YES * Step 1: TrivialSCCs YES + 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: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + 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) && -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) && -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) && -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) && -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) && -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 3: Looptree YES + 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) && -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) && -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) && -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) && -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) && -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: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[11,6,8,7,10,9] c: [8] | `- p:[11,9,10] c: [11] | `- p:[10] c: [10] YES