YES(?,O(n^1)) * Step 1: UnsatPaths 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (?,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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (?,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (?,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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (?,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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= 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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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 2: TrivialSCCs 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (?,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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (?,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (?,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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (?,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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= 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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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 3: PolyRank 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (1,1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (?,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= 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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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 + x14 + -1*x15 p(f118) = 1 + x14 + -1*x15 p(f13) = 1 + x14 + -1*x15 p(f2) = 1 + x14 + -1*x15 p(f24) = 1 + x14 + -1*x15 p(f31) = 1 + x14 + -1*x15 p(f37) = 1 + x14 + -1*x15 p(f40) = 1 + x14 + -1*x15 p(f44) = 1 + x14 + -1*x15 p(f50) = 1 + x14 + -1*x15 p(f57) = 1 + x14 + -1*x15 p(f64) = 1 + x14 + -1*x15 p(f71) = 1 + x14 + -1*x15 p(f86) = 1 + x14 + -1*x15 p(f91) = 1 + x14 + -1*x15 Following rules are strictly oriented: [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + N + -1*O > N + -1*O = f37(A,B,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) Following rules are weakly oriented: [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==> 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) = 1 + N + -1*O >= 1 + N + -1*O = f13(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] ==> 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] ==> 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) = 1 + N + -1*O >= 1 + N + -1*O = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] ==> 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) = 1 + N + -1*O >= 1 + N + -1*O = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] ==> 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] ==> 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] ==> 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] ==> 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] ==> 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && O >= 1 + N] 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) = 1 + N + -1*O >= 1 + N + -1*O = f118(A,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] ==> 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && Q >= 1] 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= Q && P = 0] 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && P >= 1 && 0 >= Q] 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + P && 0 >= Q] 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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) = 1 + N + -1*O >= 1 + N + -1*O = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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) = 1 + N + -1*O >= 1 + N + -1*O = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) = 1 + N + -1*O >= 1 + N + -1*O = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + E] 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && E >= J] 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + N + -1*O >= 1 + N + -1*O = 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,D + Q) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L >= 1] 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) = 1 + N + -1*O >= 1 + N + -1*O = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + L] 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) = 1 + N + -1*O >= 1 + N + -1*O = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L = 0] 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + N + -1*O >= 1 + N + -1*O = 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) * Step 4: KnowledgePropagation 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (1,1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (?,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= 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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (1 + N + O,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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 5: PolyRank 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (1,1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (?,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= 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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] (3 + 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (1 + N + O,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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 + -1*x17 p(f118) = 1 + -1*x17 p(f13) = 1 + -1*x17 p(f2) = 1 + -1*x17 p(f24) = 1 + -1*x17 p(f31) = 1 + -1*x17 p(f37) = 1 + -1*x17 p(f40) = 1 + -1*x17 p(f44) = 1 + -1*x17 p(f50) = 1 + -1*x17 p(f57) = 1 + -1*x17 p(f64) = 1 + -1*x17 p(f71) = 1 + -1*x17 p(f86) = 1 + -1*x17 p(f91) = 1 + -1*x17 Following rules are strictly oriented: [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + -1*Q > -1*Q = 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) Following rules are weakly oriented: [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==> 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) = 1 + -1*Q >= 1 + -1*Q = f13(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] ==> 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) = 1 + -1*Q >= 1 + -1*Q = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] ==> 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) = 1 + -1*Q >= 1 + -1*Q = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && O >= 1 + N] 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) = 1 + -1*Q >= 1 + -1*Q = f118(A,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && Q >= 1] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= Q && P = 0] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && P >= 1 && 0 >= Q] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + P && 0 >= Q] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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) = 1 + -1*Q >= 1 + -1*Q = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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) = 1 + -1*Q >= 1 + -1*Q = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) = 1 + -1*Q >= 1 + -1*Q = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + E] 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) = 1 + -1*Q >= -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && E >= J] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + -1*Q >= 1 + -1*Q = 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,D + Q) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L >= 1] 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) = 1 + -1*Q >= 1 + -1*Q = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + L] 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) = 1 + -1*Q >= 1 + -1*Q = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L = 0] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + -1*Q >= 1 + -1*Q = f37(A,B,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) * Step 6: KnowledgePropagation 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (1,1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (?,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= 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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] (3 + 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (1 + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (1 + N + O,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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 7: PolyRank 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (1,1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (?,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= 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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] (3 + 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (1 + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (1 + N + O,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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 + x5 + -1*x10 p(f118) = 1 + x5 + -1*x10 p(f13) = -1*x1 + x5 p(f2) = 3*x1 p(f24) = -1*x1 + x5 p(f31) = -1*x1 + x5 p(f37) = 1 + x5 + -1*x10 p(f40) = 1 + x5 + -1*x10 p(f44) = 1 + x5 + -1*x10 p(f50) = 1 + x5 + -1*x10 p(f57) = 1 + x5 + -1*x10 p(f64) = 1 + x5 + -1*x10 p(f71) = 1 + x5 + -1*x10 p(f86) = 1 + x5 + -1*x10 p(f91) = 1 + x5 + -1*x10 Following rules are strictly oriented: [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && E >= J] 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) = 1 + E + -1*J > -1 + E + -1*J = 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) Following rules are weakly oriented: [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==> 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) = 3*A >= 3*A = f13(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] ==> 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) = -1*A + E >= -1*A + E = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] ==> 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) = -1*A + E >= -1*A + E = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] ==> 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) = -1*A + E >= -1*A + E = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] ==> 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) = -1*A + E >= -1*A + E = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] ==> 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) = -1*A + E >= 1 + E + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] ==> 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) = -1*A + E >= -1*A + E = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] ==> 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) = -1*A + E >= -1*A + E = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] ==> 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) = -1*A + E >= -1*A + E = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && O >= 1 + N] 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) = 1 + E + -1*J >= 1 + E + -1*J = f118(A,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] ==> 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) = 1 + E + -1*J >= 1 + E + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = -1*A + E >= 1 + E + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + E + -1*J >= 1 + E + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && Q >= 1] 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) = 1 + E + -1*J >= 1 + E + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= Q && P = 0] 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) = 1 + E + -1*J >= 1 + E + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && P >= 1 && 0 >= Q] 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) = 1 + E + -1*J >= 1 + E + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + P && 0 >= Q] 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) = 1 + E + -1*J >= 1 + E + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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) = 1 + E + -1*J >= 1 + E + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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) = 1 + E + -1*J >= 1 + E + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) = 1 + E + -1*J >= 1 + E + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + E] 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) = 1 + E + -1*J >= 1 + E + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + E + -1*J >= 1 + E + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + E + -1*J >= 1 + E + -1*J = 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,D + Q) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L >= 1] 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) = 1 + E + -1*J >= 1 + E + -1*J = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + L] 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) = 1 + E + -1*J >= 1 + E + -1*J = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L = 0] 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) = 1 + E + -1*J >= 1 + E + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + E + -1*J >= 1 + E + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + E + -1*J >= 1 + E + -1*J = f37(A,B,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) * Step 8: KnowledgePropagation 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (1,1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (?,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= 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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] (3 + 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (3*A,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (1 + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (1 + N + O,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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 9: PolyRank 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (1,1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (?,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= 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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] (3 + 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (3*A,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (1 + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (1 + N + O,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = x4 + -1*x10 p(f118) = x4 + -1*x10 p(f13) = 1 + x4 + -1*x10 p(f2) = 1 + 2*x1 + -1*x10 p(f24) = x4 + -1*x10 p(f31) = x4 + -1*x10 p(f37) = x4 + -1*x10 p(f40) = x4 + -1*x10 p(f44) = x4 + -1*x10 p(f50) = x4 + -1*x10 p(f57) = x4 + -1*x10 p(f64) = x4 + -1*x10 p(f71) = x4 + -1*x10 p(f86) = x4 + -1*x10 p(f91) = x4 + -1*x10 Following rules are strictly oriented: [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] ==> 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) = 1 + D + -1*J > D + -1*J = 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) Following rules are weakly oriented: [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==> 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) = 1 + 2*A + -1*J >= 1 + 2*A + -1*J = f13(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] ==> 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) = 1 + D + -1*J >= D + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] ==> 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) = 1 + D + -1*J >= D + -1*J = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] ==> 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) = 1 + D + -1*J >= D + -1*J = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] ==> 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*J >= D + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] ==> 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*J >= D + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] ==> 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*J >= D + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] ==> 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*J >= -1 + D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && O >= 1 + N] 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*J >= D + -1*J = f118(A,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] ==> 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = D + -1*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && Q >= 1] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= Q && P = 0] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && P >= 1 && 0 >= Q] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + P && 0 >= Q] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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*J >= D + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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*J >= D + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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*J >= D + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + E] 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) = D + -1*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && E >= J] 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) = D + -1*J >= -2 + D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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*J >= D + -1*J = 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,D + Q) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L >= 1] 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) = D + -1*J >= D + -1*J = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + L] 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) = D + -1*J >= D + -1*J = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L = 0] 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) = D + -1*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = D + -1*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = D + -1*J >= D + -1*J = f37(A,B,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) * Step 10: PolyRank 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (1,1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (?,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] (1 + 2*A + 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= 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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] (3 + 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (3*A,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (1 + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (1 + N + O,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = x4 + -1*x10 p(f118) = x4 + -1*x10 p(f13) = 1 + x4 + -1*x10 p(f2) = 1 + 2*x1 + -1*x10 p(f24) = x4 + -1*x10 p(f31) = x4 + -1*x10 p(f37) = x4 + -1*x10 p(f40) = x4 + -1*x10 p(f44) = x4 + -1*x10 p(f50) = x4 + -1*x10 p(f57) = x4 + -1*x10 p(f64) = x4 + -1*x10 p(f71) = x4 + -1*x10 p(f86) = x4 + -1*x10 p(f91) = x4 + -1*x10 Following rules are strictly oriented: [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] ==> 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) = 1 + D + -1*J > D + -1*J = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] ==> 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) = 1 + D + -1*J > D + -1*J = 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) Following rules are weakly oriented: [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==> 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) = 1 + 2*A + -1*J >= 1 + 2*A + -1*J = f13(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] ==> 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) = 1 + D + -1*J >= D + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] ==> 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) = 1 + D + -1*J >= D + -1*J = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] ==> 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*J >= D + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] ==> 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*J >= D + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] ==> 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*J >= D + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] ==> 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*J >= -1 + D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && O >= 1 + N] 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*J >= D + -1*J = f118(A,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] ==> 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = D + -1*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && Q >= 1] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= Q && P = 0] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && P >= 1 && 0 >= Q] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + P && 0 >= Q] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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*J >= D + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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*J >= D + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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*J >= D + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + E] 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) = D + -1*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && E >= J] 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) = D + -1*J >= -2 + D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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*J >= D + -1*J = 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,D + Q) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L >= 1] 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) = D + -1*J >= D + -1*J = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + L] 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) = D + -1*J >= D + -1*J = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L = 0] 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) = D + -1*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = D + -1*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = D + -1*J >= D + -1*J = f37(A,B,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) * Step 11: PolyRank 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (1,1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (1 + 2*A + J,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] (1 + 2*A + 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= 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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] (3 + 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (3*A,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (1 + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (1 + N + O,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 2*x1 + -1*x8 + -1*x10 p(f118) = 2*x1 + -1*x8 + -1*x10 p(f13) = x1 + -1*x4 p(f2) = -1*x1 p(f24) = 1 + x1 + -1*x10 p(f31) = x1 + -1*x10 p(f37) = x1 + -1*x10 p(f40) = x1 + -1*x10 p(f44) = x1 + -1*x10 p(f50) = x1 + -1*x10 p(f57) = x1 + -1*x10 p(f64) = x1 + -1*x10 p(f71) = x8 + -1*x10 p(f86) = x8 + -1*x10 p(f91) = x8 + -1*x10 Following rules are strictly oriented: [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] ==> 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) = 1 + A + -1*J > A + -1*J = 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) Following rules are weakly oriented: [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==> 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) = -1*A >= -1*A = f13(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] ==> 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) = A + -1*D >= 1 + A + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] ==> 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) = A + -1*D >= A + -1*D = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] ==> 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) = A + -1*D >= A + -1*D = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] ==> 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) = A + -1*D >= A + -1*D = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] ==> 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) = 1 + A + -1*J >= A + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] ==> 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) = 1 + A + -1*J >= A + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] ==> 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) = 1 + A + -1*J >= A + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && O >= 1 + N] 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) = A + -1*J >= 2*A + -1*H + -1*J = f118(A,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] ==> 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) = A + -1*J >= A + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = A + -1*J >= A + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 2*A + -1*H + -1*J >= 2*A + -1*H + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && Q >= 1] 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) = A + -1*J >= H + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= Q && P = 0] 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) = A + -1*J >= A + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && P >= 1 && 0 >= Q] 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) = A + -1*J >= A + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + P && 0 >= Q] 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) = A + -1*J >= A + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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) = H + -1*J >= H + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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) = H + -1*J >= H + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) = H + -1*J >= H + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + E] 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) = A + -1*J >= A + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && E >= J] 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) = A + -1*J >= -2 + A + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = A + -1*J >= A + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = A + -1*J >= A + -1*J = 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,D + Q) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L >= 1] 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) = H + -1*J >= H + -1*J = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + L] 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) = H + -1*J >= H + -1*J = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L = 0] 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) = H + -1*J >= H + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = A + -1*J >= A + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = H + -1*J >= A + -1*J = f37(A,B,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) * Step 12: PolyRank 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (1,1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (1 + 2*A + J,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] (1 + 2*A + 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] (A,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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] (3 + 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (3*A,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (1 + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (1 + N + O,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = x4 + -1*x10 p(f118) = x4 + -1*x10 p(f13) = 1 + x4 + -1*x10 p(f2) = 1 + 2*x1 + -1*x10 p(f24) = x4 + -1*x10 p(f31) = x4 + -1*x10 p(f37) = x4 + -1*x10 p(f40) = x4 + -1*x10 p(f44) = x4 + -1*x10 p(f50) = x4 + -1*x10 p(f57) = x4 + -1*x10 p(f64) = x4 + -1*x10 p(f71) = x4 + -1*x10 p(f86) = x4 + -1*x10 p(f91) = x4 + -1*x10 Following rules are strictly oriented: [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] ==> 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) = 1 + D + -1*J > D + -1*J = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] ==> 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) = 1 + D + -1*J > D + -1*J = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] ==> 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) = 1 + D + -1*J > D + -1*J = 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) Following rules are weakly oriented: [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==> 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) = 1 + 2*A + -1*J >= 1 + 2*A + -1*J = f13(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] ==> 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) = 1 + D + -1*J >= D + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] ==> 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*J >= D + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] ==> 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*J >= D + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] ==> 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*J >= D + -1*J = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] ==> 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*J >= -1 + D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && O >= 1 + N] 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*J >= D + -1*J = f118(A,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] ==> 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = D + -1*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && Q >= 1] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= Q && P = 0] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && P >= 1 && 0 >= Q] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + P && 0 >= Q] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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*J >= D + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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*J >= D + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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*J >= D + -1*J = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + E] 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) = D + -1*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && E >= J] 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) = D + -1*J >= -2 + D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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*J >= D + -1*J = 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,D + Q) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L >= 1] 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) = D + -1*J >= D + -1*J = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + L] 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) = D + -1*J >= D + -1*J = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L = 0] 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) = D + -1*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = D + -1*J >= D + -1*J = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = D + -1*J >= D + -1*J = f37(A,B,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) * Step 13: PolyRank 