YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1entryin(A,B,C) True (1,1) 1. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (?,1) 2. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (?,1) 3. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1) 4. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,B) [-1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 1 + B] (?,1) 5. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 1] 6. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && 0 >= C] 7. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] 8. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] 9. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0] (?,1) 10. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [-1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && B >= A] (?,1) 11. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && E >= 0 && 1 + C >= 2*E && 2*E >= C && F >= 0 && 1 + C >= 2*F && 2*F >= C && D >= 0 && 1 + C >= 2*D && 2*D >= C] Signature: {(evalrealheapsortstep1bb2in,3) ;(evalrealheapsortstep1bb3in,3) ;(evalrealheapsortstep1bb4in,3) ;(evalrealheapsortstep1bb5in,3) ;(evalrealheapsortstep1bb6in,3) ;(evalrealheapsortstep1entryin,3) ;(evalrealheapsortstep1returnin,3) ;(evalrealheapsortstep1start,3) ;(evalrealheapsortstep1stop,3)} Flow Graph: [0->{1,2},1->{3},2->{4,10},3->{},4->{5,6},5->{7,8},6->{9},7->{9},8->{11},9->{4,10},10->{3},11->{5,6}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,10),(4,6)] * Step 2: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1entryin(A,B,C) True (1,1) 1. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] (?,1) 2. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (?,1) 3. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (?,1) 4. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,B) [-1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 1 + B] (?,1) 5. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 1] 6. evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && 0 >= C] 7. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] 8. evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] 9. evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0] (?,1) 10. evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [-1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && B >= A] (?,1) 11. evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [B + -1*C >= 0 (?,1) && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && E >= 0 && 1 + C >= 2*E && 2*E >= C && F >= 0 && 1 + C >= 2*F && 2*F >= C && D >= 0 && 1 + C >= 2*D && 2*D >= C] Signature: {(evalrealheapsortstep1bb2in,3) ;(evalrealheapsortstep1bb3in,3) ;(evalrealheapsortstep1bb4in,3) ;(evalrealheapsortstep1bb5in,3) ;(evalrealheapsortstep1bb6in,3) ;(evalrealheapsortstep1entryin,3) ;(evalrealheapsortstep1returnin,3) ;(evalrealheapsortstep1start,3) ;(evalrealheapsortstep1stop,3)} Flow Graph: [0->{1,2},1->{3},2->{4},3->{},4->{5},5->{7,8},6->{9},7->{9},8->{11},9->{4,10},10->{3},11->{5,6}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1entryin(A,B,C) True evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,B) [-1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 1 + B] evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 1] evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && 0 >= C] evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0] evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [-1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && B >= A] evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && E >= 0 && 1 + C >= 2*E && 2*E >= C && F >= 0 && 1 + C >= 2*F && 2*F >= C && D >= 0 && 1 + C >= 2*D && 2*D >= C] Signature: {(evalrealheapsortstep1bb2in,3) ;(evalrealheapsortstep1bb3in,3) ;(evalrealheapsortstep1bb4in,3) ;(evalrealheapsortstep1bb5in,3) ;(evalrealheapsortstep1bb6in,3) ;(evalrealheapsortstep1entryin,3) ;(evalrealheapsortstep1returnin,3) ;(evalrealheapsortstep1start,3) ;(evalrealheapsortstep1stop,3)} Rule Graph: [0->{1,2},1->{3},2->{4},3->{},4->{5},5->{7,8},6->{9},7->{9},8->{11},9->{4,10},10->{3},11->{5,6}] + Applied Processor: AddSinks + Details: () * Step 4: Unfold WORST_CASE(?,POLY) + Considered Problem: Rules: evalrealheapsortstep1start(A,B,C) -> evalrealheapsortstep1entryin(A,B,C) True evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [2 >= A] evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,B) [-1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 1 + B] evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb4in(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 1] evalrealheapsortstep1bb3in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && 0 >= C] evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb5in(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] evalrealheapsortstep1bb4in(A,B,C) -> evalrealheapsortstep1bb2in(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] evalrealheapsortstep1bb5in(A,B,C) -> evalrealheapsortstep1bb6in(A,1 + B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0] evalrealheapsortstep1bb6in(A,B,C) -> evalrealheapsortstep1returnin(A,B,C) [-1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && B >= A] evalrealheapsortstep1bb2in(A,B,C) -> evalrealheapsortstep1bb3in(A,B,-1 + D) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && E >= 0 && 1 + C >= 2*E && 2*E >= C && F >= 0 && 1 + C >= 2*F && 2*F >= C && D >= 0 && 1 + C >= 2*D && 2*D >= C] evalrealheapsortstep1stop(A,B,C) -> exitus616(A,B,C) True evalrealheapsortstep1stop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalrealheapsortstep1bb2in,3) ;(evalrealheapsortstep1bb3in,3) ;(evalrealheapsortstep1bb4in,3) ;(evalrealheapsortstep1bb5in,3) ;(evalrealheapsortstep1bb6in,3) ;(evalrealheapsortstep1entryin,3) ;(evalrealheapsortstep1returnin,3) ;(evalrealheapsortstep1start,3) ;(evalrealheapsortstep1stop,3) ;(exitus616,3)} Rule Graph: [0->{1,2},1->{3},2->{4},3->{12,13},4->{5},5->{7,8},6->{9},7->{9},8->{11},9->{4,10},10->{3},11->{5,6}] + Applied Processor: Unfold + Details: () * Step 5: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: evalrealheapsortstep1start.0(A,B,C) -> evalrealheapsortstep1entryin.1(A,B,C) True evalrealheapsortstep1start.0(A,B,C) -> evalrealheapsortstep1entryin.2(A,B,C) True evalrealheapsortstep1entryin.1(A,B,C) -> evalrealheapsortstep1returnin.3(A,B,C) [2 >= A] evalrealheapsortstep1entryin.2(A,B,C) -> evalrealheapsortstep1bb6in.4(A,1,C) [A >= 3] evalrealheapsortstep1returnin.3(A,B,C) -> evalrealheapsortstep1stop.12(A,B,C) True evalrealheapsortstep1returnin.3(A,B,C) -> evalrealheapsortstep1stop.13(A,B,C) True evalrealheapsortstep1bb6in.4(A,B,C) -> evalrealheapsortstep1bb3in.5(A,B,B) [-1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 1 + B] evalrealheapsortstep1bb3in.5(A,B,C) -> evalrealheapsortstep1bb4in.7(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 1] evalrealheapsortstep1bb3in.5(A,B,C) -> evalrealheapsortstep1bb4in.8(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 1] evalrealheapsortstep1bb3in.6(A,B,C) -> evalrealheapsortstep1bb5in.9(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && 0 >= C] evalrealheapsortstep1bb4in.7(A,B,C) -> evalrealheapsortstep1bb5in.9(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] evalrealheapsortstep1bb4in.8(A,B,C) -> evalrealheapsortstep1bb2in.11(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] evalrealheapsortstep1bb5in.9(A,B,C) -> evalrealheapsortstep1bb6in.4(A,1 + B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0] evalrealheapsortstep1bb5in.9(A,B,C) -> evalrealheapsortstep1bb6in.10(A,1 + B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0] evalrealheapsortstep1bb6in.10(A,B,C) -> evalrealheapsortstep1returnin.3(A,B,C) [-1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && B >= A] evalrealheapsortstep1bb2in.11(A,B,C) -> evalrealheapsortstep1bb3in.5(A,B,-1 + D) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && E >= 0 && 1 + C >= 2*E && 2*E >= C && F >= 0 && 1 + C >= 2*F && 2*F >= C && D >= 0 && 1 + C >= 2*D && 2*D >= C] evalrealheapsortstep1bb2in.11(A,B,C) -> evalrealheapsortstep1bb3in.6(A,B,-1 + D) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && E >= 0 && 1 + C >= 2*E && 2*E >= C && F >= 0 && 1 + C >= 2*F && 2*F >= C && D >= 0 && 1 + C >= 2*D && 2*D >= C] evalrealheapsortstep1stop.12(A,B,C) -> exitus616.14(A,B,C) True evalrealheapsortstep1stop.13(A,B,C) -> exitus616.14(A,B,C) True Signature: {(evalrealheapsortstep1bb2in.11,3) ;(evalrealheapsortstep1bb3in.5,3) ;(evalrealheapsortstep1bb3in.6,3) ;(evalrealheapsortstep1bb4in.7,3) ;(evalrealheapsortstep1bb4in.8,3) ;(evalrealheapsortstep1bb5in.9,3) ;(evalrealheapsortstep1bb6in.10,3) ;(evalrealheapsortstep1bb6in.4,3) ;(evalrealheapsortstep1entryin.1,3) ;(evalrealheapsortstep1entryin.2,3) ;(evalrealheapsortstep1returnin.3,3) ;(evalrealheapsortstep1start.0,3) ;(evalrealheapsortstep1stop.12,3) ;(evalrealheapsortstep1stop.13,3) ;(exitus616.14,3)} Rule Graph: [0->{2},1->{3},2->{4,5},3->{6},4->{17},5->{18},6->{7,8},7->{10},8->{11},9->{12,13},10->{12,13},11->{15,16} ,12->{6},13->{14},14->{4,5},15->{7,8},16->{9},17->{},18->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] | `- p:[6,12,9,16,11,8,15,10,7] c: [6,7,9,10,12,16] | `- p:[8,15,11] c: [8,11,15] * Step 6: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: evalrealheapsortstep1start.0(A,B,C) -> evalrealheapsortstep1entryin.1(A,B,C) True evalrealheapsortstep1start.0(A,B,C) -> evalrealheapsortstep1entryin.2(A,B,C) True evalrealheapsortstep1entryin.1(A,B,C) -> evalrealheapsortstep1returnin.3(A,B,C) [2 >= A] evalrealheapsortstep1entryin.2(A,B,C) -> evalrealheapsortstep1bb6in.4(A,1,C) [A >= 3] evalrealheapsortstep1returnin.3(A,B,C) -> evalrealheapsortstep1stop.12(A,B,C) True evalrealheapsortstep1returnin.3(A,B,C) -> evalrealheapsortstep1stop.13(A,B,C) True evalrealheapsortstep1bb6in.4(A,B,C) -> evalrealheapsortstep1bb3in.5(A,B,B) [-1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 1 + B] evalrealheapsortstep1bb3in.5(A,B,C) -> evalrealheapsortstep1bb4in.7(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 1] evalrealheapsortstep1bb3in.5(A,B,C) -> evalrealheapsortstep1bb4in.8(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 1] evalrealheapsortstep1bb3in.6(A,B,C) -> evalrealheapsortstep1bb5in.9(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && 0 >= C] evalrealheapsortstep1bb4in.7(A,B,C) -> evalrealheapsortstep1bb5in.9(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] evalrealheapsortstep1bb4in.8(A,B,C) -> evalrealheapsortstep1bb2in.11(A,B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && D >= 0 && 1 + C >= 2*D && 2*D >= C] evalrealheapsortstep1bb5in.9(A,B,C) -> evalrealheapsortstep1bb6in.4(A,1 + B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0] evalrealheapsortstep1bb5in.9(A,B,C) -> evalrealheapsortstep1bb6in.10(A,1 + B,C) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0] evalrealheapsortstep1bb6in.10(A,B,C) -> evalrealheapsortstep1returnin.3(A,B,C) [-1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && B >= A] evalrealheapsortstep1bb2in.11(A,B,C) -> evalrealheapsortstep1bb3in.5(A,B,-1 + D) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && E >= 0 && 1 + C >= 2*E && 2*E >= C && F >= 0 && 1 + C >= 2*F && 2*F >= C && D >= 0 && 1 + C >= 2*D && 2*D >= C] evalrealheapsortstep1bb2in.11(A,B,C) -> evalrealheapsortstep1bb3in.6(A,B,-1 + D) [B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -4 + A + C >= 0 && -1 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && C >= 0 && E >= 0 && 1 + C >= 2*E && 2*E >= C && F >= 0 && 1 + C >= 2*F && 2*F >= C && D >= 0 && 1 + C >= 2*D && 2*D >= C] evalrealheapsortstep1stop.12(A,B,C) -> exitus616.14(A,B,C) True evalrealheapsortstep1stop.13(A,B,C) -> exitus616.14(A,B,C) True Signature: {(evalrealheapsortstep1bb2in.11,3) ;(evalrealheapsortstep1bb3in.5,3) ;(evalrealheapsortstep1bb3in.6,3) ;(evalrealheapsortstep1bb4in.7,3) ;(evalrealheapsortstep1bb4in.8,3) ;(evalrealheapsortstep1bb5in.9,3) ;(evalrealheapsortstep1bb6in.10,3) ;(evalrealheapsortstep1bb6in.4,3) ;(evalrealheapsortstep1entryin.1,3) ;(evalrealheapsortstep1entryin.2,3) ;(evalrealheapsortstep1returnin.3,3) ;(evalrealheapsortstep1start.0,3) ;(evalrealheapsortstep1stop.12,3) ;(evalrealheapsortstep1stop.13,3) ;(exitus616.14,3)} Rule Graph: [0->{2},1->{3},2->{4,5},3->{6},4->{17},5->{18},6->{7,8},7->{10},8->{11},9->{12,13},10->{12,13},11->{15,16} ,12->{6},13->{14},14->{4,5},15->{7,8},16->{9},17->{},18->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] | `- p:[6,12,9,16,11,8,15,10,7] c: [6,7,9,10,12,16] | `- p:[8,15,11] c: [8,11,15]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0] evalrealheapsortstep1start.0 ~> evalrealheapsortstep1entryin.1 [A <= A, B <= B, C <= C] evalrealheapsortstep1start.0 ~> evalrealheapsortstep1entryin.2 [A <= A, B <= B, C <= C] evalrealheapsortstep1entryin.1 ~> evalrealheapsortstep1returnin.3 [A <= A, B <= B, C <= C] evalrealheapsortstep1entryin.2 ~> evalrealheapsortstep1bb6in.4 [A <= A, B <= K, C <= C] evalrealheapsortstep1returnin.3 ~> evalrealheapsortstep1stop.12 [A <= A, B <= B, C <= C] evalrealheapsortstep1returnin.3 ~> evalrealheapsortstep1stop.13 [A <= A, B <= B, C <= C] evalrealheapsortstep1bb6in.4 ~> evalrealheapsortstep1bb3in.5 [A <= A, B <= B, C <= B] evalrealheapsortstep1bb3in.5 ~> evalrealheapsortstep1bb4in.7 [A <= A, B <= B, C <= C] evalrealheapsortstep1bb3in.5 ~> evalrealheapsortstep1bb4in.8 [A <= A, B <= B, C <= C] evalrealheapsortstep1bb3in.6 ~> evalrealheapsortstep1bb5in.9 [A <= A, B <= B, C <= C] evalrealheapsortstep1bb4in.7 ~> evalrealheapsortstep1bb5in.9 [A <= A, B <= B, C <= C] evalrealheapsortstep1bb4in.8 ~> evalrealheapsortstep1bb2in.11 [A <= A, B <= B, C <= C] evalrealheapsortstep1bb5in.9 ~> evalrealheapsortstep1bb6in.4 [A <= A, B <= A, C <= C] evalrealheapsortstep1bb5in.9 ~> evalrealheapsortstep1bb6in.10 [A <= A, B <= A, C <= C] evalrealheapsortstep1bb6in.10 ~> evalrealheapsortstep1returnin.3 [A <= A, B <= B, C <= C] evalrealheapsortstep1bb2in.11 ~> evalrealheapsortstep1bb3in.5 [A <= A, B <= B, C <= A] evalrealheapsortstep1bb2in.11 ~> evalrealheapsortstep1bb3in.6 [A <= A, B <= B, C <= A] evalrealheapsortstep1stop.12 ~> exitus616.14 [A <= A, B <= B, C <= C] evalrealheapsortstep1stop.13 ~> exitus616.14 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A + B] evalrealheapsortstep1bb6in.4 ~> evalrealheapsortstep1bb3in.5 [A <= A, B <= B, C <= B] evalrealheapsortstep1bb5in.9 ~> evalrealheapsortstep1bb6in.4 [A <= A, B <= A, C <= C] evalrealheapsortstep1bb3in.6 ~> evalrealheapsortstep1bb5in.9 [A <= A, B <= B, C <= C] evalrealheapsortstep1bb2in.11 ~> evalrealheapsortstep1bb3in.6 [A <= A, B <= B, C <= A] evalrealheapsortstep1bb4in.8 ~> evalrealheapsortstep1bb2in.11 [A <= A, B <= B, C <= C] evalrealheapsortstep1bb3in.5 ~> evalrealheapsortstep1bb4in.8 [A <= A, B <= B, C <= C] evalrealheapsortstep1bb2in.11 ~> evalrealheapsortstep1bb3in.5 [A <= A, B <= B, C <= A] evalrealheapsortstep1bb4in.7 ~> evalrealheapsortstep1bb5in.9 [A <= A, B <= B, C <= C] evalrealheapsortstep1bb3in.5 ~> evalrealheapsortstep1bb4in.7 [A <= A, B <= B, C <= C] + Loop: [0.0.0 <= K + 4*C] evalrealheapsortstep1bb3in.5 ~> evalrealheapsortstep1bb4in.8 [A <= A, B <= B, C <= C] evalrealheapsortstep1bb2in.11 ~> evalrealheapsortstep1bb3in.5 [A <= A, B <= B, C <= A] evalrealheapsortstep1bb4in.8 ~> evalrealheapsortstep1bb2in.11 [A <= A, B <= B, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0] evalrealheapsortstep1start.0 ~> evalrealheapsortstep1entryin.1 [] evalrealheapsortstep1start.0 ~> evalrealheapsortstep1entryin.2 [] evalrealheapsortstep1entryin.1 ~> evalrealheapsortstep1returnin.3 [] evalrealheapsortstep1entryin.2 ~> evalrealheapsortstep1bb6in.4 [K ~=> B] evalrealheapsortstep1returnin.3 ~> evalrealheapsortstep1stop.12 [] evalrealheapsortstep1returnin.3 ~> evalrealheapsortstep1stop.13 [] evalrealheapsortstep1bb6in.4 ~> evalrealheapsortstep1bb3in.5 [B ~=> C] evalrealheapsortstep1bb3in.5 ~> evalrealheapsortstep1bb4in.7 [] evalrealheapsortstep1bb3in.5 ~> evalrealheapsortstep1bb4in.8 [] evalrealheapsortstep1bb3in.6 ~> evalrealheapsortstep1bb5in.9 [] evalrealheapsortstep1bb4in.7 ~> evalrealheapsortstep1bb5in.9 [] evalrealheapsortstep1bb4in.8 ~> evalrealheapsortstep1bb2in.11 [] evalrealheapsortstep1bb5in.9 ~> evalrealheapsortstep1bb6in.4 [A ~=> B] evalrealheapsortstep1bb5in.9 ~> evalrealheapsortstep1bb6in.10 [A ~=> B] evalrealheapsortstep1bb6in.10 ~> evalrealheapsortstep1returnin.3 [] evalrealheapsortstep1bb2in.11 ~> evalrealheapsortstep1bb3in.5 [A ~=> C] evalrealheapsortstep1bb2in.11 ~> evalrealheapsortstep1bb3in.6 [A ~=> C] evalrealheapsortstep1stop.12 ~> exitus616.14 [] evalrealheapsortstep1stop.13 ~> exitus616.14 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] evalrealheapsortstep1bb6in.4 ~> evalrealheapsortstep1bb3in.5 [B ~=> C] evalrealheapsortstep1bb5in.9 ~> evalrealheapsortstep1bb6in.4 [A ~=> B] evalrealheapsortstep1bb3in.6 ~> evalrealheapsortstep1bb5in.9 [] evalrealheapsortstep1bb2in.11 ~> evalrealheapsortstep1bb3in.6 [A ~=> C] evalrealheapsortstep1bb4in.8 ~> evalrealheapsortstep1bb2in.11 [] evalrealheapsortstep1bb3in.5 ~> evalrealheapsortstep1bb4in.8 [] evalrealheapsortstep1bb2in.11 ~> evalrealheapsortstep1bb3in.5 [A ~=> C] evalrealheapsortstep1bb4in.7 ~> evalrealheapsortstep1bb5in.9 [] evalrealheapsortstep1bb3in.5 ~> evalrealheapsortstep1bb4in.7 [] + Loop: [K ~+> 0.0.0,C ~*> 0.0.0] evalrealheapsortstep1bb3in.5 ~> evalrealheapsortstep1bb4in.8 [] evalrealheapsortstep1bb2in.11 ~> evalrealheapsortstep1bb3in.5 [A ~=> C] evalrealheapsortstep1bb4in.8 ~> evalrealheapsortstep1bb2in.11 [] + Applied Processor: Lare + Details: evalrealheapsortstep1start.0 ~> exitus616.14 [A ~=> B ,A ~=> C ,K ~=> C ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] + evalrealheapsortstep1bb5in.9> [A ~=> B ,A ~=> C ,B ~=> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> tick] + evalrealheapsortstep1bb3in.5> [A ~=> C ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,C ~*> 0.0.0 ,C ~*> tick] evalrealheapsortstep1bb2in.11> [A ~=> C ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,C ~*> 0.0.0 ,C ~*> tick] YES(?,POLY)