YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 (?,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,0,C,0,E,K,G,1,I,J) [H + -1*I >= 0 (?,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] 2. lbl21(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] 3. lbl21(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] 4. lbl121(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] 5. lbl121(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] 6. lbl141(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] 7. lbl141(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] 8. lbl171(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] 9. lbl171(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] 10. lbl191(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] 11. lbl191(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] 12. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 13. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 14. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] 15. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] 16. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] 17. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl191(A,-1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] 18. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,G,G,I,I,A) True (1,1) Signature: {(lbl121,10);(lbl141,10);(lbl171,10);(lbl191,10);(lbl21,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{12,13,14,15,16,17},4->{},5->{12,13,14,15,16,17},6->{},7->{12,13,14 ,15,16,17},8->{},9->{12,13,14,15,16,17},10->{},11->{12,13,14,15,16,17},12->{2,3},13->{2,3},14->{4,5},15->{6 ,7},16->{8,9},17->{10,11},18->{0,1}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,0,C,0,E,K,G,1,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] 2. lbl21(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] 3. lbl21(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] 4. lbl121(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] 5. lbl121(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] 6. lbl141(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] 7. lbl141(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] 8. lbl171(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] 9. lbl171(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] 10. lbl191(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] 11. lbl191(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] 12. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 13. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 14. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] 15. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] 16. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] 17. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl191(A,-1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] 18. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,G,G,I,I,A) True (1,1) Signature: {(lbl121,10);(lbl141,10);(lbl171,10);(lbl191,10);(lbl21,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{12,13,14,15,16,17},4->{},5->{12,13,14,15,16,17},6->{},7->{12,13,14 ,15,16,17},8->{},9->{12,13,14,15,16,17},10->{},11->{12,13,14,15,16,17},12->{2,3},13->{2,3},14->{4,5},15->{6 ,7},16->{8,9},17->{10,11},18->{0,1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl121) = x1 + -1*x8 p(lbl141) = x1 + -1*x8 p(lbl171) = 1 + x1 + -1*x8 p(lbl191) = x1 + -1*x8 p(lbl21) = x1 + -1*x8 p(lbl81) = 1 + x1 + -1*x8 p(start) = x1 p(start0) = x1 p(stop) = x1 + -1*x8 Following rules are strictly oriented: [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] lbl171(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl191(A,-1 + B,C,D,E,F,G,H,I,J) Following rules are weakly oriented: [H + -1*I >= 0 ==> && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) = A >= A = stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 ==> && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) = A >= A = lbl81(A,0,C,0,E,K,G,1,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] lbl21(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] lbl21(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] lbl121(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] lbl121(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] lbl141(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] lbl141(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] lbl171(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] lbl191(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] lbl191(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= 1 + A + -1*H = lbl171(A,1 + B,C,D,E,F,G,H,I,J) True ==> start0(A,B,C,D,E,F,G,H,I,J) = A >= A = start(A,C,C,E,E,G,G,I,I,A) * Step 3: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,0,C,0,E,K,G,1,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] 2. lbl21(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] 3. lbl21(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] 4. lbl121(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] 5. lbl121(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] 6. lbl141(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] 7. lbl141(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] 8. lbl171(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] 9. lbl171(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] 10. lbl191(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] 11. lbl191(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] 12. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 13. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 14. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] 15. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] 16. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] 17. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl191(A,-1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] 18. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,G,G,I,I,A) True (1,1) Signature: {(lbl121,10);(lbl141,10);(lbl171,10);(lbl191,10);(lbl21,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{12,13,14,15,16,17},4->{},5->{12,13,14,15,16,17},6->{},7->{12,13,14 ,15,16,17},8->{},9->{12,13,14,15,16,17},10->{},11->{12,13,14,15,16,17},12->{2,3},13->{2,3},14->{4,5},15->{6 ,7},16->{8,9},17->{10,11},18->{0,1}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,0,C,0,E,K,G,1,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] 2. lbl21(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] 3. lbl21(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] 4. lbl121(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] 5. lbl121(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] 6. lbl141(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] 7. lbl141(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] 8. lbl171(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] 9. lbl171(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] 10. lbl191(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] 11. lbl191(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] 12. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 13. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 14. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] 15. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] 16. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] 17. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl191(A,-1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] 18. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,G,G,I,I,A) True (1,1) Signature: {(lbl121,10);(lbl141,10);(lbl171,10);(lbl191,10);(lbl21,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{12,13,14,15,16,17},4->{},5->{12,13,14,15,16,17},6->{},7->{12,13,14 ,15,16,17},8->{},9->{12,13,14,15,16,17},10->{},11->{12,13,14,15,16,17},12->{2,3},13->{2,3},14->{4,5},15->{6 ,7},16->{8,9},17->{10,11},18->{0,1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl121) = 1 + x1 + -1*x8 p(lbl141) = x1 + -1*x8 p(lbl171) = x1 + -1*x8 p(lbl191) = x1 + -1*x8 p(lbl21) = x1 + -1*x8 p(lbl81) = 1 + x1 + -1*x8 p(start) = x1 p(start0) = x1 p(stop) = x1 + -1*x8 Following rules are strictly oriented: [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] lbl121(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl191(A,-1 + B,C,D,E,F,G,H,I,J) Following rules are weakly oriented: [H + -1*I >= 0 ==> && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) = A >= A = stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 ==> && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) = A >= A = lbl81(A,0,C,0,E,K,G,1,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] lbl21(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] lbl21(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] lbl121(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] lbl141(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] lbl141(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] lbl171(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] lbl171(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] lbl191(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] lbl191(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= 1 + A + -1*H = lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl141(A,B,C,-1 + D,E,F,G,H,I,J) True ==> start0(A,B,C,D,E,F,G,H,I,J) = A >= A = start(A,C,C,E,E,G,G,I,I,A) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,0,C,0,E,K,G,1,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] 2. lbl21(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] 3. lbl21(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] 4. lbl121(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] 5. lbl121(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] 6. lbl141(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] 7. lbl141(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] 8. lbl171(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] 9. lbl171(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] 10. lbl191(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] 11. lbl191(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] 12. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 13. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 14. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] 15. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] 16. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] 17. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl191(A,-1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] 18. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,G,G,I,I,A) True (1,1) Signature: {(lbl121,10);(lbl141,10);(lbl171,10);(lbl191,10);(lbl21,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{12,13,14,15,16,17},4->{},5->{12,13,14,15,16,17},6->{},7->{12,13,14 ,15,16,17},8->{},9->{12,13,14,15,16,17},10->{},11->{12,13,14,15,16,17},12->{2,3},13->{2,3},14->{4,5},15->{6 ,7},16->{8,9},17->{10,11},18->{0,1}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,0,C,0,E,K,G,1,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] 2. lbl21(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] 3. lbl21(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] 4. lbl121(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] 5. lbl121(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] 6. lbl141(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] 7. lbl141(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] 8. lbl171(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] 9. lbl171(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] 10. lbl191(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] 11. lbl191(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] 12. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 13. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 14. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] 15. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] 16. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] 17. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl191(A,-1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] 18. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,G,G,I,I,A) True (1,1) Signature: {(lbl121,10);(lbl141,10);(lbl171,10);(lbl191,10);(lbl21,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{12,13,14,15,16,17},4->{},5->{12,13,14,15,16,17},6->{},7->{12,13,14 ,15,16,17},8->{},9->{12,13,14,15,16,17},10->{},11->{12,13,14,15,16,17},12->{2,3},13->{2,3},14->{4,5},15->{6 ,7},16->{8,9},17->{10,11},18->{0,1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl121) = x1 + -1*x8 p(lbl141) = x1 + -1*x8 p(lbl171) = x1 + -1*x8 p(lbl191) = x1 + -1*x8 p(lbl21) = x1 + -1*x8 p(lbl81) = 1 + x1 + -1*x8 p(start) = x1 p(start0) = x1 p(stop) = x1 + -1*x8 Following rules are strictly oriented: [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl191(A,-1 + B,C,D,E,F,G,H,I,J) Following rules are weakly oriented: [H + -1*I >= 0 ==> && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) = A >= A = stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 ==> && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) = A >= A = lbl81(A,0,C,0,E,K,G,1,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] lbl21(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] lbl21(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] lbl121(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] lbl121(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] lbl141(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] lbl141(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] lbl171(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] lbl171(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] lbl191(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] lbl191(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl121(A,B,C,1 + D,E,F,G,H,I,J) True ==> start0(A,B,C,D,E,F,G,H,I,J) = A >= A = start(A,C,C,E,E,G,G,I,I,A) * Step 7: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,0,C,0,E,K,G,1,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] 2. lbl21(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] 3. lbl21(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] 4. lbl121(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] 5. lbl121(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] 6. lbl141(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] 7. lbl141(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] 8. lbl171(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] 9. lbl171(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] 10. lbl191(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] 11. lbl191(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] 12. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 13. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 14. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] 15. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] 16. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] 17. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl191(A,-1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] 18. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,G,G,I,I,A) True (1,1) Signature: {(lbl121,10);(lbl141,10);(lbl171,10);(lbl191,10);(lbl21,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{12,13,14,15,16,17},4->{},5->{12,13,14,15,16,17},6->{},7->{12,13,14 ,15,16,17},8->{},9->{12,13,14,15,16,17},10->{},11->{12,13,14,15,16,17},12->{2,3},13->{2,3},14->{4,5},15->{6 ,7},16->{8,9},17->{10,11},18->{0,1}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 8: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,0,C,0,E,K,G,1,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] 2. lbl21(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] 3. lbl21(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] 4. lbl121(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] 5. lbl121(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] 6. lbl141(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] 7. lbl141(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] 8. lbl171(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] 9. lbl171(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] 10. lbl191(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] 11. lbl191(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] 12. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 13. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 14. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] 15. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] 16. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] 17. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl191(A,-1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] 18. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,G,G,I,I,A) True (1,1) Signature: {(lbl121,10);(lbl141,10);(lbl171,10);(lbl191,10);(lbl21,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{12,13,14,15,16,17},4->{},5->{12,13,14,15,16,17},6->{},7->{12,13,14 ,15,16,17},8->{},9->{12,13,14,15,16,17},10->{},11->{12,13,14,15,16,17},12->{2,3},13->{2,3},14->{4,5},15->{6 ,7},16->{8,9},17->{10,11},18->{0,1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl121) = x1 + -1*x8 p(lbl141) = x1 + -1*x8 p(lbl171) = x1 + -1*x8 p(lbl191) = x1 + -1*x8 p(lbl21) = x1 + -1*x8 p(lbl81) = 1 + x1 + -1*x8 p(start) = x1 p(start0) = x1 p(stop) = x1 + -1*x8 Following rules are strictly oriented: [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl191(A,-1 + B,C,D,E,F,G,H,I,J) Following rules are weakly oriented: [H + -1*I >= 0 ==> && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) = A >= A = stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 ==> && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) = A >= A = lbl81(A,0,C,0,E,K,G,1,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] lbl21(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] lbl21(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] lbl121(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] lbl121(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] lbl141(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] lbl141(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] lbl171(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] lbl171(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] lbl191(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] lbl191(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl21(A,B,C,D,E,F,G,H,I,J) True ==> start0(A,B,C,D,E,F,G,H,I,J) = A >= A = start(A,C,C,E,E,G,G,I,I,A) * Step 9: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,0,C,0,E,K,G,1,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] 2. lbl21(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] 3. lbl21(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] 4. lbl121(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] 5. lbl121(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] 6. lbl141(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] 7. lbl141(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] 8. lbl171(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] 9. lbl171(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] 10. lbl191(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] 11. lbl191(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] 12. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 13. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 14. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] 15. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] 16. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] 17. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl191(A,-1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] 18. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,G,G,I,I,A) True (1,1) Signature: {(lbl121,10);(lbl141,10);(lbl171,10);(lbl191,10);(lbl21,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{12,13,14,15,16,17},4->{},5->{12,13,14,15,16,17},6->{},7->{12,13,14 ,15,16,17},8->{},9->{12,13,14,15,16,17},10->{},11->{12,13,14,15,16,17},12->{2,3},13->{2,3},14->{4,5},15->{6 ,7},16->{8,9},17->{10,11},18->{0,1}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 10: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,0,C,0,E,K,G,1,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] 2. lbl21(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] 3. lbl21(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] 4. lbl121(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] 5. lbl121(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] 6. lbl141(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] 7. lbl141(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] 8. lbl171(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] 9. lbl171(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] 10. lbl191(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] 11. lbl191(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] 12. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 13. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 14. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] 15. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] 16. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] 17. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl191(A,-1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] 18. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,G,G,I,I,A) True (1,1) Signature: {(lbl121,10);(lbl141,10);(lbl171,10);(lbl191,10);(lbl21,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{12,13,14,15,16,17},4->{},5->{12,13,14,15,16,17},6->{},7->{12,13,14 ,15,16,17},8->{},9->{12,13,14,15,16,17},10->{},11->{12,13,14,15,16,17},12->{2,3},13->{2,3},14->{4,5},15->{6 ,7},16->{8,9},17->{10,11},18->{0,1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl121) = x1 + -1*x8 p(lbl141) = x1 + -1*x8 p(lbl171) = x1 + -1*x8 p(lbl191) = x1 + -1*x8 p(lbl21) = x1 + -1*x8 p(lbl81) = 1 + x1 + -1*x8 p(start) = x1 p(start0) = x1 p(stop) = x1 + -1*x8 Following rules are strictly oriented: [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl191(A,-1 + B,C,D,E,F,G,H,I,J) Following rules are weakly oriented: [H + -1*I >= 0 ==> && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) = A >= A = stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 ==> && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) = A >= A = lbl81(A,0,C,0,E,K,G,1,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] lbl21(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] lbl21(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] lbl121(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] lbl121(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] lbl141(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] lbl141(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] lbl171(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] lbl171(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] lbl191(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] lbl191(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H >= A + -1*H = lbl21(A,B,C,D,E,F,G,H,I,J) True ==> start0(A,B,C,D,E,F,G,H,I,J) = A >= A = start(A,C,C,E,E,G,G,I,I,A) * Step 11: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,0,C,0,E,K,G,1,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] 2. lbl21(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] 3. lbl21(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] 4. lbl121(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] 5. lbl121(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] 6. lbl141(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] 7. lbl141(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] 8. lbl171(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] 9. lbl171(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] 10. lbl191(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] 11. lbl191(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] 12. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 13. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 14. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] 15. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] 16. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] 17. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl191(A,-1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] 18. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,G,G,I,I,A) True (1,1) Signature: {(lbl121,10);(lbl141,10);(lbl171,10);(lbl191,10);(lbl21,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{12,13,14,15,16,17},4->{},5->{12,13,14,15,16,17},6->{},7->{12,13,14 ,15,16,17},8->{},9->{12,13,14,15,16,17},10->{},11->{12,13,14,15,16,17},12->{2,3},13->{2,3},14->{4,5},15->{6 ,7},16->{8,9},17->{10,11},18->{0,1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(lbl121) = x1 + -1*x8 p(lbl141) = x1 + -1*x8 p(lbl171) = x1 + -1*x8 p(lbl191) = x1 + -1*x8 p(lbl21) = x1 + -1*x8 p(lbl81) = 1 + x1 + -1*x8 p(start) = x1 p(start0) = x1 p(stop) = x1 + -1*x8 Following rules are strictly oriented: [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] lbl81(A,B,C,D,E,F,G,H,I,J) = 1 + A + -1*H > A + -1*H = lbl191(A,-1 + B,C,D,E,F,G,H,I,J) Following rules are weakly oriented: [H + -1*I >= 0 ==> && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) = A >= A = stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 ==> && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] start(A,B,C,D,E,F,G,H,I,J) = A >= A = lbl81(A,0,C,0,E,K,G,1,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] lbl21(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] lbl21(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] lbl121(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] lbl121(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] lbl141(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] lbl141(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] lbl171(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] lbl171(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] lbl191(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 ==> && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] lbl191(A,B,C,D,E,F,G,H,I,J) = A + -1*H >= A + -1*H = lbl81(A,B,C,D,E,K,G,1 + H,I,J) True ==> start0(A,B,C,D,E,F,G,H,I,J) = A >= A = start(A,C,C,E,E,G,G,I,I,A) * Step 12: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,0,C,0,E,K,G,1,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] 2. lbl21(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] 3. lbl21(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] 4. lbl121(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] 5. lbl121(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] 6. lbl141(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] 7. lbl141(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] 8. lbl171(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] 9. lbl171(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] 10. lbl191(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] 11. lbl191(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] 12. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 13. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 14. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] 15. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] 16. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] 17. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl191(A,-1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] 18. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,G,G,I,I,A) True (1,1) Signature: {(lbl121,10);(lbl141,10);(lbl171,10);(lbl191,10);(lbl21,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{12,13,14,15,16,17},4->{},5->{12,13,14,15,16,17},6->{},7->{12,13,14 ,15,16,17},8->{},9->{12,13,14,15,16,17},10->{},11->{12,13,14,15,16,17},12->{2,3},13->{2,3},14->{4,5},15->{6 ,7},16->{8,9},17->{10,11},18->{0,1}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 13: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J) -> stop(A,0,C,0,E,F,G,0,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && 0 >= A && B = C && D = E && F = G && H = I && J = A] 1. start(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,0,C,0,E,K,G,1,I,J) [H + -1*I >= 0 (1,1) && -1*H + I >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A + -1*J >= 0 && -1*A + J >= 0 && A >= 1 && B = C && D = E && F = G && H = I && J = A] 2. lbl21(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 1 && A + D >= 1 + B && A + B >= 1 + D && A >= 1 + B + D && H = A && J = A] 3. lbl21(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (2*A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 1 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && J = A] 4. lbl121(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= 2 + B && A + B >= D && A >= B + D && H = A && F = 0 && J = A] 5. lbl121(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + F + H >= 0 && -1 + -1*F + H >= 0 && -2 + D + H >= 0 && -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1*F >= 0 && -1 + -1*F + J >= 0 && -1 + A + -1*F >= 0 && F >= 0 && -1 + F + J >= 0 && -1 + A + F >= 0 && -1*D + J >= 0 && A + -1*D >= 0 && -2 + D + J >= 0 && -2 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= 2 + B && B + H >= D && H >= B + D && F = 0 && J = A] 6. lbl141(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= B && A + B >= 2 + D && A >= 2 + B + D && H = A && F = 1 && J = A] 7. lbl141(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -2 + F + H >= 0 && -1*F + H >= 0 && D + H >= 0 && -2 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 1 + -1*F >= 0 && -1*F + J >= 0 && A + -1*F >= 0 && -1 + F >= 0 && -2 + F + J >= 0 && -2 + A + F >= 0 && -2 + -1*D + J >= 0 && -2 + A + -1*D >= 0 && D + J >= 0 && A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= B && B + H >= 2 + D && H >= 2 + B + D && F = 1 && J = A] 8. lbl171(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 2 && A + D >= B && A + B >= 2 + D && A >= B + D && H = A && F = 2 && J = A] 9. lbl171(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -3 + F + H >= 0 && 1 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -2 + B + H >= 0 && -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 2 + -1*F >= 0 && 1 + -1*F + J >= 0 && 1 + A + -1*F >= 0 && -2 + F >= 0 && -3 + F + J >= 0 && -3 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1*B + J >= 0 && A + -1*B >= 0 && -2 + B + J >= 0 && -2 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 2 && D + H >= B && B + H >= 2 + D && H >= B + D && F = 2 && J = A] 10. lbl191(A,B,C,D,E,F,G,H,I,J) -> stop(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A + B + D >= 0 && A + D >= 2 + B && A + B >= D && A >= 2 + B + D && H = A && F = 3 && J = A] 11. lbl191(A,B,C,D,E,F,G,H,I,J) -> lbl81(A,B,C,D,E,K,G,1 + H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -4 + F + H >= 0 && 2 + -1*F + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && B + H >= 0 && -2 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && 3 + -1*F >= 0 && 2 + -1*F + J >= 0 && 2 + A + -1*F >= 0 && -3 + F >= 0 && -4 + F + J >= 0 && -4 + A + F >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -2 + -1*B + J >= 0 && -2 + A + -1*B >= 0 && B + J >= 0 && A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && A >= 1 + H && A >= H && B + D + H >= 0 && D + H >= 2 + B && B + H >= D && H >= 2 + B + D && F = 3 && J = A] 12. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && 0 >= 1 + F && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 13. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl21(A,B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && F >= 4 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && J = A] 14. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl121(A,B,C,1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 0 && J = A] 15. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl141(A,B,C,-1 + D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 1 && J = A] 16. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl171(A,1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 2 && J = A] 17. lbl81(A,B,C,D,E,F,G,H,I,J) -> lbl191(A,-1 + B,C,D,E,F,G,H,I,J) [-1*H + J >= 0 (A,1) && A + -1*H >= 0 && -1 + H >= 0 && -1 + D + H >= 0 && -1 + -1*D + H >= 0 && -1 + B + H >= 0 && -1 + -1*B + H >= 0 && -2 + H + J >= 0 && -2 + A + H >= 0 && -1 + -1*D + J >= 0 && -1 + A + -1*D >= 0 && -1 + D + J >= 0 && -1 + A + D >= 0 && -1 + -1*B + J >= 0 && -1 + A + -1*B >= 0 && -1 + B + J >= 0 && -1 + A + B >= 0 && A + -1*J >= 0 && -1 + J >= 0 && -2 + A + J >= 0 && -1*A + J >= 0 && -1 + A >= 0 && D + H >= 1 + B && B + H >= 1 + D && H >= 1 + B + D && B + D + H >= 1 && A >= H && F = 3 && J = A] 18. start0(A,B,C,D,E,F,G,H,I,J) -> start(A,C,C,E,E,G,G,I,I,A) True (1,1) Signature: {(lbl121,10);(lbl141,10);(lbl171,10);(lbl191,10);(lbl21,10);(lbl81,10);(start,10);(start0,10);(stop,10)} Flow Graph: [0->{},1->{12,13,14,15,16,17},2->{},3->{12,13,14,15,16,17},4->{},5->{12,13,14,15,16,17},6->{},7->{12,13,14 ,15,16,17},8->{},9->{12,13,14,15,16,17},10->{},11->{12,13,14,15,16,17},12->{2,3},13->{2,3},14->{4,5},15->{6 ,7},16->{8,9},17->{10,11},18->{0,1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))