YES(?,O(n^1)) * Step 1: ArgumentFilter WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f13(0,0,2*D,D,4*D,3 + 4*D,4 + 4*D,D,B1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) True (1,1) 1. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (?,1) 2. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f13(A + B1,B,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,B1,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f13(A + B1,B,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,B1,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (?,1) 4. f13(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f13(A,B,C,D,E,F,G,H,I,1 + J,1,0,0,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (?,1) 5. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,0,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (?,1) 6. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (?,1) 7. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (?,1) 8. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f24(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (?,1) 9. f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f118(A,B1,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (?,1) 11. f31(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f37(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f64(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,0,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f86(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,C1,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f86(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,C1,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f86(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,1 + Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f64(A,B,C,D,E,F,G,H,I,2 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f50(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f57(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,C + Q) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,B1,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,B1,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f91(A,B,C,D,E,F,G,H,I,J,K,0,M,N,O,P,Q,R,S,T,0,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f40(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,1 + Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f37(A,A + B,C,D,E,F,G,H,I,J,K,L,M,N,1 + O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14,15,16},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28} ,27->{13,14,15,16},28->{9,10}] + Applied Processor: ArgumentFilter [0,5,6,8,10,12,17,18,19,20,21,22,23,24,25] + Details: We remove following argument positions: [0,5,6,8,10,12,17,18,19,20,21,22,23,24,25]. * Step 2: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (?,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (?,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (?,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (?,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (?,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (?,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (?,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (?,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14,15,16},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28} ,27->{13,14,15,16},28->{9,10}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(20,15),(20,16)] * Step 3: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (?,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (?,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (?,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (?,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (?,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (?,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (?,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (?,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28},27->{13 ,14,15,16},28->{9,10}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (1,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (?,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (?,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (1,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (1,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (1,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (?,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (?,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28},27->{13 ,14,15,16},28->{9,10}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = x8 + -1*x9 + x27 p(f118) = x8 + -1*x9 + x27 p(f13) = x8 + -1*x9 + x27 p(f2) = x8 + -1*x9 + x27 p(f24) = x8 + -1*x9 + x27 p(f31) = x8 + -1*x9 + x27 p(f37) = x8 + -1*x9 + x27 p(f40) = x8 + -1*x9 + x27 p(f44) = x8 + -1*x9 + x27 p(f50) = x8 + -1*x9 + x27 p(f57) = x8 + -1*x9 + x27 p(f64) = x8 + -1*x9 + x27 p(f71) = x8 + -1*x9 + x27 p(f86) = x8 + -1*x9 + x27 p(f91) = x8 + -1*x9 + x27 Following rules are strictly oriented: [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f91(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O > N + -1*O = f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) Following rules are weakly oriented: True ==> f2(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] ==> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] f31(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] f118(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f44(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f50(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f57(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + N + -1*O >= 1 + N + -1*O = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (1,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (?,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (?,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (1,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (1,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (1,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (?,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (?,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (1 + N + O,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28},27->{13 ,14,15,16},28->{9,10}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (1,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (?,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (?,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (1,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (1,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (1,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (?,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (3 + N + O,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (1 + N + O,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28},27->{13 ,14,15,16},28->{9,10}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = -1*x11 + x27 p(f118) = -1*x11 + x27 p(f13) = -1*x11 + x27 p(f2) = -1*x11 + x27 p(f24) = -1*x11 + x27 p(f31) = -1*x11 + x27 p(f37) = -1*x11 + x27 p(f40) = -1*x11 + x27 p(f44) = -1*x11 + x27 p(f50) = -1*x11 + x27 