YES(?,POLY) * Step 1: ArgumentFilter WORST_CASE(?,POLY) + 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: ArgumentFilter [1,5,6,8,10,12,17,18,19,20,21,22,23,24,25] + Details: We remove following argument positions: [1,5,6,8,10,12,17,18,19,20,21,22,23,24,25]. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f2(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,0,2*A,4*A,A,J,L,N,O,P,Q,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1) 1. f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(A,C,D,E,H,J,L,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (?,1) 2. f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) 3. f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (?,1) 4. f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,0,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] (?,1) 5. f24(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,C,D,E,H,J,L,N,O,0,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(A,C,D,E,H,1 + J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(A,C*E,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(A,C,D,E,H,J,L,N,O,0,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,1 + Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(A,C,D,E,H,2 + J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,0,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,1 + Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,B + C,D,E,H,J,L,N,1 + O,P,Q,A1) [-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 3: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f2(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,0,2*A,4*A,A,J,L,N,O,P,Q,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] (1,1) 1. f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(A,C,D,E,H,J,L,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] (?,1) 2. f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] (?,1) 3. f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] (?,1) 4. f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,0,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] (?,1) 5. f24(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,C,D,E,H,J,L,N,O,0,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(A,C,D,E,H,1 + J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(A,C*E,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(A,C,D,E,H,J,L,N,O,0,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,1 + Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(A,C,D,E,H,2 + J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,0,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,1 + Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,B + C,D,E,H,J,L,N,1 + O,P,Q,A1) [-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: FromIts + Details: () * Step 4: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: f2(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,0,2*A,4*A,A,J,L,N,O,P,Q,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(A,C,D,E,H,J,L,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,0,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] f24(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,C,D,E,H,J,L,N,O,0,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(A,C,D,E,H,1 + J,L,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] f37(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(A,C*E,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,Q,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] f31(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,C,D,E,H,J,L,N,O,P,Q,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] f118(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(A,C,D,E,H,J,L,N,O,P,Q,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] f40(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(A,C,D,E,H,J,L,N,O,0,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(A,C,D,E,H,J,L,N,O,P,Q,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] f71(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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] f64(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,1 + Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(A,C,D,E,H,2 + J,L,N,O,P,Q,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] f44(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(A,C,D,E,H,J,L,N,O,P,Q,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 && J >= 1 + A] f86(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,L,N,O,P,Q,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 >= 1] f86(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,0,N,O,P,Q,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] f57(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,1 + Q,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] f91(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,B + C,D,E,H,J,L,N,1 + O,P,Q,A1) [-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] 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)} Rule 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: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: f2(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,0,2*A,4*A,A,J,L,N,O,P,Q,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(A,C,D,E,H,J,L,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,0,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] f24(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,C,D,E,H,J,L,N,O,0,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(A,C,D,E,H,1 + J,L,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] f37(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(A,C*E,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,Q,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] f31(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,C,D,E,H,J,L,N,O,P,Q,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] f118(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(A,C,D,E,H,J,L,N,O,P,Q,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] f40(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(A,C,D,E,H,J,L,N,O,0,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(A,C,D,E,H,J,L,N,O,P,Q,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] f71(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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] f64(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,1 + Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(A,C,D,E,H,2 + J,L,N,O,P,Q,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] f44(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(A,C,D,E,H,J,L,N,O,P,Q,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 && J >= 1 + A] f86(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,L,N,O,P,Q,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 >= 1] f86(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,0,N,O,P,Q,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] f57(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,1 + Q,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] f91(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,B + C,D,E,H,J,L,N,1 + O,P,Q,A1) [-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] f1(A,C,D,E,H,J,L,N,O,P,Q,A1) -> exitus616(A,C,D,E,H,J,L,N,O,P,Q,A1) True f1(A,C,D,E,H,J,L,N,O,P,Q,A1) -> exitus616(A,C,D,E,H,J,L,N,O,P,Q,A1) True f1(A,C,D,E,H,J,L,N,O,P,Q,A1) -> exitus616(A,C,D,E,H,J,L,N,O,P,Q,A1) True Signature: {(exitus616,12) ;(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)} Rule 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->{29,30,31},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: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31] | +- p:[2,3,4] c: [2,3,4] | +- p:[8] c: [8] | `- p:[10,28,24,17,13,20,14,27,23,22,15,16,21,18,19,25,26] c: [10,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] * Step 6: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: f2(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,0,2*A,4*A,A,J,L,N,O,P,Q,A1) [1 >= A*B1 && A*B1 + B1 >= 2 && C1 >= B1 && 1 >= A*D1 && A*D1 + D1 >= 2 && D1 >= C1] f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(A,C,D,E,H,J,L,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && J >= 1 + D] f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && 0 >= C1 && D >= J] f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,1 + -1*C1,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && C1 >= 2 && D >= J] f13(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f13(A,C,D,E,H,1 + J,0,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1*C >= 0 && C >= 0 && D >= J] f24(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,C,D,E,H,J,L,N,O,0,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f31(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f24(A,C,D,E,H,1 + J,L,N,O,P,Q,A1) [A + -1*H >= 0 && -1*A + H >= 0 && -1 + -1*D + J >= 0 && -1*C >= 0 && C >= 0 && A >= J] f37(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f118(A,C*E,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,Q,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] f31(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,C,D,E,H,J,L,N,O,P,Q,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] f118(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f1(A,C,D,E,H,J,L,N,O,P,Q,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] f40(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f71(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(A,C,D,E,H,J,L,N,O,0,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f44(A,C,D,E,H,J,L,N,O,P,Q,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] f71(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f86(A,C,D,E,H,J,C1,N,O,P,Q,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] f64(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,1 + Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f64(A,C,D,E,H,2 + J,L,N,O,P,Q,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] f44(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f50(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f57(A,C,D,E,H,J,L,N,O,P,Q,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 && J >= 1 + A] f86(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,L,N,O,P,Q,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 >= 1] f86(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,L,N,O,P,Q,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,C,D,E,H,J,L,N,O,P,Q,A1) -> f91(A,C,D,E,H,J,0,N,O,P,Q,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] f57(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f40(A,C,D,E,H,J,L,N,O,P,1 + Q,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] f91(A,C,D,E,H,J,L,N,O,P,Q,A1) -> f37(A,B + C,D,E,H,J,L,N,1 + O,P,Q,A1) [-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] f1(A,C,D,E,H,J,L,N,O,P,Q,A1) -> exitus616(A,C,D,E,H,J,L,N,O,P,Q,A1) True f1(A,C,D,E,H,J,L,N,O,P,Q,A1) -> exitus616(A,C,D,E,H,J,L,N,O,P,Q,A1) True f1(A,C,D,E,H,J,L,N,O,P,Q,A1) -> exitus616(A,C,D,E,H,J,L,N,O,P,Q,A1) True Signature: {(exitus616,12) ;(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)} Rule 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->{29,30,31},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}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31] | +- p:[2,3,4] c: [2,3,4] | +- p:[8] c: [8] | `- p:[10,28,24,17,13,20,14,27,23,22,15,16,21,18,19,25,26] c: [10,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,C,D,E,H,J,L,N,O,P,Q,A1,0.0,0.1,0.2] f2 ~> f13 [A <= A, C <= 0*K, D <= 2*A, E <= 4*A, H <= A, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f13 ~> f24 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f13 ~> f13 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= K + J, L <= unknown, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f13 ~> f13 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= K + J, L <= unknown, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f13 ~> f13 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= K + J, L <= 0*K, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f24 ~> f37 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= 0*K, Q <= Q, A1 <= A1] f24 ~> f31 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f24 ~> f31 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f24 ~> f24 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= K + J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f37 ~> f118 [A <= A, C <= unknown, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f37 ~> f40 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f31 ~> f37 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f118 ~> f1 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f40 ~> f71 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f40 ~> f64 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= 0*K, Q <= Q, A1 <= A1] f40 ~> f44 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f40 ~> f44 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f71 ~> f86 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= unknown, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f71 ~> f86 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= unknown, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f71 ~> f86 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= unknown, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f64 ~> f40 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= K + Q, A1 <= A1] f64 ~> f64 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= 2*K + J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f44 ~> f50 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f50 ~> f57 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= D + Q] f86 ~> f91 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f86 ~> f91 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f86 ~> f91 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= 0*K, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f57 ~> f40 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= K + Q, A1 <= A1] f91 ~> f37 [A <= A, C <= unknown, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= K + O, P <= P, Q <= Q, A1 <= A1] f1 ~> exitus616 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f1 ~> exitus616 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f1 ~> exitus616 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] + Loop: [0.0 <= D + J] f13 ~> f13 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= K + J, L <= unknown, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f13 ~> f13 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= K + J, L <= unknown, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f13 ~> f13 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= K + J, L <= 0*K, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] + Loop: [0.1 <= A + J] f24 ~> f24 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= K + J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] + Loop: [0.2 <= E + J + N + O + Q] f37 ~> f40 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f91 ~> f37 [A <= A, C <= unknown, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= K + O, P <= P, Q <= Q, A1 <= A1] f86 ~> f91 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f71 ~> f86 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= unknown, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f40 ~> f71 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f64 ~> f40 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= K + Q, A1 <= A1] f40 ~> f64 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= 0*K, Q <= Q, A1 <= A1] f57 ~> f40 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= K + Q, A1 <= A1] f50 ~> f57 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= D + Q] f44 ~> f50 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f40 ~> f44 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f40 ~> f44 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f64 ~> f64 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= 2*K + J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f71 ~> f86 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= unknown, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f71 ~> f86 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= unknown, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f86 ~> f91 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= L, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] f86 ~> f91 [A <= A, C <= C, D <= D, E <= E, H <= H, J <= J, L <= 0*K, N <= N, O <= O, P <= P, Q <= Q, A1 <= A1] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,C,D,E,H,J,L,N,O,P,Q,A1,0.0,0.1,0.2] f2 ~> f13 [A ~=> H,K ~=> C,A ~*> D,A ~*> E] f13 ~> f24 [] f13 ~> f13 [huge ~=> L,J ~+> J,K ~+> J] f13 ~> f13 [huge ~=> L,J ~+> J,K ~+> J] f13 ~> f13 [K ~=> L,J ~+> J,K ~+> J] f24 ~> f37 [K ~=> P] f24 ~> f31 [] f24 ~> f31 [] f24 ~> f24 [J ~+> J,K ~+> J] f37 ~> f118 [huge ~=> C] f37 ~> f40 [] f31 ~> f37 [] f118 ~> f1 [] f40 ~> f71 [] f40 ~> f64 [K ~=> P] f40 ~> f44 [] f40 ~> f44 [] f71 ~> f86 [huge ~=> L] f71 ~> f86 [huge ~=> L] f71 ~> f86 [huge ~=> L] f64 ~> f40 [Q ~+> Q,K ~+> Q] f64 ~> f64 [J ~+> J,K ~*> J] f44 ~> f50 [] f50 ~> f57 [D ~+> A1,Q ~+> A1] f86 ~> f91 [] f86 ~> f91 [] f86 ~> f91 [K ~=> L] f57 ~> f40 [Q ~+> Q,K ~+> Q] f91 ~> f37 [huge ~=> C,O ~+> O,K ~+> O] f1 ~> exitus616 [] f1 ~> exitus616 [] f1 ~> exitus616 [] + Loop: [D ~+> 0.0,J ~+> 0.0] f13 ~> f13 [huge ~=> L,J ~+> J,K ~+> J] f13 ~> f13 [huge ~=> L,J ~+> J,K ~+> J] f13 ~> f13 [K ~=> L,J ~+> J,K ~+> J] + Loop: [A ~+> 0.1,J ~+> 0.1] f24 ~> f24 [J ~+> J,K ~+> J] + Loop: [E ~+> 0.2,J ~+> 0.2,N ~+> 0.2,O ~+> 0.2,Q ~+> 0.2] f37 ~> f40 [] f91 ~> f37 [huge ~=> C,O ~+> O,K ~+> O] f86 ~> f91 [] f71 ~> f86 [huge ~=> L] f40 ~> f71 [] f64 ~> f40 [Q ~+> Q,K ~+> Q] f40 ~> f64 [K ~=> P] f57 ~> f40 [Q ~+> Q,K ~+> Q] f50 ~> f57 [D ~+> A1,Q ~+> A1] f44 ~> f50 [] f40 ~> f44 [] f40 ~> f44 [] f64 ~> f64 [J ~+> J,K ~*> J] f71 ~> f86 [huge ~=> L] f71 ~> f86 [huge ~=> L] f86 ~> f91 [] f86 ~> f91 [K ~=> L] + Applied Processor: Lare + Details: f2 ~> exitus616 [A ~=> H ,K ~=> L ,K ~=> P ,huge ~=> C ,huge ~=> L ,A ~+> 0.1 ,A ~+> tick ,J ~+> J ,J ~+> 0.0 ,J ~+> 0.1 ,J ~+> 0.2 ,J ~+> tick ,N ~+> 0.2 ,N ~+> tick ,O ~+> O ,O ~+> 0.2 ,O ~+> tick ,Q ~+> A1 ,Q ~+> Q ,Q ~+> 0.2 ,Q ~+> tick ,tick ~+> tick ,K ~+> A1 ,K ~+> J ,K ~+> O ,K ~+> Q ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> tick ,A ~*> A1 ,A ~*> D ,A ~*> E ,A ~*> J ,A ~*> O ,A ~*> Q ,A ~*> 0.0 ,A ~*> 0.1 ,A ~*> 0.2 ,A ~*> tick ,J ~*> A1 ,J ~*> J ,J ~*> O ,J ~*> Q ,J ~*> 0.1 ,J ~*> 0.2 ,J ~*> tick ,N ~*> A1 ,N ~*> J ,N ~*> O ,N ~*> Q ,O ~*> A1 ,O ~*> J ,O ~*> O ,O ~*> Q ,Q ~*> A1 ,Q ~*> J ,Q ~*> O ,Q ~*> Q ,K ~*> A1 ,K ~*> J ,K ~*> O ,K ~*> Q ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> tick] + f13> [K ~=> L ,huge ~=> L ,D ~+> 0.0 ,D ~+> tick ,J ~+> J ,J ~+> 0.0 ,J ~+> tick ,tick ~+> tick ,K ~+> J ,D ~*> J ,J ~*> J ,K ~*> J] + f24> [A ~+> 0.1 ,A ~+> tick ,J ~+> J ,J ~+> 0.1 ,J ~+> tick ,tick ~+> tick ,K ~+> J ,A ~*> J ,J ~*> J ,K ~*> J] + f37> [K ~=> L ,K ~=> P ,huge ~=> C ,huge ~=> L ,D ~+> A1 ,E ~+> 0.2 ,E ~+> tick ,J ~+> J ,J ~+> 0.2 ,J ~+> tick ,N ~+> 0.2 ,N ~+> tick ,O ~+> O ,O ~+> 0.2 ,O ~+> tick ,Q ~+> A1 ,Q ~+> Q ,Q ~+> 0.2 ,Q ~+> tick ,tick ~+> tick ,K ~+> A1 ,K ~+> O ,K ~+> Q ,E ~*> A1 ,E ~*> J ,E ~*> O ,E ~*> Q ,J ~*> A1 ,J ~*> J ,J ~*> O ,J ~*> Q ,N ~*> A1 ,N ~*> J ,N ~*> O ,N ~*> Q ,O ~*> A1 ,O ~*> J ,O ~*> O ,O ~*> Q ,Q ~*> A1 ,Q ~*> J ,Q ~*> O ,Q ~*> Q ,K ~*> A1 ,K ~*> J ,K ~*> O ,K ~*> Q] YES(?,POLY)