YES * Step 1: TrivialSCCs YES + 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: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + 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->{13,14,15,16},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: Looptree YES + 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: Looptree + 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] | +- p:[2,3,4] c: [4] | | | `- p:[2,3] c: [3] | | | `- p:[2] c: [2] | +- p:[8] c: [8] | `- p:[10,28,24,17,13,20,14,27,23,22,15,16,21,18,19,25,26] c: [28] | +- p:[15,27,23,22,16] c: [27] | `- p:[14,20,21] c: [21] | `- p:[14,20] c: [20] YES