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