YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalNestedSinglestart(A,B,C) -> evalNestedSingleentryin(A,B,C) True (1,1) 1. evalNestedSingleentryin(A,B,C) -> evalNestedSinglebb5in(0,B,C) True (?,1) 2. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglebb2in(A,B,A) [B >= 1 + A] (?,1) 3. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglereturnin(A,B,C) [A >= B] (?,1) 4. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb4in(A,B,C) [C >= B] (?,1) 5. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb3in(A,B,C) [B >= 1 + C] (?,1) 6. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [0 >= 1 + D] (?,1) 7. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [D >= 1] (?,1) 8. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb4in(A,B,C) True (?,1) 9. evalNestedSinglebb1in(A,B,C) -> evalNestedSinglebb2in(A,B,1 + C) True (?,1) 10. evalNestedSinglebb4in(A,B,C) -> evalNestedSinglebb5in(1 + C,B,C) True (?,1) 11. evalNestedSinglereturnin(A,B,C) -> evalNestedSinglestop(A,B,C) True (?,1) Signature: {(evalNestedSinglebb1in,3) ;(evalNestedSinglebb2in,3) ;(evalNestedSinglebb3in,3) ;(evalNestedSinglebb4in,3) ;(evalNestedSinglebb5in,3) ;(evalNestedSingleentryin,3) ;(evalNestedSinglereturnin,3) ;(evalNestedSinglestart,3) ;(evalNestedSinglestop,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{11},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{}] + 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. evalNestedSinglestart(A,B,C) -> evalNestedSingleentryin(A,B,C) True (1,1) 1. evalNestedSingleentryin(A,B,C) -> evalNestedSinglebb5in(0,B,C) True (1,1) 2. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglebb2in(A,B,A) [B >= 1 + A] (?,1) 3. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglereturnin(A,B,C) [A >= B] (1,1) 4. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb4in(A,B,C) [C >= B] (?,1) 5. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb3in(A,B,C) [B >= 1 + C] (?,1) 6. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [0 >= 1 + D] (?,1) 7. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [D >= 1] (?,1) 8. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb4in(A,B,C) True (?,1) 9. evalNestedSinglebb1in(A,B,C) -> evalNestedSinglebb2in(A,B,1 + C) True (?,1) 10. evalNestedSinglebb4in(A,B,C) -> evalNestedSinglebb5in(1 + C,B,C) True (?,1) 11. evalNestedSinglereturnin(A,B,C) -> evalNestedSinglestop(A,B,C) True (1,1) Signature: {(evalNestedSinglebb1in,3) ;(evalNestedSinglebb2in,3) ;(evalNestedSinglebb3in,3) ;(evalNestedSinglebb4in,3) ;(evalNestedSinglebb5in,3) ;(evalNestedSingleentryin,3) ;(evalNestedSinglereturnin,3) ;(evalNestedSinglestart,3) ;(evalNestedSinglestop,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{11},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,4)] * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalNestedSinglestart(A,B,C) -> evalNestedSingleentryin(A,B,C) True (1,1) 1. evalNestedSingleentryin(A,B,C) -> evalNestedSinglebb5in(0,B,C) True (1,1) 2. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglebb2in(A,B,A) [B >= 1 + A] (?,1) 3. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglereturnin(A,B,C) [A >= B] (1,1) 4. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb4in(A,B,C) [C >= B] (?,1) 5. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb3in(A,B,C) [B >= 1 + C] (?,1) 6. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [0 >= 1 + D] (?,1) 7. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [D >= 1] (?,1) 8. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb4in(A,B,C) True (?,1) 9. evalNestedSinglebb1in(A,B,C) -> evalNestedSinglebb2in(A,B,1 + C) True (?,1) 10. evalNestedSinglebb4in(A,B,C) -> evalNestedSinglebb5in(1 + C,B,C) True (?,1) 11. evalNestedSinglereturnin(A,B,C) -> evalNestedSinglestop(A,B,C) True (1,1) Signature: {(evalNestedSinglebb1in,3) ;(evalNestedSinglebb2in,3) ;(evalNestedSinglebb3in,3) ;(evalNestedSinglebb4in,3) ;(evalNestedSinglebb5in,3) ;(evalNestedSingleentryin,3) ;(evalNestedSinglereturnin,3) ;(evalNestedSinglestart,3) ;(evalNestedSinglestop,3)} Flow Graph: [0->{1},1->{2,3},2->{5},3->{11},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalNestedSinglestart(A,B,C) -> evalNestedSingleentryin(A,B,C) True (1,1) 1. evalNestedSingleentryin(A,B,C) -> evalNestedSinglebb5in(0,B,C) True (?,1) 2. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglebb2in(A,B,A) [B >= 1 + A] (?,1) 3. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglereturnin(A,B,C) [A >= B] (?,1) 4. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb4in(A,B,C) [C >= B] (?,1) 5. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb3in(A,B,C) [B >= 1 + C] (?,1) 6. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [0 >= 1 + D] (?,1) 7. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [D >= 1] (?,1) 8. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb4in(A,B,C) True (?,1) 9. evalNestedSinglebb1in(A,B,C) -> evalNestedSinglebb2in(A,B,1 + C) True (?,1) 10. evalNestedSinglebb4in(A,B,C) -> evalNestedSinglebb5in(1 + C,B,C) True (?,1) 11. evalNestedSinglereturnin(A,B,C) -> evalNestedSinglestop(A,B,C) True (?,1) 12. evalNestedSinglereturnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalNestedSinglebb1in,3) ;(evalNestedSinglebb2in,3) ;(evalNestedSinglebb3in,3) ;(evalNestedSinglebb4in,3) ;(evalNestedSinglebb5in,3) ;(evalNestedSingleentryin,3) ;(evalNestedSinglereturnin,3) ;(evalNestedSinglestart,3) ;(evalNestedSinglestop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{11,12},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{} ,12->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,4)] * Step 5: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalNestedSinglestart(A,B,C) -> evalNestedSingleentryin(A,B,C) True (1,1) 1. evalNestedSingleentryin(A,B,C) -> evalNestedSinglebb5in(0,B,C) True (?,1) 2. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglebb2in(A,B,A) [B >= 1 + A] (?,1) 3. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglereturnin(A,B,C) [A >= B] (?,1) 4. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb4in(A,B,C) [C >= B] (?,1) 5. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb3in(A,B,C) [B >= 1 + C] (?,1) 6. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [0 >= 1 + D] (?,1) 7. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [D >= 1] (?,1) 8. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb4in(A,B,C) True (?,1) 9. evalNestedSinglebb1in(A,B,C) -> evalNestedSinglebb2in(A,B,1 + C) True (?,1) 10. evalNestedSinglebb4in(A,B,C) -> evalNestedSinglebb5in(1 + C,B,C) True (?,1) 11. evalNestedSinglereturnin(A,B,C) -> evalNestedSinglestop(A,B,C) True (?,1) 12. evalNestedSinglereturnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalNestedSinglebb1in,3) ;(evalNestedSinglebb2in,3) ;(evalNestedSinglebb3in,3) ;(evalNestedSinglebb4in,3) ;(evalNestedSinglebb5in,3) ;(evalNestedSingleentryin,3) ;(evalNestedSinglereturnin,3) ;(evalNestedSinglestart,3) ;(evalNestedSinglestop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{5},3->{11,12},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{} ,12->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[2,10,4,9,6,5,7,8] c: [5] * Step 6: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. evalNestedSinglestart(A,B,C) -> evalNestedSingleentryin(A,B,C) True (1,1) 1. evalNestedSingleentryin(A,B,C) -> evalNestedSinglebb5in(0,B,C) True (?,1) 2. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglebb2in(A,B,A) [B >= 1 + A] (?,1) 3. evalNestedSinglebb5in(A,B,C) -> evalNestedSinglereturnin(A,B,C) [A >= B] (?,1) 4. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb4in(A,B,C) [C >= B] (?,1) 5. evalNestedSinglebb2in(A,B,C) -> evalNestedSinglebb3in(A,B,C) [B >= 1 + C] (?,1) 6. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [0 >= 1 + D] (?,1) 7. