YES(?,O(n^1)) * Step 1: ArgumentFilter WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f23(0,0,2*D,D,4*D,3 + 4*D,4 + 4*D,D,B1,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) True (1,1) 1. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f23(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) [C >= J] (?,1) 2. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f23(A + B1,B,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,B1,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [C1 >= 2 && C >= J] (?,1) 3. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f23(A + B1,B,C,D,E,F,G,H,I,1 + J,C1,1 + -1*C1,B1,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [0 >= C1 && C >= J] (?,1) 4. f33(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f33(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D >= J] (?,1) 5. f39(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f39(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D >= J] (?,1) 6. 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) -> f46(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [N >= O] (?,1) 7. f46(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f49(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [0 >= 1 + P && 0 >= Q] (?,1) 8. f46(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f49(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [P >= 1 && 0 >= Q] (?,1) 9. f49(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f49(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D >= J] (?,1) 10. f54(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f54(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D >= J] (?,1) 11. f60(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f60(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D >= J] (?,1) 12. f46(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f66(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) [0 >= Q && P = 0] (?,1) 13. f66(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f66(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) [E >= J] (?,1) 14. f72(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f72(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,2*J,B1,1 + -1*B1,U,V,W,X,Y,Z,A1) [C >= J] (?,1) 15. f87(A,B,C,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) [L = 0] (?,1) 16. f87(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,B1,V,W,X,Y,Z,A1) [0 >= 1 + L] (?,1) 17. f87(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f91(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,B1,V,W,X,Y,Z,A1) [L >= 1] (?,1) 18. 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) -> f99(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,2*J,S,T,U,0,W,X,Y,Z,A1) [D >= J] (?,1) 19. 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) -> f99(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,2*J,S,T,U,C1,W,X,Y,Z,A1) [0 >= 1 + D1 && D >= J] (?,1) 20. 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) -> f99(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,2*J,S,T,U,C1,W,X,Y,Z,A1) [D1 >= 1 && D >= J] (?,1) 21. f99(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f103(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,R,S,T,U,V,0,X,Y,Z,A1) [L = 0] (?,1) 22. f99(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f103(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,R,S,T,U,V,C1,X,Y,Z,A1) [0 >= 1 + L] (?,1) 23. f99(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f103(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,R,S,T,U,V,C1,X,Y,Z,A1) [L >= 1] (?,1) 24. f103(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f107(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,R,S,T,U,V,W,0,Y,Z,A1) [L = 0] (?,1) 25. f103(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f107(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,R,S,T,U,V,W,C1,Y,Z,A1) [0 >= 1 + L] (?,1) 26. f103(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f107(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,R,S,T,U,V,W,C1,Y,Z,A1) [L >= 1] (?,1) 27. f107(A,B,C,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,1 + J,K,0,M,N,O,P,Q,R,S,T,U,V,W,X,0,Z,A1) [L = 0] (?,1) 28. f107(A,B,C,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,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,B1,Z,A1) [0 >= 1 + L] (?,1) 29. f107(A,B,C,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,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,B1,Z,A1) [L >= 1] (?,1) 30. f117(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f117(A,B,C,D,E,F,G,H,I,1 + J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [D >= J] (?,1) 31. f117(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f125(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [J >= 1 + D] (?,1) 32. 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) -> f44(A,A + B,C,D,E,F,G,H,I,J,K,L,M,N,1 + O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [J >= 1 + D] (?,1) 33. f72(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f87(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,0,A1) [J >= 1 + C] (?,1) 34. f72(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f87(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,C1,A1) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f87(A,B,C,D,E,F,G,H,I,J,K,B1,M,N,O,P,Q,R,S,T,U,V,W,X,Y,C1,A1) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f46(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) [J >= 1 + E] (?,1) 37. f60(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f46(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) [J >= 1 + D] (?,1) 38. f54(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f60(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,C + Q) [J >= 1 + D] (?,1) 39. f49(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f54(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [J >= 1 + D] (?,1) 40. f46(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f72(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [Q >= 1] (?,1) 41. 