YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalrealbubblestart(A,B,C,D) -> evalrealbubbleentryin(A,B,C,D) True (1,1) 1. evalrealbubbleentryin(A,B,C,D) -> evalrealbubblebb7in(-1 + A,B,C,D) True (?,1) 2. evalrealbubblebb7in(A,B,C,D) -> evalrealbubblebb4in(A,0,0,D) [A >= 1] (?,1) 3. evalrealbubblebb7in(A,B,C,D) -> evalrealbubblereturnin(A,B,C,D) [0 >= A] (?,1) 4. evalrealbubblebb4in(A,B,C,D) -> evalrealbubblebb1in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B] 5. evalrealbubblebb4in(A,B,C,D) -> evalrealbubblebb5in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= A] 6. evalrealbubblebb1in(A,B,C,D) -> evalrealbubblebb2in(A,B,C,D) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && E >= 1 + F] 7. evalrealbubblebb1in(A,B,C,D) -> evalrealbubblebb3in(A,B,C,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && F >= E] 8. evalrealbubblebb2in(A,B,C,D) -> evalrealbubblebb3in(A,B,C,1) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 9. evalrealbubblebb3in(A,B,C,D) -> evalrealbubblebb4in(A,1 + B,D,D) [1 + C + -1*D >= 0 (?,1) && 1 + B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 10. evalrealbubblebb5in(A,B,C,D) -> evalrealbubblereturnin(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C = 0] 11. evalrealbubblebb5in(A,B,C,D) -> evalrealbubblebb6in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] 12. evalrealbubblebb6in(A,B,C,D) -> evalrealbubblebb7in(-1 + A,B,C,D) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 13. evalrealbubblereturnin(A,B,C,D) -> evalrealbubblestop(A,B,C,D) True (?,1) Signature: {(evalrealbubblebb1in,4) ;(evalrealbubblebb2in,4) ;(evalrealbubblebb3in,4) ;(evalrealbubblebb4in,4) ;(evalrealbubblebb5in,4) ;(evalrealbubblebb6in,4) ;(evalrealbubblebb7in,4) ;(evalrealbubbleentryin,4) ;(evalrealbubblereturnin,4) ;(evalrealbubblestart,4) ;(evalrealbubblestop,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{13},4->{6,7},5->{10,11},6->{8},7->{9},8->{9},9->{4,5},10->{13},11->{12} ,12->{2,3},13->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalrealbubblestart(A,B,C,D) -> evalrealbubbleentryin(A,B,C,D) True (1,1) 1. evalrealbubbleentryin(A,B,C,D) -> evalrealbubblebb7in(-1 + A,B,C,D) True (1,1) 2. evalrealbubblebb7in(A,B,C,D) -> evalrealbubblebb4in(A,0,0,D) [A >= 1] (?,1) 3. evalrealbubblebb7in(A,B,C,D) -> evalrealbubblereturnin(A,B,C,D) [0 >= A] (1,1) 4. evalrealbubblebb4in(A,B,C,D) -> evalrealbubblebb1in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B] 5. evalrealbubblebb4in(A,B,C,D) -> evalrealbubblebb5in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= A] 6. evalrealbubblebb1in(A,B,C,D) -> evalrealbubblebb2in(A,B,C,D) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && E >= 1 + F] 7. evalrealbubblebb1in(A,B,C,D) -> evalrealbubblebb3in(A,B,C,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && F >= E] 8. evalrealbubblebb2in(A,B,C,D) -> evalrealbubblebb3in(A,B,C,1) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 9. evalrealbubblebb3in(A,B,C,D) -> evalrealbubblebb4in(A,1 + B,D,D) [1 + C + -1*D >= 0 (?,1) && 1 + B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 10. evalrealbubblebb5in(A,B,C,D) -> evalrealbubblereturnin(A,B,C,D) [B + -1*C >= 0 (1,1) && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C = 0] 11. evalrealbubblebb5in(A,B,C,D) -> evalrealbubblebb6in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] 12. evalrealbubblebb6in(A,B,C,D) -> evalrealbubblebb7in(-1 + A,B,C,D) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 