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb1in(A,B,C) [D >= 1] (?,1) 8. evalNestedSinglebb3in(A,B,C) -> evalNestedSinglebb4in(A,B,C) True (?,1) 9. evalNestedSinglebb1in(A,B,C) -> evalNestedSinglebb2in(A,B,1 + C) True (?,1) 10. evalNestedSinglebb4in(A,B,C) -> evalNestedSinglebb5in(1 + C,B,C) True (?,1) 11. evalNestedSinglereturnin(A,B,C) -> evalNestedSinglestop(A,B,C) True (?,1) 12. evalNestedSinglereturnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalNestedSinglebb1in,3) ;(evalNestedSinglebb2in,3) ;(evalNestedSinglebb3in,3) ;(evalNestedSinglebb4in,3) ;(evalNestedSinglebb5in,3) ;(evalNestedSingleentryin,3) ;(evalNestedSinglereturnin,3) ;(evalNestedSinglestart,3) ;(evalNestedSinglestop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{5},3->{11,12},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{} ,12->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[2,10,4,9,6,5,7,8] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0] evalNestedSinglestart ~> evalNestedSingleentryin [A <= A, B <= B, C <= C] evalNestedSingleentryin ~> evalNestedSinglebb5in [A <= 0*K, B <= B, C <= C] evalNestedSinglebb5in ~> evalNestedSinglebb2in [A <= A, B <= B, C <= A] evalNestedSinglebb5in ~> evalNestedSinglereturnin [A <= A, B <= B, C <= C] evalNestedSinglebb2in ~> evalNestedSinglebb4in [A <= A, B <= B, C <= C] evalNestedSinglebb2in ~> evalNestedSinglebb3in [A <= A, B <= B, C <= C] evalNestedSinglebb3in ~> evalNestedSinglebb1in [A <= A, B <= B, C <= C] evalNestedSinglebb3in ~> evalNestedSinglebb1in [A <= A, B <= B, C <= C] evalNestedSinglebb3in ~> evalNestedSinglebb4in [A <= A, B <= B, C <= C] evalNestedSinglebb1in ~> evalNestedSinglebb2in [A <= A, B <= B, C <= K + C] evalNestedSinglebb4in ~> evalNestedSinglebb5in [A <= K + C, B <= B, C <= C] evalNestedSinglereturnin ~> evalNestedSinglestop [A <= A, B <= B, C <= C] evalNestedSinglereturnin ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= 2*K + A + B + C] evalNestedSinglebb5in ~> evalNestedSinglebb2in [A <= A, B <= B, C <= A] evalNestedSinglebb4in ~> evalNestedSinglebb5in [A <= K + C, B <= B, C <= C] evalNestedSinglebb2in ~> evalNestedSinglebb4in [A <= A, B <= B, C <= C] evalNestedSinglebb1in ~> evalNestedSinglebb2in [A <= A, B <= B, C <= K + C] evalNestedSinglebb3in ~> evalNestedSinglebb1in [A <= A, B <= B, C <= C] evalNestedSinglebb2in ~> evalNestedSinglebb3in [A <= A, B <= B, C <= C] evalNestedSinglebb3in ~> evalNestedSinglebb1in [A <= A, B <= B, C <= C] evalNestedSinglebb3in ~> evalNestedSinglebb4in [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] evalNestedSinglestart ~> evalNestedSingleentryin [] evalNestedSingleentryin ~> evalNestedSinglebb5in [K ~=> A] evalNestedSinglebb5in ~> evalNestedSinglebb2in [A ~=> C] evalNestedSinglebb5in ~> evalNestedSinglereturnin [] evalNestedSinglebb2in ~> evalNestedSinglebb4in [] evalNestedSinglebb2in ~> evalNestedSinglebb3in [] evalNestedSinglebb3in ~> evalNestedSinglebb1in [] evalNestedSinglebb3in ~> evalNestedSinglebb1in [] evalNestedSinglebb3in ~> evalNestedSinglebb4in [] evalNestedSinglebb1in ~> evalNestedSinglebb2in [C ~+> C,K ~+> C] evalNestedSinglebb4in ~> evalNestedSinglebb5in [C ~+> A,K ~+> A] evalNestedSinglereturnin ~> evalNestedSinglestop [] evalNestedSinglereturnin ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0,K ~*> 0.0] evalNestedSinglebb5in ~> evalNestedSinglebb2in [A ~=> C] evalNestedSinglebb4in ~> evalNestedSinglebb5in [C ~+> A,K ~+> A] evalNestedSinglebb2in ~> evalNestedSinglebb4in [] evalNestedSinglebb1in ~> evalNestedSinglebb2in [C ~+> C,K ~+> C] evalNestedSinglebb3in ~> evalNestedSinglebb1in [] evalNestedSinglebb2in ~> evalNestedSinglebb3in [] evalNestedSinglebb3in ~> evalNestedSinglebb1in [] evalNestedSinglebb3in ~> evalNestedSinglebb4in [] + Applied Processor: LareProcessor + Details: evalNestedSinglestart ~> exitus616 [K ~=> A ,K ~=> C ,B ~+> 0.0 ,B ~+> tick ,C ~+> A ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0 ,K ~+> tick ,B ~*> A ,B ~*> C ,C ~*> A ,C ~*> C ,K ~*> A ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] evalNestedSinglestart ~> evalNestedSinglestop [K ~=> A ,K ~=> C ,B ~+> 0.0 ,B ~+> tick ,C ~+> A ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0 ,K ~+> tick ,B ~*> A ,B ~*> C ,C ~*> A ,C ~*> C ,K ~*> A ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] + evalNestedSinglebb5in> [A ~=> C ,A ~+> A ,A ~+> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,C ~+> A ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,A ~*> A ,A ~*> C ,B ~*> A ,B ~*> C ,C ~*> A ,C ~*> C ,K ~*> A ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] YES(?,O(n^1))