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) -> f117(A,B1,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [O >= 1 + N] (?,1) 42. f39(A,B,C,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) [J >= 1 + D] (?,1) 43. f33(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f39(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [0 >= 1 + P && J >= 1 + D] (?,1) 44. f33(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f39(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [P >= 1 && J >= 1 + D] (?,1) 45. f33(A,B,C,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,0,Q,R,S,T,U,V,W,X,Y,Z,A1) [J >= 1 + D && P = 0] (?,1) 46. f23(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f33(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [J >= 1 + C] (?,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},5->{5,42},6->{7,8,12,40},7->{9 ,39},8->{9,39},9->{9,39},10->{10,38},11->{11,37},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32} ,16->{18,19,20,32},17->{18,19,20,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25 ,26},23->{24,25,26},24->{27,28,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18 ,19,20,32},30->{30,31},31->{},32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7 ,8,12,40},38->{11,37},39->{10,38},40->{14,33,34,35},41->{30,31},42->{6,41},43->{5,42},44->{5,42},45->{6,41} ,46->{4,43,44,45}] + Applied Processor: ArgumentFilter [0,1,5,6,7,8,10,12,17,18,19,20,21,22,23,24,25,26] + Details: We remove following argument positions: [0,1,5,6,7,8,10,12,17,18,19,20,21,22,23,24,25,26]. * Step 2: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 5. f39(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (?,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 10. f54(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 11. f60(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (?,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (?,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (?,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (?,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (?,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (?,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (?,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (?,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (?,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},5->{5,42},6->{7,8,12,40},7->{9 ,39},8->{9,39},9->{9,39},10->{10,38},11->{11,37},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32} ,16->{18,19,20,32},17->{18,19,20,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25 ,26},23->{24,25,26},24->{27,28,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18 ,19,20,32},30->{30,31},31->{},32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7 ,8,12,40},38->{11,37},39->{10,38},40->{14,33,34,35},41->{30,31},42->{6,41},43->{5,42},44->{5,42},45->{6,41} ,46->{4,43,44,45}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(38,11),(39,10),(43,5),(44,5)] * Step 3: UnreachableRules WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 5. f39(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (?,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 10. f54(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 11. f60(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (?,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (?,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (?,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (?,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (?,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (?,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (?,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (?,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (?,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},5->{5,42},6->{7,8,12,40},7->{9 ,39},8->{9,39},9->{9,39},10->{10,38},11->{11,37},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32} ,16->{18,19,20,32},17->{18,19,20,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25 ,26},23->{24,25,26},24->{27,28,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18 ,19,20,32},30->{30,31},31->{},32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7 ,8,12,40},38->{37},39->{38},40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43 ,44,45}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [5,10,11] * Step 4: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (?,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (?,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (?,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (?,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (?,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (?,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (?,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (?,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (?,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (?,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 5: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (?,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (?,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (?,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (?,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (?,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 0 p(f103) = x2 + -1*x4 + x27 p(f107) = x2 + -1*x4 + x27 p(f117) = x2 + -1*x4 + x27 p(f125) = x2 + -1*x4 + x27 p(f23) = 0 p(f33) = 0 p(f39) = 0 p(f44) = x2 + -1*x4 + x27 p(f46) = x2 + -1*x4 + x27 p(f49) = x2 + -1*x4 + x27 p(f54) = x2 + -1*x4 + x27 p(f60) = x2 + -1*x4 + x27 p(f66) = x2 + -1*x4 + x27 p(f72) = x2 + -1*x4 + x27 p(f87) = x2 + -1*x4 + x27 p(f91) = x2 + -1*x4 + x27 p(f99) = x2 + -1*x4 + x27 Following rules are strictly oriented: [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f117(C,D,E,1 + J,L,N,O,P,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(2*D,D,4*D,J,L,N,O,P,Q) [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,0,N,O,P,Q) [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f33(C,D,E,1 + J,L,N,O,P,Q) [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f49(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f49(C,D,E,1 + J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f66(C,D,E,J,L,N,O,0,Q) [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= -1 + D + -1*J = f66(C,D,E,2 + J,L,N,O,P,Q) [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f72(C,D,E,1 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = 0 >= 1 + D + -1*J = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 1 + D + -1*J = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f33(C,D,E,J,L,N,O,P,Q) * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (?,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (?,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (?,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (?,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (?,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 0 p(f103) = x2 + -1*x4 p(f107) = x2 + -1*x4 p(f117) = x2 + -1*x4 + x27 p(f125) = x2 + -1*x4 + x27 p(f23) = 0 p(f33) = 0 p(f39) = 0 p(f44) = x2 + -1*x4 + x27 p(f46) = x2 + -1*x4 + x27 p(f49) = x2 + -1*x4 + x27 p(f54) = x2 + -1*x4 + x27 p(f60) = x2 + -1*x4 + x27 p(f66) = x2 + -1*x4 + x27 p(f72) = x2 + -1*x4 + x27 p(f87) = x2 + -1*x4 + x27 p(f91) = x2 + -1*x4 + x27 p(f99) = x2 + -1*x4 Following rules are strictly oriented: [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f117(C,D,E,1 + J,L,N,O,P,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(2*D,D,4*D,J,L,N,O,P,Q) [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,0,N,O,P,Q) [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f33(C,D,E,1 + J,L,N,O,P,Q) [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f49(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f49(C,D,E,1 + J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f66(C,D,E,J,L,N,O,0,Q) [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= -1 + D + -1*J = f66(C,D,E,2 + J,L,N,O,P,Q) [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f72(C,D,E,1 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = 0 >= 1 + D + -1*J = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 1 + D + -1*J = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f33(C,D,E,J,L,N,O,P,Q) * Step 7: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (?,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (?,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (?,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (?,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 0 p(f103) = x2 + -1*x4 p(f107) = x2 + -1*x4 p(f117) = x2 + -1*x4 + x27 p(f125) = x2 + -1*x4 + x27 p(f23) = 0 p(f33) = 0 p(f39) = 0 p(f44) = x2 + -1*x4 + x27 p(f46) = x2 + -1*x4 + x27 p(f49) = x2 + -1*x4 + x27 p(f54) = x2 + -1*x4 + x27 p(f60) = x2 + -1*x4 + x27 p(f66) = x2 + -1*x4 + x27 p(f72) = x2 + -1*x4 + x27 p(f87) = x2 + -1*x4 + x27 p(f91) = x2 + -1*x4 + x27 p(f99) = x2 + -1*x4 Following rules are strictly oriented: [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f117(C,D,E,1 + J,L,N,O,P,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(2*D,D,4*D,J,L,N,O,P,Q) [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,0,N,O,P,Q) [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f33(C,D,E,1 + J,L,N,O,P,Q) [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f49(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f49(C,D,E,1 + J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f66(C,D,E,J,L,N,O,0,Q) [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= -1 + D + -1*J = f66(C,D,E,2 + J,L,N,O,P,Q) [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f72(C,D,E,1 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = 0 >= 1 + D + -1*J = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 1 + D + -1*J = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f33(C,D,E,J,L,N,O,P,Q) * Step 8: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (?,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (?,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (?,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 0 p(f103) = x2 + -1*x4 p(f107) = x2 + -1*x4 p(f117) = x2 + -1*x4 + x27 p(f125) = x2 + -1*x4 + x27 p(f23) = 0 p(f33) = 0 p(f39) = 0 p(f44) = x2 + -1*x4 + x27 p(f46) = x2 + -1*x4 + x27 p(f49) = x2 + -1*x4 + x27 p(f54) = x2 + -1*x4 + x27 p(f60) = x2 + -1*x4 + x27 p(f66) = x2 + -1*x4 + x27 p(f72) = x2 + -1*x4 + x27 p(f87) = x2 + -1*x4 + x27 p(f91) = x2 + -1*x4 + x27 p(f99) = x2 + -1*x4 Following rules are strictly oriented: [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f117(C,D,E,1 + J,L,N,O,P,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(2*D,D,4*D,J,L,N,O,P,Q) [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,0,N,O,P,Q) [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f33(C,D,E,1 + J,L,N,O,P,Q) [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f49(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f49(C,D,E,1 + J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f66(C,D,E,J,L,N,O,0,Q) [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= -1 + D + -1*J = f66(C,D,E,2 + J,L,N,O,P,Q) [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f72(C,D,E,1 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,L,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = 0 >= 1 + D + -1*J = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 1 + D + -1*J = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f33(C,D,E,J,L,N,O,P,Q) * Step 9: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (?,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (?,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (?,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 10: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (?,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (?,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = x6 + -1*x7 + 2*x27 p(f103) = x6 + -1*x7 + x27 p(f107) = x6 + -1*x7 + x27 p(f117) = x6 + -1*x7 + 2*x27 p(f125) = x6 + -1*x7 + 2*x27 p(f23) = x6 + -1*x7 + 2*x27 p(f33) = x6 + -1*x7 + 2*x27 p(f39) = x6 + -1*x7 + 2*x27 p(f44) = x6 + -1*x7 + 2*x27 p(f46) = x6 + -1*x7 + x27 p(f49) = x6 + -1*x7 + x27 p(f54) = x6 + -1*x7 + x27 p(f60) = x6 + -1*x7 + x27 p(f66) = x6 + -1*x7 + x27 p(f72) = x6 + -1*x7 + x27 p(f87) = x6 + -1*x7 + x27 p(f91) = x6 + -1*x7 + x27 p(f99) = x6 + -1*x7 + x27 Following rules