= K, H <= H] start ~> lbl91 [A <= A, B <= unknown, C <= C, D <= D, E <= 0*K, F <= F, G <= D, H <= H] start ~> lbl131 [A <= A, B <= B, C <= C, D <= D, E <= K, F <= F, G <= D, H <= H] lbl142 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl142 ~> lbl142 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= K, H <= H] lbl142 ~> lbl91 [A <= A, B <= unknown, C <= C, D <= D, E <= 0*K, F <= F, G <= G, H <= H] lbl142 ~> lbl131 [A <= A, B <= B, C <= C, D <= D, E <= K, F <= F, G <= G, H <= H] lbl131 ~> lbl142 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= D, H <= H] lbl131 ~> lbl91 [A <= A, B <= unknown, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl131 ~> lbl131 [A <= A, B <= B, C <= C, D <= D, E <= D, F <= F, G <= G, H <= H] lbl91 ~> lbl131 [A <= A, B <= B, C <= C, D <= D, E <= D, 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] + Loop: [0.0 <= G] lbl91 ~> lbl131 [A <= A, B <= B, C <= C, D <= D, E <= D, F <= F, G <= G, H <= H] lbl142 ~> lbl91 [A <= A, B <= unknown, C <= C, D <= D, E <= 0*K, F <= F, G <= G, H <= H] lbl131 ~> lbl142 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= D, H <= H] lbl142 ~> lbl131 [A <= A, B <= B, C <= C, D <= D, E <= K, F <= F, G <= G, H <= H] lbl131 ~> lbl131 [A <= A, B <= B, C <= C, D <= D, E <= D, F <= F, G <= G, H <= H] lbl131 ~> lbl91 [A <= A, B <= unknown, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] + Loop: [0.0.0 <= K + A + E + G] lbl131 ~> lbl91 [A <= A, B <= unknown, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl131 ~> lbl131 [A <= A, B <= B, C <= C, D <= D, E <= D, F <= F, G <= G, H <= H] lbl91 ~> lbl131 [A <= A, B <= B, C <= C, D <= D, E <= D, 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 [D ~=> G] start ~> lbl142 [K ~=> E,K ~=> G] start ~> lbl91 [D ~=> G,K ~=> E,huge ~=> B] start ~> lbl131 [D ~=> G,K ~=> E] lbl142 ~> stop [] lbl142 ~> lbl142 [K ~=> E,K ~=> G] lbl142 ~> lbl91 [K ~=> E,huge ~=> B] lbl142 ~> lbl131 [K ~=> E] lbl131 ~> lbl142 [D ~=> G] lbl131 ~> lbl91 [huge ~=> B] lbl131 ~> lbl131 [D ~=> E] lbl91 ~> lbl131 [D ~=> E] start0 ~> start [A ~=> D,C ~=> B,F ~=> E,H ~=> G] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] + Loop: [G ~=> 0.0] lbl91 ~> lbl131 [D ~=> E] lbl142 ~> lbl91 [K ~=> E,huge ~=> B] lbl131 ~> lbl142 [D ~=> G] lbl142 ~> lbl131 [K ~=> E] lbl131 ~> lbl131 [D ~=> E] lbl131 ~> lbl91 [huge ~=> B] + Loop: [A ~+> 0.0.0,E ~+> 0.0.0,G ~+> 0.0.0,K ~+> 0.0.0] lbl131 ~> lbl91 [huge ~=> B] lbl131 ~> lbl131 [D ~=> E] lbl91 ~> lbl131 [D ~=> E] + Applied Processor: Lare + Details: start0 ~> exitus616 [A ~=> D ,A ~=> E ,A ~=> G ,A ~=> 0.0 ,C ~=> B ,F ~=> E ,K ~=> E ,K ~=> G ,K ~=> 0.0 ,huge ~=> B ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + lbl142> [D ~=> E ,D ~=> G ,G ~=> 0.0 ,K ~=> E ,huge ~=> B ,A ~+> 0.0.0 ,A ~+> tick ,D ~+> 0.0.0 ,D ~+> tick ,E ~+> 0.0.0 ,E ~+> tick ,G ~+> 0.0.0 ,G ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,D ~*> 0.0.0 ,D ~*> tick ,E ~*> tick ,G ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] lbl142> [D ~=> E ,D ~=> G ,G ~=> 0.0 ,K ~=> E ,huge ~=> B ,A ~+> 0.0.0 ,A ~+> tick ,D ~+> 0.0.0 ,D ~+> tick ,G ~+> 0.0.0 ,G ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,D ~*> 0.0.0 ,D ~*> tick ,G ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] lbl142> [D ~=> E ,D ~=> G ,G ~=> 0.0 ,K ~=> E ,huge ~=> B ,A ~+> 0.0.0 ,A ~+> tick ,D ~+> 0.0.0 ,D ~+> tick ,E ~+> 0.0.0 ,E ~+> tick ,G ~+> 0.0.0 ,G ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,D ~*> 0.0.0 ,D ~*> tick ,E ~*> tick ,G ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + lbl131> [D ~=> E ,huge ~=> B ,A ~+> 0.0.0 ,A ~+> tick ,E ~+> 0.0.0 ,E ~+> tick ,G ~+> 0.0.0 ,G ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] lbl131> [D ~=> E ,huge ~=> B ,A ~+> 0.0.0 ,A ~+> tick ,E ~+> 0.0.0 ,E ~+> tick ,G ~+> 0.0.0 ,G ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] YES(?,POLY)