YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb5in(0,B,C) True (?,1) 2. evalfbb5in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (?,1) 3. evalfbb5in(A,B,C) -> evalfbb6in(A,B,C) [A >= 0 && B >= 1 + A] (?,1) 4. evalfbb6in(A,B,C) -> evalfbb2in(A,B,A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + D] (?,1) 5. evalfbb6in(A,B,C) -> evalfbb2in(A,B,A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= 1] (?,1) 6. evalfbb6in(A,B,C) -> evalfreturnin(A,B,C) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 7. evalfbb2in(A,B,C) -> evalfbb4in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= B] 8. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + C] 9. evalfbb3in(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + D] 10. evalfbb3in(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= 1] 11. evalfbb3in(A,B,C) -> evalfbb4in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 12. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 13. evalfbb4in(A,B,C) -> evalfbb5in(1 + C,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 14. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A >= 0] (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfbb5in,3) ;(evalfbb6in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Flow Graph: [0->{1},1->{2,3},2->{14},3->{4,5,6},4->{7,8},5->{7,8},6->{14},7->{13},8->{9,10,11},9->{12},10->{12} ,11->{13},12->{7,8},13->{2,3},14->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb5in(0,B,C) True (1,1) 2. evalfbb5in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (1,1) 3. evalfbb5in(A,B,C) -> evalfbb6in(A,B,C) [A >= 0 && B >= 1 + A] (?,1) 4. evalfbb6in(A,B,C) -> evalfbb2in(A,B,A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + D] (?,1) 5. evalfbb6in(A,B,C) -> evalfbb2in(A,B,A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= 1] (?,1) 6. evalfbb6in(A,B,C) -> evalfreturnin(A,B,C) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (1,1) 7. evalfbb2in(A,B,C) -> evalfbb4in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= B] 8. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + C] 9. evalfbb3in(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + D] 10. evalfbb3in(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= 1] 11. evalfbb3in(A,B,C) -> evalfbb4in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 12. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 13. evalfbb4in(A,B,C) -> evalfbb5in(1 + C,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 14. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A >= 0] (1,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfbb5in,3) ;(evalfbb6in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Flow Graph: [0->{1},1->{2,3},2->{14},3->{4,5,6},4->{7,8},5->{7,8},6->{14},7->{13},8->{9,10,11},9->{12},10->{12} ,11->{13},12->{7,8},13->{2,3},14->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,7),(5,7)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb5in(0,B,C) True (1,1) 2. evalfbb5in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (1,1) 3. evalfbb5in(A,B,C) -> evalfbb6in(A,B,C) [A >= 0 && B >= 1 + A] (?,1) 4. evalfbb6in(A,B,C) -> evalfbb2in(A,B,A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + D] (?,1) 5. evalfbb6in(A,B,C) -> evalfbb2in(A,B,A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= 1] (?,1) 6. evalfbb6in(A,B,C) -> evalfreturnin(A,B,C) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (1,1) 7. evalfbb2in(A,B,C) -> evalfbb4in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= B] 8. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + C] 9. evalfbb3in(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + D] 10. evalfbb3in(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= 1] 11. evalfbb3in(A,B,C) -> evalfbb4in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 12. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 13. evalfbb4in(A,B,C) -> evalfbb5in(1 + C,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 14. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A >= 0] (1,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfbb5in,3) ;(evalfbb6in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Flow Graph: [0->{1},1->{2,3},2->{14},3->{4,5,6},4->{8},5->{8},6->{14},7->{13},8->{9,10,11},9->{12},10->{12},11->{13} ,12->{7,8},13->{2,3},14->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb5in(0,B,C) True (?,1) 2. evalfbb5in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (?,1) 3. evalfbb5in(A,B,C) -> evalfbb6in(A,B,C) [A >= 0 && B >= 1 + A] (?,1) 4. evalfbb6in(A,B,C) -> evalfbb2in(A,B,A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + D] (?,1) 5. evalfbb6in(A,B,C) -> evalfbb2in(A,B,A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= 1] (?,1) 6. evalfbb6in(A,B,C) -> evalfreturnin(A,B,C) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 7. evalfbb2in(A,B,C) -> evalfbb4in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= B] 8. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + C] 9. evalfbb3in(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + D] 10. evalfbb3in(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= 1] 11. evalfbb3in(A,B,C) -> evalfbb4in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 12. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 13. evalfbb4in(A,B,C) -> evalfbb5in(1 + C,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 14. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A >= 0] (?,1) 15. evalfreturnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfbb5in,3) ;(evalfbb6in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{14,15},3->{4,5,6},4->{7,8},5->{7,8},6->{14,15},7->{13},8->{9,10,11},9->{12},10->{12} ,11->{13},12->{7,8},13->{2,3},14->{},15->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,7),(5,7)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb5in(0,B,C) True (?,1) 2. evalfbb5in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (?,1) 3. evalfbb5in(A,B,C) -> evalfbb6in(A,B,C) [A >= 0 && B >= 1 + A] (?,1) 4. evalfbb6in(A,B,C) -> evalfbb2in(A,B,A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + D] (?,1) 5. evalfbb6in(A,B,C) -> evalfbb2in(A,B,A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= 1] (?,1) 6. evalfbb6in(A,B,C) -> evalfreturnin(A,B,C) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 7. evalfbb2in(A,B,C) -> evalfbb4in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= B] 8. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + C] 9. evalfbb3in(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + D] 10. evalfbb3in(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= 1] 11. evalfbb3in(A,B,C) -> evalfbb4in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 12. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 13. evalfbb4in(A,B,C) -> evalfbb5in(1 + C,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 14. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A >= 0] (?,1) 15. evalfreturnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfbb5in,3) ;(evalfbb6in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{14,15},3->{4,5,6},4->{8},5->{8},6->{14,15},7->{13},8->{9,10,11},9->{12},10->{12} ,11->{13},12->{7,8},13->{2,3},14->{},15->{}] + 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] | `- p:[3,13,7,12,9,8,4,5,10,11] c: [13] | `- p:[8,12,9,10] c: [12] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb5in(0,B,C) True (?,1) 2. evalfbb5in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (?,1) 3. evalfbb5in(A,B,C) -> evalfbb6in(A,B,C) [A >= 0 && B >= 1 + A] (?,1) 4. evalfbb6in(A,B,C) -> evalfbb2in(A,B,A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + D] (?,1) 5. evalfbb6in(A,B,C) -> evalfbb2in(A,B,A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= 1] (?,1) 6. evalfbb6in(A,B,C) -> evalfreturnin(A,B,C) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 7. evalfbb2in(A,B,C) -> evalfbb4in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= B] 8. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + C] 9. evalfbb3in(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + D] 10. evalfbb3in(A,B,C) -> evalfbb1in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= 1] 11. evalfbb3in(A,B,C) -> evalfbb4in(A,B,C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 12. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 13. evalfbb4in(A,B,C) -> evalfbb5in(1 + C,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 14. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A >= 0] (?,1) 15. evalfreturnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfbb5in,3) ;(evalfbb6in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{14,15},3->{4,5,6},4->{8},5->{8},6->{14,15},7->{13},8->{9,10,11},9->{12},10->{12} ,11->{13},12->{7,8},13->{2,3},14->{},15->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | `- p:[3,13,7,12,9,8,4,5,10,11] c: [13] | `- p:[8,12,9,10] c: [12]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0] evalfstart ~> evalfentryin [A <= A, B <= B, C <= C] evalfentryin ~> evalfbb5in [A <= 0*K, B <= B, C <= C] evalfbb5in ~> evalfreturnin [A <= A, B <= B, C <= C] evalfbb5in ~> evalfbb6in [A <= A, B <= B, C <= C] evalfbb6in ~> evalfbb2in [A <= A, B <= B, C <= A] evalfbb6in ~> evalfbb2in [A <= A, B <= B, C <= A] evalfbb6in ~> evalfreturnin [A <= A, B <= B, C <= C] evalfbb2in ~> evalfbb4in [A <= A, B <= B, C <= C] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= C] evalfbb3in ~> evalfbb1in [A <= A, B <= B, C <= C] evalfbb3in ~> evalfbb1in [A <= A, B <= B, C <= C] evalfbb3in ~> evalfbb4in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= B] evalfbb4in ~> evalfbb5in [A <= B + C, B <= B, C <= C] evalfreturnin ~> evalfstop [A <= A, B <= B, C <= C] evalfreturnin ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= A + B] evalfbb5in ~> evalfbb6in [A <= A, B <= B, C <= C] evalfbb4in ~> evalfbb5in [A <= B + C, B <= B, C <= C] evalfbb2in ~> evalfbb4in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= B] evalfbb3in ~> evalfbb1in [A <= A, B <= B, C <= C] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= C] evalfbb6in ~> evalfbb2in [A <= A, B <= B, C <= A] evalfbb6in ~> evalfbb2in [A <= A, B <= B, C <= A] evalfbb3in ~> evalfbb1in [A <= A, B <= B, C <= C] evalfbb3in ~> evalfbb4in [A <= A, B <= B, C <= C] + Loop: [0.0.0 <= B + C] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= B] evalfbb3in ~> evalfbb1in [A <= A, B <= B, C <= C] evalfbb3in ~> evalfbb1in [A <= A, B <= B, C <= C] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0] evalfstart ~> evalfentryin [] evalfentryin ~> evalfbb5in [K ~=> A] evalfbb5in ~> evalfreturnin [] evalfbb5in ~> evalfbb6in [] evalfbb6in ~> evalfbb2in [A ~=> C] evalfbb6in ~> evalfbb2in [A ~=> C] evalfbb6in ~> evalfreturnin [] evalfbb2in ~> evalfbb4in [] evalfbb2in ~> evalfbb3in [] evalfbb3in ~> evalfbb1in [] evalfbb3in ~> evalfbb1in [] evalfbb3in ~> evalfbb4in [] evalfbb1in ~> evalfbb2in [B ~=> C] evalfbb4in ~> evalfbb5in [B ~+> A,C ~+> A] evalfreturnin ~> evalfstop [] evalfreturnin ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0] evalfbb5in ~> evalfbb6in [] evalfbb4in ~> evalfbb5in [B ~+> A,C ~+> A] evalfbb2in ~> evalfbb4in [] evalfbb1in ~> evalfbb2in [B ~=> C] evalfbb3in ~> evalfbb1in [] evalfbb2in ~> evalfbb3in [] evalfbb6in ~> evalfbb2in [A ~=> C] evalfbb6in ~> evalfbb2in [A ~=> C] evalfbb3in ~> evalfbb1in [] evalfbb3in ~> evalfbb4in [] + Loop: [B ~+> 0.0.0,C ~+> 0.0.0] evalfbb2in ~> evalfbb3in [] evalfbb1in ~> evalfbb2in [B ~=> C] evalfbb3in ~> evalfbb1in [] evalfbb3in ~> evalfbb1in [] + Applied Processor: LareProcessor + Details: evalfstart ~> exitus616 [B ~=> C ,K ~=> A ,K ~=> C ,B ~+> A ,B ~+> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> A ,B ~*> C ,B ~*> 0.0 ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> A ,K ~*> C ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] evalfstart ~> evalfstop [B ~=> C ,K ~=> A ,K ~=> C ,B ~+> A ,B ~+> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> A ,B ~*> C ,B ~*> 0.0 ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> A ,K ~*> C ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] + evalfbb6in> [A ~=> C ,B ~=> C ,A ~+> A ,A ~+> C ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> A ,B ~+> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,A ~*> A ,A ~*> tick ,B ~*> A ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick] evalfbb5in> [A ~=> C ,B ~=> C ,A ~+> A ,A ~+> C ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> A ,B ~+> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,A ~*> A ,A ~*> C ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> A ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick] + evalfbb3in> [B ~=> C,B ~+> 0.0.0,B ~+> tick,C ~+> 0.0.0,C ~+> tick,tick ~+> tick] evalfbb2in> [B ~=> C,B ~+> 0.0.0,B ~+> tick,C ~+> 0.0.0,C ~+> tick,tick ~+> tick] YES(?,POLY)