are strictly oriented: [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O > 1 + N + -1*O = f46(C,D,E,J,L,N,O,P,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O >= 2 + N + -1*O = f23(2*D,D,4*D,J,L,N,O,P,Q) [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O >= 2 + N + -1*O = f23(C,D,E,1 + J,0,N,O,P,Q) [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O >= 2 + N + -1*O = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O >= 2 + N + -1*O = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O >= 2 + N + -1*O = f33(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f49(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f49(C,D,E,1 + J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f66(C,D,E,J,L,N,O,0,Q) [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f66(C,D,E,2 + J,L,N,O,P,Q) [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f72(C,D,E,1 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f91(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f99(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f91(C,D,E,1 + J,L,N,O,P,Q) [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O >= 2 + N + -1*O = f117(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O >= 2 + N + -1*O = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + N + -1*O >= 1 + N + -1*O = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O >= 2 + N + -1*O = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O >= 2 + N + -1*O = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O >= 2 + N + -1*O = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O >= 2 + N + -1*O = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O >= 2 + N + -1*O = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = 2 + N + -1*O >= 2 + N + -1*O = f33(C,D,E,J,L,N,O,P,Q) * Step 11: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (2 + N + O,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (?,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (?,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (?,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (?,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 12: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (2 + N + O,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (?,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (?,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (0,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (0,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = -1*x9 + x27 p(f103) = -1*x9 + x27 p(f107) = -1*x9 + x27 p(f117) = -1*x9 + x27 p(f125) = -1*x9 + x27 p(f23) = -1*x9 + x27 p(f33) = -1*x9 + x27 p(f39) = -1*x9 + x27 p(f44) = -1*x9 + x27 p(f46) = -1*x9 + x27 p(f49) = -1*x9 p(f54) = -1*x9 p(f60) = -1*x9 p(f66) = -1*x9 p(f72) = -1*x9 + x27 p(f87) = -1*x9 + x27 p(f91) = -1*x9 + x27 p(f99) = -1*x9 + x27 Following rules are strictly oriented: [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q > -1*Q = f49(C,D,E,J,L,N,O,P,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f23(2*D,D,4*D,J,L,N,O,P,Q) [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f23(C,D,E,1 + J,0,N,O,P,Q) [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f33(C,D,E,1 + J,L,N,O,P,Q) [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f46(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= -1*Q = f49(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = -1*Q >= -1*Q = f49(C,D,E,1 + J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= -1*Q = f66(C,D,E,J,L,N,O,0,Q) [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = -1*Q >= -1*Q = f66(C,D,E,2 + J,L,N,O,P,Q) [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f72(C,D,E,1 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f91(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f99(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f91(C,D,E,1 + J,L,N,O,P,Q) [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f117(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = -1*Q >= -1*Q = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = -1*Q >= -1*Q = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = -1*Q >= -1*Q = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = -1*Q >= -1*Q = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f33(C,D,E,J,L,N,O,P,Q) * Step 13: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (2 + N + O,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (?,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (?,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (0,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (0,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 14: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (2 + N + O,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (?,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (0,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (0,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (0,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 0 p(f103) = x1 + -1*x4 p(f107) = x1 + -1*x4 p(f117) = x1 + -1*x4 + x27 p(f125) = x1 + -1*x4 + x27 p(f23) = 0 p(f33) = x1 + -1*x4 + x27 p(f39) = x1 + -1*x4 + x27 p(f44) = x1 + -1*x4 + x27 p(f46) = x1 + -1*x4 + x27 p(f49) = x1 + -1*x4 + x27 p(f54) = x1 + -1*x4 + x27 p(f60) = x1 + -1*x4 + x27 p(f66) = x1 + -1*x4 + x27 p(f72) = x1 + -1*x4 + x27 p(f87) = x1 + -1*x4 + x27 p(f91) = x1 + -1*x4 + x27 p(f99) = x1 + -1*x4 Following rules are strictly oriented: [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J > C + -1*J = f72(C,D,E,1 + J,L,N,O,P,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(2*D,D,4*D,J,L,N,O,P,Q) [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,0,N,O,P,Q) [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= C + -1*J = f33(C,D,E,1 + J,L,N,O,P,Q) [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f46(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f49(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= C + -1*J = f49(C,D,E,1 + J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f66(C,D,E,J,L,N,O,0,Q) [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= -1 + C + -1*J = f66(C,D,E,2 