13. evalrealbubblereturnin(A,B,C,D) -> evalrealbubblestop(A,B,C,D) True (1,1) Signature: {(evalrealbubblebb1in,4) ;(evalrealbubblebb2in,4) ;(evalrealbubblebb3in,4) ;(evalrealbubblebb4in,4) ;(evalrealbubblebb5in,4) ;(evalrealbubblebb6in,4) ;(evalrealbubblebb7in,4) ;(evalrealbubbleentryin,4) ;(evalrealbubblereturnin,4) ;(evalrealbubblestart,4) ;(evalrealbubblestop,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{13},4->{6,7},5->{10,11},6->{8},7->{9},8->{9},9->{4,5},10->{13},11->{12} ,12->{2,3},13->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,5)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalrealbubblestart(A,B,C,D) -> evalrealbubbleentryin(A,B,C,D) True (1,1) 1. evalrealbubbleentryin(A,B,C,D) -> evalrealbubblebb7in(-1 + A,B,C,D) True (1,1) 2. evalrealbubblebb7in(A,B,C,D) -> evalrealbubblebb4in(A,0,0,D) [A >= 1] (?,1) 3. evalrealbubblebb7in(A,B,C,D) -> evalrealbubblereturnin(A,B,C,D) [0 >= A] (1,1) 4. evalrealbubblebb4in(A,B,C,D) -> evalrealbubblebb1in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B] 5. evalrealbubblebb4in(A,B,C,D) -> evalrealbubblebb5in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= A] 6. evalrealbubblebb1in(A,B,C,D) -> evalrealbubblebb2in(A,B,C,D) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && E >= 1 + F] 7. evalrealbubblebb1in(A,B,C,D) -> evalrealbubblebb3in(A,B,C,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && F >= E] 8. evalrealbubblebb2in(A,B,C,D) -> evalrealbubblebb3in(A,B,C,1) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 9. evalrealbubblebb3in(A,B,C,D) -> evalrealbubblebb4in(A,1 + B,D,D) [1 + C + -1*D >= 0 (?,1) && 1 + B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 10. evalrealbubblebb5in(A,B,C,D) -> evalrealbubblereturnin(A,B,C,D) [B + -1*C >= 0 (1,1) && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C = 0] 11. evalrealbubblebb5in(A,B,C,D) -> evalrealbubblebb6in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] 12. evalrealbubblebb6in(A,B,C,D) -> evalrealbubblebb7in(-1 + A,B,C,D) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 13. evalrealbubblereturnin(A,B,C,D) -> evalrealbubblestop(A,B,C,D) True (1,1) Signature: {(evalrealbubblebb1in,4) ;(evalrealbubblebb2in,4) ;(evalrealbubblebb3in,4) ;(evalrealbubblebb4in,4) ;(evalrealbubblebb5in,4) ;(evalrealbubblebb6in,4) ;(evalrealbubblebb7in,4) ;(evalrealbubbleentryin,4) ;(evalrealbubblereturnin,4) ;(evalrealbubblestart,4) ;(evalrealbubblestop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{13},4->{6,7},5->{10,11},6->{8},7->{9},8->{9},9->{4,5},10->{13},11->{12},12->{2 ,3},13->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalrealbubblestart(A,B,C,D) -> evalrealbubbleentryin(A,B,C,D) True (1,1) 1. evalrealbubbleentryin(A,B,C,D) -> evalrealbubblebb7in(-1 + A,B,C,D) True (?,1) 2. evalrealbubblebb7in(A,B,C,D) -> evalrealbubblebb4in(A,0,0,D) [A >= 1] (?,1) 3. evalrealbubblebb7in(A,B,C,D) -> evalrealbubblereturnin(A,B,C,D) [0 >= A] (?,1) 4. evalrealbubblebb4in(A,B,C,D) -> evalrealbubblebb1in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B] 5. evalrealbubblebb4in(A,B,C,D) -> evalrealbubblebb5in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= A] 6. evalrealbubblebb1in(A,B,C,D) -> evalrealbubblebb2in(A,B,C,D) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && E >= 1 + F] 7. evalrealbubblebb1in(A,B,C,D) -> evalrealbubblebb3in(A,B,C,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && F >= E] 8. evalrealbubblebb2in(A,B,C,D) -> evalrealbubblebb3in(A,B,C,1) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 