YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalperfectstart(A,B,C,D) -> evalperfectentryin(A,B,C,D) True (1,1) 1. evalperfectentryin(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [1 >= A] (?,1) 2. evalperfectentryin(A,B,C,D) -> evalperfectbb1in(A,B,C,D) [A >= 2] (?,1) 3. evalperfectbb1in(A,B,C,D) -> evalperfectbb8in(A,A,-1 + A,D) [-2 + A >= 0] (?,1) 4. evalperfectbb8in(A,B,C,D) -> evalperfectbb4in(A,B,C,A) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1] (?,1) 5. evalperfectbb8in(A,B,C,D) -> evalperfectbb9in(B,B,C,D) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= C] (?,1) 6. evalperfectbb4in(A,B,C,D) -> evalperfectbb3in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= C] 7. evalperfectbb4in(A,B,C,D) -> evalperfectbb5in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + D] 8. evalperfectbb3in(A,B,C,D) -> evalperfectbb4in(A,B,C,-1*C + D) [A + -1*D >= 0 (?,1) && -1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + A + D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0] 9. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B + -1*C,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D = 0] 10. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + D] 11. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= 1] 12. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (?,1) 13. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 1] (?,1) 14. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0] (?,1) 15. evalperfectreturnin(A,B,C,D) -> evalperfectstop(A,B,C,D) True (?,1) Signature: {(evalperfectbb1in,4) ;(evalperfectbb3in,4) ;(evalperfectbb4in,4) ;(evalperfectbb5in,4) ;(evalperfectbb8in,4) ;(evalperfectbb9in,4) ;(evalperfectentryin,4) ;(evalperfectreturnin,4) ;(evalperfectstart,4) ;(evalperfectstop,4)} Flow Graph: [0->{1,2},1->{15},2->{3},3->{4,5},4->{6,7},5->{12,13,14},6->{8},7->{9,10,11},8->{6,7},9->{4,5},10->{4,5} ,11->{4,5},12->{15},13->{15},14->{15},15->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalperfectstart(A,B,C,D) -> evalperfectentryin(A,B,C,D) True (1,1) 1. evalperfectentryin(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [1 >= A] (1,1) 2. evalperfectentryin(A,B,C,D) -> evalperfectbb1in(A,B,C,D) [A >= 2] (1,1) 3. evalperfectbb1in(A,B,C,D) -> evalperfectbb8in(A,A,-1 + A,D) [-2 + A >= 0] (1,1) 4. evalperfectbb8in(A,B,C,D) -> evalperfectbb4in(A,B,C,A) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1] (?,1) 5. evalperfectbb8in(A,B,C,D) -> evalperfectbb9in(B,B,C,D) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= C] (1,1) 6. evalperfectbb4in(A,B,C,D) -> evalperfectbb3in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= C] 7. evalperfectbb4in(A,B,C,D) -> evalperfectbb5in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + D] 8. evalperfectbb3in(A,B,C,D) -> evalperfectbb4in(A,B,C,-1*C + D) [A + -1*D >= 0 (?,1) && -1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + A + D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0] 9. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B + -1*C,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D = 0] 10. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + D] 11. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= 1] 12. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (1,1) 13. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 1] (1,1) 14. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0] (1,1) 15. evalperfectreturnin(A,B,C,D) -> evalperfectstop(A,B,C,D) True (1,1) Signature: {(evalperfectbb1in,4) ;(evalperfectbb3in,4) ;(evalperfectbb4in,4) ;(evalperfectbb5in,4) ;(evalperfectbb8in,4) ;(evalperfectbb9in,4) ;(evalperfectentryin,4) ;(evalperfectreturnin,4) ;(evalperfectstart,4) ;(evalperfectstop,4)} Flow Graph: [0->{1,2},1->{15},2->{3},3->{4,5},4->{6,7},5->{12,13,14},6->{8},7->{9,10,11},8->{6,7},9->{4,5},10->{4,5} ,11->{4,5},12->{15},13->{15},14->{15},15->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,5),(4,7),(11,5)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalperfectstart(A,B,C,D) -> evalperfectentryin(A,B,C,D) True (1,1) 1. evalperfectentryin(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [1 >= A] (1,1) 2. evalperfectentryin(A,B,C,D) -> evalperfectbb1in(A,B,C,D) [A >= 2] (1,1) 3. evalperfectbb1in(A,B,C,D) -> evalperfectbb8in(A,A,-1 + A,D) [-2 + A >= 0] (1,1) 4. evalperfectbb8in(A,B,C,D) -> evalperfectbb4in(A,B,C,A) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1] (?,1) 5. evalperfectbb8in(A,B,C,D) -> evalperfectbb9in(B,B,C,D) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= C] (1,1) 6. evalperfectbb4in(A,B,C,D) -> evalperfectbb3in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= C] 7. evalperfectbb4in(A,B,C,D) -> evalperfectbb5in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + D] 8. evalperfectbb3in(A,B,C,D) -> evalperfectbb4in(A,B,C,-1*C + D) [A + -1*D >= 0 (?,1) && -1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + A + D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0] 9. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B + -1*C,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D = 0] 10. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + D] 11. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= 1] 12. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (1,1) 13. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 1] (1,1) 14. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0] (1,1) 15. evalperfectreturnin(A,B,C,D) -> evalperfectstop(A,B,C,D) True (1,1) Signature: {(evalperfectbb1in,4) ;(evalperfectbb3in,4) ;(evalperfectbb4in,4) ;(evalperfectbb5in,4) ;(evalperfectbb8in,4) ;(evalperfectbb9in,4) ;(evalperfectentryin,4) ;(evalperfectreturnin,4) ;(evalperfectstart,4) ;(evalperfectstop,4)} Flow Graph: [0->{1,2},1->{15},2->{3},3->{4},4->{6},5->{12,13,14},6->{8},7->{9,10,11},8->{6,7},9->{4,5},10->{4,5} ,11->{4},12->{15},13->{15},14->{15},15->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalperfectstart(A,B,C,D) -> evalperfectentryin(A,B,C,D) True (1,1) 1. evalperfectentryin(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [1 >= A] (?,1) 2. evalperfectentryin(A,B,C,D) -> evalperfectbb1in(A,B,C,D) [A >= 2] (?,1) 3. evalperfectbb1in(A,B,C,D) -> evalperfectbb8in(A,A,-1 + A,D) [-2 + A >= 0] (?,1) 4. evalperfectbb8in(A,B,C,D) -> evalperfectbb4in(A,B,C,A) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1] (?,1) 5. evalperfectbb8in(A,B,C,D) -> evalperfectbb9in(B,B,C,D) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= C] (?,1) 6. evalperfectbb4in(A,B,C,D) -> evalperfectbb3in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= C] 7. evalperfectbb4in(A,B,C,D) -> evalperfectbb5in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + D] 8. evalperfectbb3in(A,B,C,D) -> evalperfectbb4in(A,B,C,-1*C + D) [A + -1*D >= 0 (?,1) && -1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + A + D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0] 9. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B + -1*C,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D = 0] 10. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + D] 11. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= 1] 12. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (?,1) 13. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 1] (?,1) 14. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0] (?,1) 15. evalperfectreturnin(A,B,C,D) -> evalperfectstop(A,B,C,D) True (?,1) 16. evalperfectreturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalperfectbb1in,4) ;(evalperfectbb3in,4) ;(evalperfectbb4in,4) ;(evalperfectbb5in,4) ;(evalperfectbb8in,4) ;(evalperfectbb9in,4) ;(evalperfectentryin,4) ;(evalperfectreturnin,4) ;(evalperfectstart,4) ;(evalperfectstop,4) ;(exitus616,4)} Flow Graph: [0->{1,2},1->{15,16},2->{3},3->{4,5},4->{6,7},5->{12,13,14},6->{8},7->{9,10,11},8->{6,7},9->{4,5},10->{4 ,5},11->{4,5},12->{15,16},13->{15,16},14->{15,16},15->{},16->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,5),(4,7),(11,5)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalperfectstart(A,B,C,D) -> evalperfectentryin(A,B,C,D) True (1,1) 1. evalperfectentryin(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [1 >= A] (?,1) 2. evalperfectentryin(A,B,C,D) -> evalperfectbb1in(A,B,C,D) [A >= 2] (?,1) 3. evalperfectbb1in(A,B,C,D) -> evalperfectbb8in(A,A,-1 + A,D) [-2 + A >= 0] (?,1) 4. evalperfectbb8in(A,B,C,D) -> evalperfectbb4in(A,B,C,A) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1] (?,1) 5. evalperfectbb8in(A,B,C,D) -> evalperfectbb9in(B,B,C,D) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= C] (?,1) 6. evalperfectbb4in(A,B,C,D) -> evalperfectbb3in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= C] 7. evalperfectbb4in(A,B,C,D) -> evalperfectbb5in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + D] 8. evalperfectbb3in(A,B,C,D) -> evalperfectbb4in(A,B,C,-1*C + D) [A + -1*D >= 0 (?,1) && -1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + A + D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0] 9. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B + -1*C,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D = 0] 10. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + D] 11. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= 1] 12. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (?,1) 13. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 1] (?,1) 14. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0] (?,1) 15. evalperfectreturnin(A,B,C,D) -> evalperfectstop(A,B,C,D) True (?,1) 16. evalperfectreturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalperfectbb1in,4) ;(evalperfectbb3in,4) ;(evalperfectbb4in,4) ;(evalperfectbb5in,4) ;(evalperfectbb8in,4) ;(evalperfectbb9in,4) ;(evalperfectentryin,4) ;(evalperfectreturnin,4) ;(evalperfectstart,4) ;(evalperfectstop,4) ;(exitus616,4)} Flow Graph: [0->{1,2},1->{15,16},2->{3},3->{4},4->{6},5->{12,13,14},6->{8},7->{9,10,11},8->{6,7},9->{4,5},10->{4,5} ,11->{4},12->{15,16},13->{15,16},14->{15,16},15->{},16->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[4,9,7,8,6,10,11] c: [11] | `- p:[4,9,7,8,6,10] c: [10] | `- p:[4,9,7,8,6] c: [9] | `- p:[6,8] c: [8] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. evalperfectstart(A,B,C,D) -> evalperfectentryin(A,B,C,D) True (1,1) 1. evalperfectentryin(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [1 >= A] (?,1) 2. evalperfectentryin(A,B,C,D) -> evalperfectbb1in(A,B,C,D) [A >= 2] (?,1) 3. evalperfectbb1in(A,B,C,D) -> evalperfectbb8in(A,A,-1 + A,D) [-2 + A >= 0] (?,1) 4. evalperfectbb8in(A,B,C,D) -> evalperfectbb4in(A,B,C,A) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1] (?,1) 5. evalperfectbb8in(A,B,C,D) -> evalperfectbb9in(B,B,C,D) [-1 + A + -1*C >= 0 && C >= 0 && -2 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= C] (?,1) 6. evalperfectbb4in(A,B,C,D) -> evalperfectbb3in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= C] 7. evalperfectbb4in(A,B,C,D) -> evalperfectbb5in(A,B,C,D) [A + -1*D >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && C >= 1 + D] 8. evalperfectbb3in(A,B,C,D) -> evalperfectbb4in(A,B,C,-1*C + D) [A + -1*D >= 0 (?,1) && -1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + A + D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0] 9. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B + -1*C,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D = 0] 10. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && 0 >= 1 + D] 11. evalperfectbb5in(A,B,C,D) -> evalperfectbb8in(A,B,-1 + C,D) [-1 + C + -1*D >= 0 (?,1) && -2 + A + -1*D >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + A >= 0 && D >= 1] 12. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 0 >= 1 + A] (?,1) 13. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 1] (?,1) 14. evalperfectbb9in(A,B,C,D) -> evalperfectreturnin(A,B,C,D) [-1*C >= 0 && C >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A = 0] (?,1) 15. evalperfectreturnin(A,B,C,D) -> evalperfectstop(A,B,C,D) True (?,1) 16. evalperfectreturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalperfectbb1in,4) ;(evalperfectbb3in,4) ;(evalperfectbb4in,4) ;(evalperfectbb5in,4) ;(evalperfectbb8in,4) ;(evalperfectbb9in,4) ;(evalperfectentryin,4) ;(evalperfectreturnin,4) ;(evalperfectstart,4) ;(evalperfectstop,4) ;(exitus616,4)} Flow Graph: [0->{1,2},1->{15,16},2->{3},3->{4},4->{6},5->{12,13,14},6->{8},7->{9,10,11},8->{6,7},9->{4,5},10->{4,5} ,11->{4},12->{15,16},13->{15,16},14->{15,16},15->{},16->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[4,9,7,8,6,10,11] c: [11] | `- p:[4,9,7,8,6,10] c: [10] | `- p:[4,9,7,8,6] c: [9] | `- p:[6,8] c: [8]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.0.0,0.0.0.0,0.0.0.0.0] evalperfectstart ~> evalperfectentryin [A <= A, B <= B, C <= C, D <= D] evalperfectentryin ~> evalperfectreturnin [A <= A, B <= B, C <= C, D <= D] evalperfectentryin ~> evalperfectbb1in [A <= A, B <= B, C <= C, D <= D] evalperfectbb1in ~> evalperfectbb8in [A <= A, B <= A, C <= A, D <= D] evalperfectbb8in ~> evalperfectbb4in [A <= A, B <= B, C <= C, D <= A] evalperfectbb8in ~> evalperfectbb9in [A <= B, B <= B, C <= C, D <= D] evalperfectbb4in ~> evalperfectbb3in [A <= A, B <= B, C <= C, D <= D] evalperfectbb4in ~> evalperfectbb5in [A <= A, B <= B, C <= C, D <= D] evalperfectbb3in ~> evalperfectbb4in [A <= A, B <= B, C <= C, D <= A] evalperfectbb5in ~> evalperfectbb8in [A <= A, B <= B + C, C <= C, D <= D] evalperfectbb5in ~> evalperfectbb8in [A <= A, B <= B, C <= C, D <= D] evalperfectbb5in ~> evalperfectbb8in [A <= A, B <= B, C <= C, D <= D] evalperfectbb9in ~> evalperfectreturnin [A <= A, B <= B, C <= C, D <= D] evalperfectbb9in ~> evalperfectreturnin [A <= A, B <= B, C <= C, D <= D] evalperfectbb9in ~> evalperfectreturnin [A <= A, B <= B, C <= C, D <= D] evalperfectreturnin ~> evalperfectstop [A <= A, B <= B, C <= C, D <= D] evalperfectreturnin ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= C] evalperfectbb8in ~> evalperfectbb4in [A <= A, B <= B, C <= C, D <= A] evalperfectbb5in ~> evalperfectbb8in [A <= A, B <= B + C, C <= C, D <= D] evalperfectbb4in ~> evalperfectbb5in [A <= A, B <= B, C <= C, D <= D] evalperfectbb3in ~> evalperfectbb4in [A <= A, B <= B, C <= C, D <= A] evalperfectbb4in ~> evalperfectbb3in [A <= A, B <= B, C <= C, D <= D] evalperfectbb5in ~> evalperfectbb8in [A <= A, B <= B, C <= C, D <= D] evalperfectbb5in ~> evalperfectbb8in [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0.0 <= C] evalperfectbb8in ~> evalperfectbb4in [A <= A, B <= B, C <= C, D <= A] evalperfectbb5in ~> evalperfectbb8in [A <= A, B <= B + C, C <= C, D <= D] evalperfectbb4in ~> evalperfectbb5in [A <= A, B <= B, C <= C, D <= D] evalperfectbb3in ~> evalperfectbb4in [A <= A, B <= B, C <= C, D <= A] evalperfectbb4in ~> evalperfectbb3in [A <= A, B <= B, C <= C, D <= D] evalperfectbb5in ~> evalperfectbb8in [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0.0.0 <= C] evalperfectbb8in ~> evalperfectbb4in [A <= A, B <= B, C <= C, D <= A] evalperfectbb5in ~> evalperfectbb8in [A <= A, B <= B + C, C <= C, D <= D] evalperfectbb4in ~> evalperfectbb5in [A <= A, B <= B, C <= C, D <= D] evalperfectbb3in ~> evalperfectbb4in [A <= A, B <= B, C <= C, D <= A] evalperfectbb4in ~> evalperfectbb3in [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0.0.0.0 <= D] evalperfectbb4in ~> evalperfectbb3in [A <= A, B <= B, C <= C, D <= D] evalperfectbb3in ~> evalperfectbb4in [A <= A, B <= B, C <= C, D <= A] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0,0.0.0,0.0.0.0,0.0.0.0.0] evalperfectstart ~> evalperfectentryin [] evalperfectentryin ~> evalperfectreturnin [] evalperfectentryin ~> evalperfectbb1in [] evalperfectbb1in ~> evalperfectbb8in [A ~=> B,A ~=> C] evalperfectbb8in ~> evalperfectbb4in [A ~=> D] evalperfectbb8in ~> evalperfectbb9in [B ~=> A] evalperfectbb4in ~> evalperfectbb3in [] evalperfectbb4in ~> evalperfectbb5in [] evalperfectbb3in ~> evalperfectbb4in [A ~=> D] evalperfectbb5in ~> evalperfectbb8in [B ~+> B,C ~+> B] evalperfectbb5in ~> evalperfectbb8in [] evalperfectbb5in ~> evalperfectbb8in [] evalperfectbb9in ~> evalperfectreturnin [] evalperfectbb9in ~> evalperfectreturnin [] evalperfectbb9in ~> evalperfectreturnin [] evalperfectreturnin ~> evalperfectstop [] evalperfectreturnin ~> exitus616 [] + Loop: [C ~=> 0.0] evalperfectbb8in ~> evalperfectbb4in [A ~=> D] evalperfectbb5in ~> evalperfectbb8in [B ~+> B,C ~+> B] evalperfectbb4in ~> evalperfectbb5in [] evalperfectbb3in ~> evalperfectbb4in [A ~=> D] evalperfectbb4in ~> evalperfectbb3in [] evalperfectbb5in ~> evalperfectbb8in [] evalperfectbb5in ~> evalperfectbb8in [] + Loop: [C ~=> 0.0.0] evalperfectbb8in ~> evalperfectbb4in [A ~=> D] evalperfectbb5in ~> evalperfectbb8in [B ~+> B,C ~+> B] evalperfectbb4in ~> evalperfectbb5in [] evalperfectbb3in ~> evalperfectbb4in [A ~=> D] evalperfectbb4in ~> evalperfectbb3in [] evalperfectbb5in ~> evalperfectbb8in [] + Loop: [C ~=> 0.0.0.0] evalperfectbb8in ~> evalperfectbb4in [A ~=> D] evalperfectbb5in ~> evalperfectbb8in [B ~+> B,C ~+> B] evalperfectbb4in ~> evalperfectbb5in [] evalperfectbb3in ~> evalperfectbb4in [A ~=> D] evalperfectbb4in ~> evalperfectbb3in [] + Loop: [D ~=> 0.0.0.0.0] evalperfectbb4in ~> evalperfectbb3in [] evalperfectbb3in ~> evalperfectbb4in [A ~=> D] + Applied Processor: LareProcessor + Details: evalperfectstart ~> exitus616 [A ~=> B ,A ~=> C ,A ~=> D ,A ~=> 0.0 ,A ~=> 0.0.0 ,A ~=> 0.0.0.0 ,A ~=> 0.0.0.0.0 ,A ~+> A ,A ~+> B ,A ~+> tick ,tick ~+> tick ,A ~*> A ,A ~*> B ,A ~*> tick] evalperfectstart ~> evalperfectstop [A ~=> B ,A ~=> C ,A ~=> D ,A ~=> 0.0 ,A ~=> 0.0.0 ,A ~=> 0.0.0.0 ,A ~=> 0.0.0.0.0 ,A ~+> A ,A ~+> B ,A ~+> tick ,tick ~+> tick ,A ~*> A ,A ~*> B ,A ~*> tick] + evalperfectbb8in> [A ~=> D ,A ~=> 0.0.0.0.0 ,C ~=> 0.0 ,C ~=> 0.0.0 ,C ~=> 0.0.0.0 ,A ~+> tick ,B ~+> B ,C ~+> B ,C ~+> tick ,tick ~+> tick ,A ~*> tick ,C ~*> B ,C ~*> tick] + evalperfectbb8in> [A ~=> D ,A ~=> 0.0.0.0.0 ,C ~=> 0.0.0 ,C ~=> 0.0.0.0 ,A ~+> tick ,B ~+> B ,C ~+> B ,C ~+> tick ,tick ~+> tick ,A ~*> tick ,C ~*> B ,C ~*> tick] + evalperfectbb8in> [A ~=> D ,A ~=> 0.0.0.0.0 ,C ~=> 0.0.0.0 ,A ~+> tick ,B ~+> B ,C ~+> B ,C ~+> tick ,tick ~+> tick ,A ~*> tick ,C ~*> B ,C ~*> tick] evalperfectbb5in> [A ~=> D ,A ~=> 0.0.0.0.0 ,C ~=> 0.0.0.0 ,A ~+> tick ,B ~+> B ,C ~+> B ,C ~+> tick ,tick ~+> tick ,A ~*> tick ,C ~*> B ,C ~*> tick] + evalperfectbb4in> [A ~=> D,D ~=> 0.0.0.0.0,D ~+> tick,tick ~+> tick] YES(?,POLY)