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f91(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= C + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= C + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= C + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= C + -1*J = f117(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= 1 + C + -1*J = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 1 + C + -1*J = f33(C,D,E,J,L,N,O,P,Q) * Step 15: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (2 + N + O,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (?,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (0,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (0,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (0,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (0,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 2*x2 p(f103) = x3 + -1*x4 p(f107) = x3 + -1*x4 p(f117) = x3 + -1*x4 + x27 p(f125) = x3 + -1*x4 + x27 p(f23) = -1*x1 + x3 p(f33) = x3 + -1*x4 + x27 p(f39) = x3 + -1*x4 + x27 p(f44) = x3 + -1*x4 + x27 p(f46) = x3 + -1*x4 + x27 p(f49) = x3 + -1*x4 + x27 p(f54) = x3 + -1*x4 + x27 p(f60) = x3 + -1*x4 + x27 p(f66) = x3 + -1*x4 + x27 p(f72) = x3 + -1*x4 + x27 p(f87) = x3 + -1*x4 + x27 p(f91) = x3 + -1*x4 + x27 p(f99) = x3 + -1*x4 Following rules are strictly oriented: [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J > -1 + E + -1*J = f66(C,D,E,2 + J,L,N,O,P,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = 2*D >= 2*D = f23(2*D,D,4*D,J,L,N,O,P,Q) [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = -1*C + E >= -1*C + E = f23(C,D,E,1 + J,0,N,O,P,Q) [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = -1*C + E >= -1*C + E = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = -1*C + E >= -1*C + E = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= E + -1*J = f33(C,D,E,1 + J,L,N,O,P,Q) [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f46(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f49(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= E + -1*J = f49(C,D,E,1 + J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f66(C,D,E,J,L,N,O,0,Q) [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= E + -1*J = f72(C,D,E,1 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f91(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= E + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= E + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= E + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = E + -1*J >= E + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = E + -1*J >= E + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = E + -1*J >= E + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = E + -1*J >= E + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = E + -1*J >= E + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = E + -1*J >= E + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = E + -1*J >= E + -1*J = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = E + -1*J >= E + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = E + -1*J >= E + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= E + -1*J = f117(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + E + -1*J >= 1 + E + -1*J = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = -1*C + E >= 1 + E + -1*J = f33(C,D,E,J,L,N,O,P,Q) * Step 16: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (2 + N + O,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*D,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (0,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (0,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (0,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (0,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 0 p(f103) = x2 + -1*x4 p(f107) = x2 + -1*x4 p(f117) = x2 + -1*x4 + x27 p(f125) = x2 + -1*x4 + x27 p(f23) = 0 p(f33) = 0 p(f39) = 0 p(f44) = x2 + -1*x4 + x27 p(f46) = x2 + -1*x4 + x27 p(f49) = x2 + -1*x4 + x27 p(f54) = x2 + -1*x4 + x27 p(f60) = x2 + -1*x4 + x27 p(f66) = x2 + -1*x4 + x27 p(f72) = x2 + -1*x4 + x27 p(f87) = x2 + -1*x4 + x27 p(f91) = x2 + -1*x4 + x27 p(f99) = x2 + -1*x4 Following rules are strictly oriented: [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f117(C,D,E,1 + J,L,N,O,P,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(2*D,D,4*D,J,L,N,O,P,Q) [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,0,N,O,P,Q) [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f33(C,D,E,1 + J,L,N,O,P,Q) [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f49(C,D,E,J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f66(C,D,E,J,L,N,O,0,Q) [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= -1 + D + -1*J = f66(C,D,E,2 + J,L,N,O,P,Q) [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f72(C,D,E,1 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f91(C,D,E,J,L,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= 1 + D + -1*J = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = 0 >= 1 + D + -1*J = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = 0 >= 1 + D + -1*J = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = 0 >= 0 = f33(C,D,E,J,L,N,O,P,Q) * Step 17: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (?,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (2 + N + O,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*D,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (0,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (0,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (0,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (0,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = -1*x2 p(f103) = x2 + -1*x4 p(f107) = x2 + -1*x4 p(f117) = x2 + -1*x4 p(f125) = x2 + -1*x4 p(f23) = -1*x1 + x2 p(f33) = x2 + -1*x4 + x27 p(f39) = x2 + -1*x4 p(f44) = x2 + -1*x4 p(f46) = x2 + -1*x4 p(f49) = x2 + -1*x4 p(f54) = x2 + -1*x4 p(f60) = x2 + -1*x4 p(f66) = x2 + -1*x4 p(f72) = x2 + -1*x4 p(f87) = x2 + -1*x4 p(f91) = x2 + -1*x4 p(f99) = x2 + -1*x4 Following rules are strictly oriented: [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J > D + -1*J = f33(C,D,E,1 + J,L,N,O,P,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = -1*D >= -1*D = f23(2*D,D,4*D,J,L,N,O,P,Q) [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = -1*C + D >= -1*C + D = f23(C,D,E,1 + J,0,N,O,P,Q) [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = -1*C + D >= -1*C + D = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = -1*C + D >= -1*C + D = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f46(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f49(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = D + -1*J >= -1 + D + -1*J = f49(C,D,E,1 + J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f66(C,D,E,J,L,N,O,0,Q) [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = D + -1*J >= -2 + D + -1*J = f66(C,D,E,2 + J,L,N,O,P,Q) [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = D + -1*J >= -1 + D + -1*J = f72(C,D,E,1 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f91(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= -1 + D + -1*J = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= -1 + D + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = D + -1*J >= -1 + D + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = D + -1*J >= -1 + D + -1*J = f117(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = D + -1*J >= D + -1*J = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + D + -1*J >= D + -1*J = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = -1*C + D >= 1 + D + -1*J = f33(C,D,E,J,L,N,O,P,Q) * Step 18: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (?,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (D,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (2 + N + O,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*D,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (0,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (0,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (0,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (0,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 2*x2 + -1*x4 + x27 p(f103) = x1 + -1*x4 p(f107) = x1 + -1*x4 p(f117) = x1 + -1*x4 p(f125) = x1 + -1*x4 p(f23) = x1 + -1*x4 + x27 p(f33) = x1 + -1*x4 p(f39) = x1 + -1*x4 p(f44) = x1 + -1*x4 p(f46) = x1 + -1*x4 p(f49) = x1 + -1*x4 p(f54) = x1 + -1*x4 p(f60) = x1 + -1*x4 p(f66) = x1 + -1*x4 p(f72) = x1 + -1*x4 p(f87) = x1 + -1*x4 p(f91) = x1 + -1*x4 p(f99) = x1 + -1*x4 Following rules are strictly oriented: [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J > C + -1*J = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = 1 + 2*D + -1*J >= 1 + 2*D + -1*J = f23(2*D,D,4*D,J,L,N,O,P,Q) [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= C + -1*J = f23(C,D,E,1 + J,0,N,O,P,Q) [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= C + -1*J = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f33(C,D,E,1 + J,L,N,O,P,Q) [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f46(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f49(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f49(C,D,E,1 + J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f66(C,D,E,J,L,N,O,0,Q) [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -2 + C + -1*J = f66(C,D,E,2 + J,L,N,O,P,Q) [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f72(C,D,E,1 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f91(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f117(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= C + -1*J = f33(C,D,E,J,L,N,O,P,Q) * Step 19: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (?,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (1 + 2*D + J,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (D,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (2 + N + O,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*D,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (0,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (0,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (0,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (0,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 2*x2 + -1*x4 + x27 p(f103) = x1 + -1*x4 p(f107) = x1 + -1*x4 p(f117) = x1 + -1*x4 p(f125) = x1 + -1*x4 p(f23) = x1 + -1*x4 + x27 p(f33) = x1 + -1*x4 p(f39) = x1 + -1*x4 p(f44) = x1 + -1*x4 p(f46) = x1 + -1*x4 p(f49) = x1 + -1*x4 p(f54) = x1 + -1*x4 p(f60) = x1 + -1*x4 p(f66) = x1 + -1*x4 p(f72) = x1 + -1*x4 p(f87) = x1 + -1*x4 p(f91) = x1 + -1*x4 p(f99) = x1 + -1*x4 Following rules are strictly oriented: [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J > C + -1*J = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J > C + -1*J = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = 1 + 2*D + -1*J >= 1 + 2*D + -1*J = f23(2*D,D,4*D,J,L,N,O,P,Q) [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= C + -1*J = f23(C,D,E,1 + J,0,N,O,P,Q) [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f33(C,D,E,1 + J,L,N,O,P,Q) [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f46(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f49(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f49(C,D,E,1 + J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f66(C,D,E,J,L,N,O,0,Q) [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -2 + C + -1*J = f66(C,D,E,2 + J,L,N,O,P,Q) [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f72(C,D,E,1 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f91(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f117(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= C + -1*J = f33(C,D,E,J,L,N,O,P,Q) * Step 20: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (?,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (1 + 2*D + J,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (1 + 2*D + J,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (D,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (2 + N + O,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*D,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (0,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (0,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (0,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (0,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 2*x2 + -1*x4 + x27 p(f103) = x1 + -1*x4 p(f107) = x1 + -1*x4 p(f117) = x1 + -1*x4 p(f125) = x1 + -1*x4 p(f23) = x1 + -1*x4 + x27 p(f33) = x1 + -1*x4 p(f39) = x1 + -1*x4 p(f44) = x1 + -1*x4 p(f46) = x1 + -1*x4 p(f49) = x1 + -1*x4 p(f54) = x1 + -1*x4 p(f60) = x1 + -1*x4 p(f66) = x1 + -1*x4 p(f72) = x1 + -1*x4 p(f87) = x1 + -1*x4 p(f91) = x1 + -1*x4 p(f99) = x1 + -1*x4 Following rules are strictly oriented: [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J > C + -1*J = f23(C,D,E,1 + J,0,N,O,P,Q) [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J > C + -1*J = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J > C + -1*J = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = 1 + 2*D + -1*J >= 1 + 2*D + -1*J = f23(2*D,D,4*D,J,L,N,O,P,Q) [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f33(C,D,E,1 + J,L,N,O,P,Q) [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f46(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f49(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f49(C,D,E,1 + J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f66(C,D,E,J,L,N,O,0,Q) [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -2 + C + -1*J = f66(C,D,E,2 + J,L,N,O,P,Q) [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f72(C,D,E,1 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f91(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f99(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f91(C,D,E,1 + J,L,N,O,P,Q) [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = C + -1*J >= -1 + C + -1*J = f117(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = C + -1*J >= C + -1*J = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + C + -1*J >= C + -1*J = f33(C,D,E,J,L,N,O,P,Q) * Step 21: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (1 + 2*D + J,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (1 + 2*D + J,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (1 + 2*D + J,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (D,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (2 + N + O,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (?,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (?,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*D,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (0,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (0,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (0,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (0,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = -1*x9 + x27 p(f103) = -1*x9 + x27 p(f107) = -1*x9 + x27 p(f117) = -1*x9 + x27 p(f125) = -1*x9 + x27 p(f23) = -1*x9 + x27 p(f33) = -1*x9 + x27 p(f39) = -1*x9 + x27 p(f44) = -1*x9 + x27 p(f46) = -1*x9 + x27 p(f49) = -1*x9 p(f54) = -1*x9 p(f60) = -1*x9 p(f66) = -1*x9 p(f72) = -1*x9 + x27 p(f87) = -1*x9 + x27 p(f91) = -1*x9 + x27 p(f99) = -1*x9 + x27 Following rules are strictly oriented: [0 >= 1 + P && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q > -1*Q = f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q > -1*Q = f49(C,D,E,J,L,N,O,P,Q) [0 >= Q && P = 0] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q > -1*Q = f66(C,D,E,J,L,N,O,0,Q) Following rules are weakly oriented: True ==> f0(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f23(2*D,D,4*D,J,L,N,O,P,Q) [C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f23(C,D,E,1 + J,0,N,O,P,Q) [C1 >= 2 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [D >= J] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f33(C,D,E,1 + J,L,N,O,P,Q) [N >= O] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f46(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f49(C,D,E,J,L,N,O,P,Q) = -1*Q >= -1*Q = f49(C,D,E,1 + J,L,N,O,P,Q) [E >= J] ==> f66(C,D,E,J,L,N,O,P,Q) = -1*Q >= -1*Q = f66(C,D,E,2 + J,L,N,O,P,Q) [C >= J] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f72(C,D,E,1 + J,L,N,O,P,Q) [L = 0] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f91(C,D,E,J,0,N,O,P,Q) [0 >= 1 + L] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f91(C,D,E,J,L,N,O,P,Q) [L >= 1] ==> f87(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f91(C,D,E,J,L,N,O,P,Q) [D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f99(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f99(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f99(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f99(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f103(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f103(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] ==> f103(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] ==> f103(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f107(C,D,E,J,B1,N,O,P,Q) [L = 0] ==> f107(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f91(C,D,E,1 + J,0,N,O,P,Q) [0 >= 1 + L] ==> f107(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] ==> f107(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f91(C,D,E,1 + J,L,N,O,P,Q) [D >= J] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f117(C,D,E,1 + J,L,N,O,P,Q) [J >= 1 + D] ==> f117(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f91(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] ==> f72(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + E] ==> f66(C,D,E,J,L,N,O,P,Q) = -1*Q >= -1*Q = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f60(C,D,E,J,L,N,O,P,Q) = -1*Q >= -1*Q = f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] ==> f54(C,D,E,J,L,N,O,P,Q) = -1*Q >= -1*Q = f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f49(C,D,E,J,L,N,O,P,Q) = -1*Q >= -1*Q = f54(C,D,E,J,L,N,O,P,Q) [Q >= 1] ==> f46(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f72(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] ==> f44(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f117(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] ==> f39(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f44(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f39(C,D,E,J,L,N,O,P,Q) [J >= 1 + D && P = 0] ==> f33(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + C] ==> f23(C,D,E,J,L,N,O,P,Q) = 1 + -1*Q >= 1 + -1*Q = f33(C,D,E,J,L,N,O,P,Q) * Step 