9. evalrealbubblebb3in(A,B,C,D) -> evalrealbubblebb4in(A,1 + B,D,D) [1 + C + -1*D >= 0 (?,1) && 1 + B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 10. evalrealbubblebb5in(A,B,C,D) -> evalrealbubblereturnin(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C = 0] 11. evalrealbubblebb5in(A,B,C,D) -> evalrealbubblebb6in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] 12. evalrealbubblebb6in(A,B,C,D) -> evalrealbubblebb7in(-1 + A,B,C,D) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 13. evalrealbubblereturnin(A,B,C,D) -> evalrealbubblestop(A,B,C,D) True (?,1) 14. evalrealbubblereturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalrealbubblebb1in,4) ;(evalrealbubblebb2in,4) ;(evalrealbubblebb3in,4) ;(evalrealbubblebb4in,4) ;(evalrealbubblebb5in,4) ;(evalrealbubblebb6in,4) ;(evalrealbubblebb7in,4) ;(evalrealbubbleentryin,4) ;(evalrealbubblereturnin,4) ;(evalrealbubblestart,4) ;(evalrealbubblestop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{13,14},4->{6,7},5->{10,11},6->{8},7->{9},8->{9},9->{4,5},10->{13,14} ,11->{12},12->{2,3},13->{},14->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,5)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalrealbubblestart(A,B,C,D) -> evalrealbubbleentryin(A,B,C,D) True (1,1) 1. evalrealbubbleentryin(A,B,C,D) -> evalrealbubblebb7in(-1 + A,B,C,D) True (?,1) 2. evalrealbubblebb7in(A,B,C,D) -> evalrealbubblebb4in(A,0,0,D) [A >= 1] (?,1) 3. evalrealbubblebb7in(A,B,C,D) -> evalrealbubblereturnin(A,B,C,D) [0 >= A] (?,1) 4. evalrealbubblebb4in(A,B,C,D) -> evalrealbubblebb1in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B] 5. evalrealbubblebb4in(A,B,C,D) -> evalrealbubblebb5in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= A] 6. evalrealbubblebb1in(A,B,C,D) -> evalrealbubblebb2in(A,B,C,D) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && E >= 1 + F] 7. evalrealbubblebb1in(A,B,C,D) -> evalrealbubblebb3in(A,B,C,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && F >= E] 8. evalrealbubblebb2in(A,B,C,D) -> evalrealbubblebb3in(A,B,C,1) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 9. evalrealbubblebb3in(A,B,C,D) -> evalrealbubblebb4in(A,1 + B,D,D) [1 + C + -1*D >= 0 (?,1) && 1 + B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 10. evalrealbubblebb5in(A,B,C,D) -> evalrealbubblereturnin(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C = 0] 11. evalrealbubblebb5in(A,B,C,D) -> evalrealbubblebb6in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] 12. evalrealbubblebb6in(A,B,C,D) -> evalrealbubblebb7in(-1 + A,B,C,D) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 13. evalrealbubblereturnin(A,B,C,D) -> evalrealbubblestop(A,B,C,D) True (?,1) 14. evalrealbubblereturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalrealbubblebb1in,4) ;(evalrealbubblebb2in,4) ;(evalrealbubblebb3in,4) ;(evalrealbubblebb4in,4) ;(evalrealbubblebb5in,4) ;(evalrealbubblebb6in,4) ;(evalrealbubblebb7in,4) ;(evalrealbubbleentryin,4) ;(evalrealbubblereturnin,4) ;(evalrealbubblestart,4) ;(evalrealbubblestop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{13,14},4->{6,7},5->{10,11},6->{8},7->{9},8->{9},9->{4,5},10->{13,14},11->{12} ,12->{2,3},13->{},14->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14] | `- p:[2,12,11,5,9,7,4,8,6] c: [12] | `- p:[4,9,7,8,6] c: [9] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. evalrealbubblestart(A,B,C,D) -> evalrealbubbleentryin(A,B,C,D) True (1,1) 1. evalrealbubbleentryin(A,B,C,D) -> evalrealbubblebb7in(-1 + A,B,C,D) True (?,1) 2. evalrealbubblebb7in(A,B,C,D) -> evalrealbubblebb4in(A,0,0,D) [A >= 1] (?,1) 3. evalrealbubblebb7in(A,B,C,D) -> evalrealbubblereturnin(A,B,C,D) [0 >= A] (?,1) 4. evalrealbubblebb4in(A,B,C,D) -> evalrealbubblebb1in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B] 5. evalrealbubblebb4in(A,B,C,D) -> evalrealbubblebb5in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= A] 6. evalrealbubblebb1in(A,B,C,D) -> evalrealbubblebb2in(A,B,C,D) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && E >= 1 + F] 7. evalrealbubblebb1in(A,B,C,D) -> evalrealbubblebb3in(A,B,C,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && F >= E] 8. evalrealbubblebb2in(A,B,C,D) -> evalrealbubblebb3in(A,B,C,1) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 9. evalrealbubblebb3in(A,B,C,D) -> evalrealbubblebb4in(A,1 + B,D,D) [1 + C + -1*D >= 0 (?,1) && 1 + B + -1*D >= 0 && A + -1*D >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -1 + A + D >= 0 && B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && B + C >= 0 && -1 + A + C >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0] 10. evalrealbubblebb5in(A,B,C,D) -> evalrealbubblereturnin(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C = 0] 11. evalrealbubblebb5in(A,B,C,D) -> evalrealbubblebb6in(A,B,C,D) [B + -1*C >= 0 (?,1) && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] 12. evalrealbubblebb6in(A,B,C,D) -> evalrealbubblebb7in(-1 + A,B,C,D) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 13. evalrealbubblereturnin(A,B,C,D) -> evalrealbubblestop(A,B,C,D) True (?,1) 14. evalrealbubblereturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalrealbubblebb1in,4) ;(evalrealbubblebb2in,4) ;(evalrealbubblebb3in,4) ;(evalrealbubblebb4in,4) ;(evalrealbubblebb5in,4) ;(evalrealbubblebb6in,4) ;(evalrealbubblebb7in,4) ;(evalrealbubbleentryin,4) ;(evalrealbubblereturnin,4) ;(evalrealbubblestart,4) ;(evalrealbubblestop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{13,14},4->{6,7},5->{10,11},6->{8},7->{9},8->{9},9->{4,5},10->{13,14},11->{12} ,12->{2,3},13->{},14->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14] | `- p:[2,12,11,5,9,7,4,8,6] c: [12] | `- p:[4,9,7,8,6] c: [9]) + 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] evalrealbubblestart ~> evalrealbubbleentryin [A <= A, B <= B, C <= C, D <= D] evalrealbubbleentryin ~> evalrealbubblebb7in [A <= K + A, B <= B, C <= C, D <= D] evalrealbubblebb7in ~> evalrealbubblebb4in [A <= A, B <= 0*K, C <= 0*K, D <= D] evalrealbubblebb7in ~> evalrealbubblereturnin [A <= A, B <= B, C <= C, D <= D] evalrealbubblebb4in ~> evalrealbubblebb1in [A <= A, B <= B, C <= C, D <= D] evalrealbubblebb4in ~> evalrealbubblebb5in [A <= A, B <= B, C <= C, D <= D] evalrealbubblebb1in ~> evalrealbubblebb2in [A <= A, B <= B, C <= C, D <= D] evalrealbubblebb1in ~> evalrealbubblebb3in [A <= A, B <= B, C <= C, D <= C] evalrealbubblebb2in ~> evalrealbubblebb3in [A <= A, B <= B, C <= C, D <= K] evalrealbubblebb3in ~> evalrealbubblebb4in [A <= A, B <= A, C <= D, D <= D] evalrealbubblebb5in ~> evalrealbubblereturnin [A <= A, B <= B, C <= C, D <= D] evalrealbubblebb5in ~> evalrealbubblebb6in [A <= A, B <= B, C <= C, D <= D] evalrealbubblebb6in ~> evalrealbubblebb7in [A <= B, B <= B, C <= C, D <= D] evalrealbubblereturnin ~> evalrealbubblestop [A <= A, B <= B, C <= C, D <= D] evalrealbubblereturnin ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= A] evalrealbubblebb7in ~> evalrealbubblebb4in [A <= A, B <= 0*K, C <= 0*K, D <= D] evalrealbubblebb6in ~> evalrealbubblebb7in [A <= B, B <= B, C <= C, D <= D] evalrealbubblebb5in ~> evalrealbubblebb6in [A <= A, B <= B, C <= C, D <= D] evalrealbubblebb4in ~> evalrealbubblebb5in [A <= A, B <= B, C <= C, D <= D] evalrealbubblebb3in ~> evalrealbubblebb4in [A <= A, B <= A, C <= D, D <= D] evalrealbubblebb1in ~> evalrealbubblebb3in [A <= A, B <= B, C <= C, D <= C] evalrealbubblebb4in ~> evalrealbubblebb1in [A <= A, B <= B, C <= C, D <= D] evalrealbubblebb2in ~> evalrealbubblebb3in [A <= A, B <= B, C <= C, D <= K] evalrealbubblebb1in ~> evalrealbubblebb2in [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0.0 <= A + B] evalrealbubblebb4in ~> evalrealbubblebb1in [A <= A, B <= B, C <= C, D <= D] evalrealbubblebb3in ~> evalrealbubblebb4in [A <= A, B <= A, C <= D, D <= D] evalrealbubblebb1in ~> evalrealbubblebb3in [A <= A, B <= B, C <= C, D <= C] evalrealbubblebb2in ~> evalrealbubblebb3in [A <= A, B <= B, C <= C, D <= K] evalrealbubblebb1in ~> evalrealbubblebb2in [A <= A, B <= B, C <= C, D <= D] + 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] evalrealbubblestart ~> evalrealbubbleentryin [] evalrealbubbleentryin ~> evalrealbubblebb7in [A ~+> A,K ~+> A] evalrealbubblebb7in ~> evalrealbubblebb4in [K ~=> B,K ~=> C] evalrealbubblebb7in ~> evalrealbubblereturnin [] evalrealbubblebb4in ~> evalrealbubblebb1in [] evalrealbubblebb4in ~> evalrealbubblebb5in [] evalrealbubblebb1in ~> evalrealbubblebb2in [] evalrealbubblebb1in ~> evalrealbubblebb3in [C ~=> D] evalrealbubblebb2in ~> evalrealbubblebb3in [K ~=> D] evalrealbubblebb3in ~> evalrealbubblebb4in [A ~=> B,D ~=> C] evalrealbubblebb5in ~> evalrealbubblereturnin [] evalrealbubblebb5in ~> evalrealbubblebb6in [] evalrealbubblebb6in ~> evalrealbubblebb7in [B ~=> A] evalrealbubblereturnin ~> evalrealbubblestop [] evalrealbubblereturnin ~> exitus616 [] + Loop: [A ~=> 0.0] evalrealbubblebb7in ~> evalrealbubblebb4in [K ~=> B,K ~=> C] evalrealbubblebb6in ~> evalrealbubblebb7in [B ~=> A] evalrealbubblebb5in ~> evalrealbubblebb6in [] evalrealbubblebb4in ~> evalrealbubblebb5in [] evalrealbubblebb3in ~> evalrealbubblebb4in [A ~=> B,D ~=> C] evalrealbubblebb1in ~> evalrealbubblebb3in [C ~=> D] evalrealbubblebb4in ~> evalrealbubblebb1in [] evalrealbubblebb2in ~> evalrealbubblebb3in [K ~=> D] evalrealbubblebb1in ~> evalrealbubblebb2in [] + Loop: [A ~+> 0.0.0,B ~+> 0.0.0] evalrealbubblebb4in ~> evalrealbubblebb1in [] evalrealbubblebb3in ~> evalrealbubblebb4in [A ~=> B,D ~=> C] evalrealbubblebb1in ~> evalrealbubblebb3in [C ~=> D] evalrealbubblebb2in ~> evalrealbubblebb3in [K ~=> D] evalrealbubblebb1in ~> evalrealbubblebb2in [] + Applied Processor: LareProcessor + Details: evalrealbubblestart ~> exitus616 [B ~=> A ,B ~=> 0.0 ,K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> 0.0 ,A ~+> A ,A ~+> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] evalrealbubblestart ~> evalrealbubblestop [B ~=> A ,B ~=> 0.0 ,K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> 0.0 ,A ~+> A ,A ~+> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + evalrealbubblebb7in> [A ~=> B ,A ~=> 0.0 ,B ~=> A ,K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] evalrealbubblebb5in> [A ~=> B ,A ~=> 0.0 ,B ~=> A ,K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + evalrealbubblebb4in> [A ~=> B ,C ~=> D ,K ~=> C ,K ~=> D ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick] YES(?,POLY)