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (1,1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (1 + 2*A + J,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (1 + 2*A + J,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] (1 + 2*A + 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] (A,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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] (3 + 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (3*A,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (1 + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (1 + N + O,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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 + -1*x17 p(f118) = 1 + -1*x17 p(f13) = 1 + -1*x17 p(f2) = 1 + -1*x17 p(f24) = 1 + -1*x17 p(f31) = 1 + -1*x17 p(f37) = 1 + -1*x17 p(f40) = 1 + -1*x17 p(f44) = -1*x17 p(f50) = -1*x17 p(f57) = -1*x17 p(f64) = 1 + -1*x17 p(f71) = 1 + -1*x17 p(f86) = 1 + -1*x17 p(f91) = 1 + -1*x17 Following rules are strictly oriented: [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && P >= 1 && 0 >= Q] 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) = 1 + -1*Q > -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + P && 0 >= Q] 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) = 1 + -1*Q > -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + E] 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) = 1 + -1*Q > -1*Q = 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) Following rules are weakly oriented: [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] ==> 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) = 1 + -1*Q >= 1 + -1*Q = f13(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] ==> 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) = 1 + -1*Q >= 1 + -1*Q = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] ==> 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) = 1 + -1*Q >= 1 + -1*Q = f13(A,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && O >= 1 + N] 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) = 1 + -1*Q >= 1 + -1*Q = f118(A,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] ==> 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && Q >= 1] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= Q && P = 0] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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) = 1 + -1*Q >= 1 + -1*Q = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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) = 1 + -1*Q >= 1 + -1*Q = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) = 1 + -1*Q >= 1 + -1*Q = f86(A,B,C,D,E,F,G,H,I,J,K,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && E >= J] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = -1*Q >= -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = -1*Q >= -1*Q = 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,D + Q) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L >= 1] 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) = 1 + -1*Q >= 1 + -1*Q = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + L] 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) = 1 + -1*Q >= 1 + -1*Q = f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && L = 0] 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) = 1 + -1*Q >= 1 + -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = -1*Q >= -1*Q = 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) [-1 + -1*H + J >= 0 ==> && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) = 1 + -1*Q >= 1 + -1*Q = f37(A,B,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) * Step 14: KnowledgePropagation 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (1,1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (1 + 2*A + J,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (1 + 2*A + J,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] (1 + 2*A + 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] (A,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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] (3 + 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (1 + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (3*A,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (?,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (1 + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (1 + N + O,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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 15: PolyRank 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(A,0,0,2*A,4*A,3 + 4*A,4 + 4*A,A,C1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (1,1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (1 + 2*A + J,1) ,A1) 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,1 + B + -2*C1 + C1^2,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,1 + -2*C1 + C1^2,N,O,P,Q,R,S,T,U,V,W,X,Y,Z[A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (1 + 2*A + J,1) ,A1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] (1 + 2*A + 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + A && P = 0] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && P >= 1 && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && 0 >= 1 + P && J >= 1 + A] (1,1) 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) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] (A,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,B,C*E,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + 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) [-1 + -1*H + J >= 0 && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*A + J >= 0 && N >= O] (3 + 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (1,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + -1*N + O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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) [-1 + -1*H + J >= 0 (5 + N + O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (5 + N + O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (4 + N + O + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (5 + N + O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && B1 >= 1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,B1^2,A1) [-1 + -1*H + J >= 0 (5 + N + O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && 0 >= 1 + B1 && J >= 1 + D] 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,C1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [-1 + -1*H + J >= 0 (5 + N + O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + D] 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) [-1 + -1*H + J >= 0 (1 + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (3*A,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && P + -1*Q >= 0 && -1*P + -1*Q >= 0 && -1*P >= 0 && P >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,D + Q) [-1 + -1*H + J >= 0 (8 + 2*N + 2*O + 2*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (15 + 3*N + 3*O + 6*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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,L^2,V,W,X,Y,Z,A1) [-1 + -1*H + J >= 0 (15 + 3*N + 3*O + 6*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (15 + 3*N + 3*O + 6*Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 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) [-1 + -1*H + J >= 0 (1 + Q,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*A1 + D >= 0 && -1 + -1*A1 + J >= 0 && -1*Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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,B,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) [-1 + -1*H + J >= 0 (1 + N + O,1) && A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1 + Q >= 0 && N + -1*O >= 0 && -1 + -1*A + J >= 0 && J >= 1 + A] 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: The problem is already solved. YES(?,O(n^1))