YES * Step 1: TrivialSCCs YES + 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: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + 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] (1,1) 2. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,1) 3. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (1,1) 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] (1,1) 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 3: Looptree YES + 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] (1,1) 2. evalrealheapsortstep1entryin(A,B,C) -> evalrealheapsortstep1bb6in(A,1,C) [A >= 3] (1,1) 3. evalrealheapsortstep1returnin(A,B,C) -> evalrealheapsortstep1stop(A,B,C) True (1,1) 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] (1,1) 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: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[4,9,6,11,8,5,7] c: [9] | `- p:[5,11,8] c: [11] YES