p(f57) = -1*x11 + x27 p(f64) = -1*x11 + x27 p(f71) = -1*x11 + x27 p(f86) = -1*x11 + x27 p(f91) = -1*x11 + x27 Following rules are strictly oriented: [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f57(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q > -1*Q = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) Following rules are weakly oriented: True ==> f2(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] ==> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] f31(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] f118(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= -1*Q = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f44(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f50(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f91(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) * Step 7: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (1,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (?,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (?,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (1,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (1,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (1,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (?,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (3 + N + O,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (1 + N + O,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28},27->{13 ,14,15,16},28->{9,10}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 8: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (1,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (?,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (?,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (1,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (1,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (1,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (?,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (3 + N + O,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (1 + N + O,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28},27->{13 ,14,15,16},28->{9,10}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = -1*x11 + x27 p(f118) = -1*x11 + x27 p(f13) = -1*x11 + x27 p(f2) = -1*x11 + x27 p(f24) = -1*x11 + x27 p(f31) = -1*x11 + x27 p(f37) = -1*x11 + x27 p(f40) = -1*x11 + x27 p(f44) = -1*x11 + x27 p(f50) = -1*x11 + x27 p(f57) = -1*x11 + x27 p(f64) = -1*x11 + x27 p(f71) = -1*x11 + x27 p(f86) = -1*x11 + x27 p(f91) = -1*x11 + x27 Following rules are strictly oriented: [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q > -1*Q = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f57(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q > -1*Q = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) Following rules are weakly oriented: True ==> f2(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] ==> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] f31(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] f118(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f44(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f50(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f91(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + -1*Q >= 1 + -1*Q = f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) * Step 9: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (1,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (?,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (?,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (1,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (1,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (1,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (?,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (3 + N + O,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (1 + N + O,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28},27->{13 ,14,15,16},28->{9,10}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 10: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (1,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (?,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (?,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (1,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (1,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (1,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (?,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (3 + N + O,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (?,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (8 + 2*N + 2*O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (8 + 2*N + 2*O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (1 + N + O,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28},27->{13 ,14,15,16},28->{9,10}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = -1*x3 + 2*x4 + -1*x6 p(f118) = -1*x3 + 2*x4 + -1*x6 p(f13) = -2*x3 + 2*x4 p(f2) = 6*x3 p(f24) = -2*x3 + 2*x4 p(f31) = -2*x3 + 2*x4 p(f37) = -1*x3 + 2*x4 + -1*x6 p(f40) = -1*x3 + 2*x4 + -1*x6 p(f44) = -1*x3 + 2*x4 + -1*x6 p(f50) = -1*x3 + 2*x4 + -1*x6 p(f57) = -1*x3 + 2*x4 + -1*x6 p(f64) = -1*x3 + 2*x4 + -1*x6 p(f71) = -1*x3 + 2*x4 + -1*x6 p(f86) = -1*x3 + 2*x4 + -1*x6 p(f91) = -1*x3 + 2*x4 + -1*x6 Following rules are strictly oriented: [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J > -2 + -1*D + 2*E + -1*J = f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) Following rules are weakly oriented: True ==> f2(B,C,D,E,H,J,L,N,O,P,Q,A1) = 6*D >= 6*D = f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = -2*D + 2*E >= -2*D + 2*E = f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = -2*D + 2*E >= -2*D + 2*E = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = -2*D + 2*E >= -2*D + 2*E = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = -2*D + 2*E >= -2*D + 2*E = f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = -2*D + 2*E >= -1*D + 2*E + -1*J = f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = -2*D + 2*E >= -2*D + 2*E = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = -2*D + 2*E >= -2*D + 2*E = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = -2*D + 2*E >= -2*D + 2*E = f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] ==> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] f31(B,C,D,E,H,J,L,N,O,P,Q,A1) = -2*D + 2*E >= -1*D + 2*E + -1*J = f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] f118(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f44(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f50(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f57(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f91(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D + 2*E + -1*J >= -1*D + 2*E + -1*J = f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) * Step 11: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (1,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (?,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (?,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (1,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (1,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (1,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (?,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (3 + N + O,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (6*D,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (8 + 2*N + 2*O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (8 + 2*N + 2*O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (1 + N + O,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28},27->{13 ,14,15,16},28->{9,10}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = x3 + -1*x6 p(f118) = x3 + -1*x6 p(f13) = -1*x2 + x3 p(f2) = -1*x3 p(f24) = x3 + -1*x6 + x27 p(f31) = x3 + -1*x6 p(f37) = x3 + -1*x6 p(f40) = x3 + -1*x6 p(f44) = x3 + -1*x6 p(f50) = x3 + -1*x6 p(f57) = x3 + -1*x6 p(f64) = x3 + -1*x6 p(f71) = x3 + -1*x6 p(f86) = x3 + -1*x6 p(f91) = x3 + -1*x6 Following rules are strictly oriented: [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + D + -1*J > D + -1*J = f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) Following rules are weakly oriented: True ==> f2(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*D >= -1*D = f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*C + D >= 1 + D + -1*J = f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*C + D >= -1*C + D = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*C + D >= -1*C + D = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = -1*C + D >= -1*C + D = f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + D + -1*J >= D + -1*J = f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + D + -1*J >= D + -1*J = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + D + -1*J >= D + -1*J = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] ==> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] f31(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] f118(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= -2 + D + -1*J = f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f44(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f50(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f57(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f91(B,C,D,E,H,J,L,N,O,P,Q,A1) = D + -1*J >= D + -1*J = f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) * Step 12: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (1,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (?,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (?,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (1,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (1,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (1,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (D,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (3 + N + O,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (6*D,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (8 + 2*N + 2*O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (8 + 2*N + 2*O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (1 + N + O,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28},27->{13 ,14,15,16},28->{9,10}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = x2 + -1*x6 p(f118) = x2 + -1*x6 p(f13) = x2 + -1*x6 + x27 p(f2) = 2*x3 + -1*x6 + x27 p(f24) = x2 + -1*x6 p(f31) = x2 + -1*x6 p(f37) = x2 + -1*x6 p(f40) = x2 + -1*x6 p(f44) = x2 + -1*x6 p(f50) = x2 + -1*x6 p(f57) = x2 + -1*x6 p(f64) = x2 + -1*x6 p(f71) = x2 + -1*x6 p(f86) = x2 + -1*x6 p(f91) = x2 + -1*x6 Following rules are strictly oriented: [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J > C + -1*J = f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) Following rules are weakly oriented: True ==> f2(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + 2*D + -1*J >= 1 + 2*D + -1*J = f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J >= C + -1*J = f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J >= C + -1*J = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J >= C + -1*J = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= -1 + C + -1*J = f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] ==> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] f31(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] f118(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= -2 + C + -1*J = f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f44(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f50(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f57(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f91(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) * Step 13: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (1,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (?,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (1 + 2*D + J,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (1,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (1,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (1,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (D,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (3 + N + O,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (6*D,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (8 + 2*N + 2*O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (8 + 2*N + 2*O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (1 + N + O,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28},27->{13 ,14,15,16},28->{9,10}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = x2 + -1*x6 p(f118) = x2 + -1*x6 p(f13) = x2 + -1*x6 + x27 p(f2) = 2*x3 + -1*x6 + x27 p(f24) = x2 + -1*x6 p(f31) = x2 + -1*x6 p(f37) = x2 + -1*x6 p(f40) = x2 + -1*x6 p(f44) = x2 + -1*x6 p(f50) = x2 + -1*x6 p(f57) = x2 + -1*x6 p(f64) = x2 + -1*x6 p(f71) = x2 + -1*x6 p(f86) = x2 + -1*x6 p(f91) = x2 + -1*x6 Following rules are strictly oriented: [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J > C + -1*J = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J > C + -1*J = f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) Following rules are weakly oriented: True ==> f2(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + 2*D + -1*J >= 1 + 2*D + -1*J = f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J >= C + -1*J = f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J >= C + -1*J = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= -1 + C + -1*J = f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] ==> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] f31(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] f118(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= -2 + C + -1*J = f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f44(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f50(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f57(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f91(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) * Step 14: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (1,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (?,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (1 + 2*D + J,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (1 + 2*D + J,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (1,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (1,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (1,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (D,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (3 + N + O,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (6*D,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (8 + 2*N + 2*O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (8 + 2*N + 2*O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (1 + N + O,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28},27->{13 ,14,15,16},28->{9,10}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f1) = x2 + -1*x6 p(f118) = x2 + -1*x6 p(f13) = x2 + -1*x6 + x27 p(f2) = 2*x3 + -1*x6 + x27 p(f24) = x2 + -1*x6 + x27 p(f31) = x2 + -1*x6 p(f37) = x2 + -1*x6 p(f40) = x2 + -1*x6 p(f44) = x2 + -1*x6 p(f50) = x2 + -1*x6 p(f57) = x2 + -1*x6 p(f64) = x2 + -1*x6 p(f71) = x2 + -1*x6 p(f86) = x2 + -1*x6 p(f91) = x2 + -1*x6 Following rules are strictly oriented: [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J > C + -1*J = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J > C + -1*J = f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J > C + -1*J = f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) Following rules are weakly oriented: True ==> f2(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + 2*D + -1*J >= 1 + 2*D + -1*J = f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] ==> f13(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J >= 1 + C + -1*J = f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J >= C + -1*J = f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J >= C + -1*J = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J >= C + -1*J = f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] ==> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) = 1 + C + -1*J >= C + -1*J = f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] ==> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] f31(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] f118(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] f40(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] f71(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] f64(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= -2 + C + -1*J = f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f44(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f50(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] f86(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f57(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 ==> && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] f91(B,C,D,E,H,J,L,N,O,P,Q,A1) = C + -1*J >= C + -1*J = f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) * Step 15: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(0,2*D,D,4*D,D,J,L,N,O,P,Q,A1) True (1,1) 1. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + C] (1,1) 2. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && 0 >= C1 && C >= J] (1 + 2*D + J,1) 3. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C1 >= 2 && C >= J] (1 + 2*D + J,1) 4. f13(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(B,C,D,E,H,1 + J,0,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1*B >= 0 && B >= 0 && C >= J] (1 + 2*D + J,1) 5. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D && P = 0] (1,1) 6. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && P >= 1 && J >= 1 + D] (1,1) 7. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && 0 >= 1 + P && J >= 1 + D] (1,1) 8. f24(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(B,C,D,E,H,1 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1*D + H >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && D >= J] (D,1) 9. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(B1,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && O >= 1 + N] 10. f37(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N >= O] (3 + N + O,1) 11. f31(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*B >= 0 && B >= 0 && J >= 1 + D] 12. f118(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (1,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + -1*N + O >= 0 && J >= 1 + D] 13. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && Q >= 1] 14. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,J,L,N,O,0,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= Q && P = 0] 15. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && P >= 1 && 0 >= Q] 16. f40(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (4 + N + O + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && N + -1*O >= 0 && 0 >= 1 + P && 0 >= Q] 17. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && D1 >= 1 && J >= 1 + C] 18. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + D1 && J >= 1 + C] 19. f71(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(B,C,D,E,H,J,B1,N,O,P,Q,A1) [D + -1*H >= 0 (5 + N + O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + C] 20. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && J >= 1 + E] 21. f64(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(B,C,D,E,H,2 + J,L,N,O,P,Q,A1) [D + -1*H >= 0 (6*D,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && E >= J] 22. f44(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (8 + 2*N + 2*O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 23. f50(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(B,C,D,E,H,J,L,N,O,P,Q,C + Q) [D + -1*H >= 0 (8 + 2*N + 2*O + 2*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 24. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L >= 1] 25. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,L,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && 0 >= 1 + L] 26. f86(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(B,C,D,E,H,J,0,N,O,P,Q,A1) [D + -1*H >= 0 (15 + 3*N + 3*O + 6*Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && L = 0] 27. f57(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(B,C,D,E,H,J,L,N,O,P,1 + Q,A1) [D + -1*H >= 0 (1 + Q,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1*A1 + C >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && J >= 1 + D] 28. f91(B,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A + B,C,D,E,H,J,L,N,1 + O,P,Q,A1) [D + -1*H >= 0 (1 + N + O,1) && -1 + -1*H + J >= 0 && -1*D + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*C + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && J >= 1 + D] Signature: {(f1,27) ;(f118,27) ;(f13,27) ;(f2,27) ;(f24,27) ;(f31,27) ;(f37,27) ;(f40,27) ;(f44,27) ;(f50,27) ;(f57,27) ;(f64,27) ;(f71,27) ;(f86,27) ;(f91,27)} Flow Graph: [0->{1,2,3,4},1->{5,6,7,8},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4},5->{9,10},6->{11},7->{11},8->{5,6,7,8} ,9->{12},10->{13,14,15,16},11->{9,10},12->{},13->{17,18,19},14->{20,21},15->{22},16->{22},17->{24,25,26} ,18->{24,25,26},19->{24,25,26},20->{13,14},21->{20,21},22->{23},23->{27},24->{28},25->{28},26->{28},27->{13 ,14,15,16},28->{9,10}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(n^1))