22: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (1 + 2*D + J,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (1 + 2*D + J,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (1 + 2*D + J,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (D,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (2 + N + O,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (1 + Q,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (1 + Q,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*D,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (0,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (?,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (?,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (?,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (0,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (0,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (0,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (?,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (?,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (?,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (?,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (?,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (?,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (?,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (?,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 23: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(C,D,E,J,L,N,O,P,Q) -> f23(2*D,D,4*D,J,L,N,O,P,Q) True (1,1) 1. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,0,N,O,P,Q) [C >= J] (1 + 2*D + J,1) 2. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [C1 >= 2 && C >= J] (1 + 2*D + J,1) 3. f23(C,D,E,J,L,N,O,P,Q) -> f23(C,D,E,1 + J,1 + -1*C1,N,O,P,Q) [0 >= C1 && C >= J] (1 + 2*D + J,1) 4. f33(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (D,1) 6. f44(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,Q) [N >= O] (2 + N + O,1) 7. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && 0 >= Q] (1 + Q,1) 8. f46(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,J,L,N,O,P,Q) [P >= 1 && 0 >= Q] (1 + Q,1) 9. f49(C,D,E,J,L,N,O,P,Q) -> f49(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 12. f46(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,J,L,N,O,0,Q) [0 >= Q && P = 0] (1 + Q,1) 13. f66(C,D,E,J,L,N,O,P,Q) -> f66(C,D,E,2 + J,L,N,O,P,Q) [E >= J] (2*D,1) 14. f72(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,1 + J,L,N,O,P,Q) [C >= J] (0,1) 15. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,0,N,O,P,Q) [L = 0] (15 + 6*D + 3*N + 3*O + 9*Q,1) 16. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [0 >= 1 + L] (15 + 6*D + 3*N + 3*O + 9*Q,1) 17. f87(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,J,L,N,O,P,Q) [L >= 1] (15 + 6*D + 3*N + 3*O + 9*Q,1) 18. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D >= J] (0,1) 19. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && D >= J] (0,1) 20. f91(C,D,E,J,L,N,O,P,Q) -> f99(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && D >= J] (0,1) 21. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 22. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 23. f99(C,D,E,J,L,N,O,P,Q) -> f103(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 24. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L = 0] (0,1) 25. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + L] (0,1) 26. f103(C,D,E,J,L,N,O,P,Q) -> f107(C,D,E,J,B1,N,O,P,Q) [L >= 1] (0,1) 27. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,0,N,O,P,Q) [L = 0] (0,1) 28. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [0 >= 1 + L] (0,1) 29. f107(C,D,E,J,L,N,O,P,Q) -> f91(C,D,E,1 + J,L,N,O,P,Q) [L >= 1] (0,1) 30. f117(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,1 + J,L,N,O,P,Q) [D >= J] (0,1) 31. f117(C,D,E,J,L,N,O,P,Q) -> f125(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 32. f91(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,1 + O,P,Q) [J >= 1 + D] (45 + 18*D + 9*N + 9*O + 27*Q,1) 33. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [J >= 1 + C] (5 + 2*D + N + O + 3*Q,1) 34. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [0 >= 1 + D1 && J >= 1 + C] (5 + 2*D + N + O + 3*Q,1) 35. f72(C,D,E,J,L,N,O,P,Q) -> f87(C,D,E,J,B1,N,O,P,Q) [D1 >= 1 && J >= 1 + C] (5 + 2*D + N + O + 3*Q,1) 36. f66(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + E] (1 + 2*D + Q,1) 37. f60(C,D,E,J,L,N,O,P,Q) -> f46(C,D,E,J,L,N,O,P,1 + Q) [J >= 1 + D] (2 + 2*Q,1) 38. f54(C,D,E,J,L,N,O,P,Q) -> f60(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (2 + 2*Q,1) 39. f49(C,D,E,J,L,N,O,P,Q) -> f54(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (2 + 2*Q,1) 40. f46(C,D,E,J,L,N,O,P,Q) -> f72(C,D,E,J,L,N,O,P,Q) [Q >= 1] (5 + 2*D + N + O + 3*Q,1) 41. f44(C,D,E,J,L,N,O,P,Q) -> f117(C,D,E,J,L,N,O,P,Q) [O >= 1 + N] (1,1) 42. f39(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,P,Q) [J >= 1 + D] (1,1) 43. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [0 >= 1 + P && J >= 1 + D] (1,1) 44. f33(C,D,E,J,L,N,O,P,Q) -> f39(C,D,E,J,L,N,O,P,Q) [P >= 1 && J >= 1 + D] (1,1) 45. f33(C,D,E,J,L,N,O,P,Q) -> f44(C,D,E,J,L,N,O,0,Q) [J >= 1 + D && P = 0] (1,1) 46. f23(C,D,E,J,L,N,O,P,Q) -> f33(C,D,E,J,L,N,O,P,Q) [J >= 1 + C] (1,1) Signature: {(f0,27) ;(f103,27) ;(f107,27) ;(f117,27) ;(f125,27) ;(f23,27) ;(f33,27) ;(f39,27) ;(f44,27) ;(f46,27) ;(f49,27) ;(f54,27) ;(f60,27) ;(f66,27) ;(f72,27) ;(f87,27) ;(f91,27) ;(f99,27)} Flow Graph: [0->{1,2,3,46},1->{1,2,3,46},2->{1,2,3,46},3->{1,2,3,46},4->{4,43,44,45},6->{7,8,12,40},7->{9,39},8->{9 ,39},9->{9,39},12->{13,36},13->{13,36},14->{14,33,34,35},15->{18,19,20,32},16->{18,19,20,32},17->{18,19,20 ,32},18->{21,22,23},19->{21,22,23},20->{21,22,23},21->{24,25,26},22->{24,25,26},23->{24,25,26},24->{27,28 ,29},25->{27,28,29},26->{27,28,29},27->{18,19,20,32},28->{18,19,20,32},29->{18,19,20,32},30->{30,31},31->{} ,32->{6,41},33->{15,16,17},34->{15,16,17},35->{15,16,17},36->{7,8,12,40},37->{7,8,12,40},38->{37},39->{38} ,40->{14,33,34,35},41->{30,31},42->{6,41},43->{42},44->{42},45->{6,41},46->{4,43,44,45}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))