YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalexministart(A,B,C) -> evalexminientryin(A,B,C) True (1,1) 1. evalexminientryin(A,B,C) -> evalexminibb1in(B,A,C) True (?,1) 2. evalexminibb1in(A,B,C) -> evalexminibbin(A,B,C) [100 >= B && A >= C] (?,1) 3. evalexminibb1in(A,B,C) -> evalexminireturnin(A,B,C) [B >= 101] (?,1) 4. evalexminibb1in(A,B,C) -> evalexminireturnin(A,B,C) [C >= 1 + A] (?,1) 5. evalexminibbin(A,B,C) -> evalexminibb1in(-1 + A,C,1 + B) [A + -1*C >= 0 && 100 + -1*B >= 0] (?,1) 6. evalexminireturnin(A,B,C) -> evalexministop(A,B,C) True (?,1) Signature: {(evalexminibb1in,3) ;(evalexminibbin,3) ;(evalexminientryin,3) ;(evalexminireturnin,3) ;(evalexministart,3) ;(evalexministop,3)} Flow Graph: [0->{1},1->{2,3,4},2->{5},3->{6},4->{6},5->{2,3,4},6->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalexministart(A,B,C) -> evalexminientryin(A,B,C) True (1,1) 1. evalexminientryin(A,B,C) -> evalexminibb1in(B,A,C) True (1,1) 2. evalexminibb1in(A,B,C) -> evalexminibbin(A,B,C) [100 >= B && A >= C] (?,1) 3. evalexminibb1in(A,B,C) -> evalexminireturnin(A,B,C) [B >= 101] (1,1) 4. evalexminibb1in(A,B,C) -> evalexminireturnin(A,B,C) [C >= 1 + A] (1,1) 5. evalexminibbin(A,B,C) -> evalexminibb1in(-1 + A,C,1 + B) [A + -1*C >= 0 && 100 + -1*B >= 0] (?,1) 6. evalexminireturnin(A,B,C) -> evalexministop(A,B,C) True (1,1) Signature: {(evalexminibb1in,3) ;(evalexminibbin,3) ;(evalexminientryin,3) ;(evalexminireturnin,3) ;(evalexministart,3) ;(evalexministop,3)} Flow Graph: [0->{1},1->{2,3,4},2->{5},3->{6},4->{6},5->{2,3,4},6->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalexministart(A,B,C) -> evalexminientryin(A,B,C) True (1,1) 1. evalexminientryin(A,B,C) -> evalexminibb1in(B,A,C) True (?,1) 2. evalexminibb1in(A,B,C) -> evalexminibbin(A,B,C) [100 >= B && A >= C] (?,1) 3. evalexminibb1in(A,B,C) -> evalexminireturnin(A,B,C) [B >= 101] (?,1) 4. evalexminibb1in(A,B,C) -> evalexminireturnin(A,B,C) [C >= 1 + A] (?,1) 5. evalexminibbin(A,B,C) -> evalexminibb1in(-1 + A,C,1 + B) [A + -1*C >= 0 && 100 + -1*B >= 0] (?,1) 6. evalexminireturnin(A,B,C) -> evalexministop(A,B,C) True (?,1) 7. evalexminireturnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalexminibb1in,3) ;(evalexminibbin,3) ;(evalexminientryin,3) ;(evalexminireturnin,3) ;(evalexministart,3) ;(evalexministop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3,4},2->{5},3->{6,7},4->{6,7},5->{2,3,4},6->{},7->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[2,5] c: [5] * Step 4: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. evalexministart(A,B,C) -> evalexminientryin(A,B,C) True (1,1) 1. evalexminientryin(A,B,C) -> evalexminibb1in(B,A,C) True (?,1) 2. evalexminibb1in(A,B,C) -> evalexminibbin(A,B,C) [100 >= B && A >= C] (?,1) 3. evalexminibb1in(A,B,C) -> evalexminireturnin(A,B,C) [B >= 101] (?,1) 4. evalexminibb1in(A,B,C) -> evalexminireturnin(A,B,C) [C >= 1 + A] (?,1) 5. evalexminibbin(A,B,C) -> evalexminibb1in(-1 + A,C,1 + B) [A + -1*C >= 0 && 100 + -1*B >= 0] (?,1) 6. evalexminireturnin(A,B,C) -> evalexministop(A,B,C) True (?,1) 7. evalexminireturnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalexminibb1in,3) ;(evalexminibbin,3) ;(evalexminientryin,3) ;(evalexminireturnin,3) ;(evalexministart,3) ;(evalexministop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3,4},2->{5},3->{6,7},4->{6,7},5->{2,3,4},6->{},7->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[2,5] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0] evalexministart ~> evalexminientryin [A <= A, B <= B, C <= C] evalexminientryin ~> evalexminibb1in [A <= B, B <= A, C <= C] evalexminibb1in ~> evalexminibbin [A <= A, B <= B, C <= C] evalexminibb1in ~> evalexminireturnin [A <= A, B <= B, C <= C] evalexminibb1in ~> evalexminireturnin [A <= A, B <= B, C <= C] evalexminibbin ~> evalexminibb1in [A <= K + A, B <= C, C <= K + B] evalexminireturnin ~> evalexministop [A <= A, B <= B, C <= C] evalexminireturnin ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= 102*K + A + B + C] evalexminibb1in ~> evalexminibbin [A <= A, B <= B, C <= C] evalexminibbin ~> evalexminibb1in [A <= K + A, B <= C, C <= K + B] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] evalexministart ~> evalexminientryin [] evalexminientryin ~> evalexminibb1in [A ~=> B,B ~=> A] evalexminibb1in ~> evalexminibbin [] evalexminibb1in ~> evalexminireturnin [] evalexminibb1in ~> evalexminireturnin [] evalexminibbin ~> evalexminibb1in [C ~=> B,A ~+> A,B ~+> C,K ~+> A,K ~+> C] evalexminireturnin ~> evalexministop [] evalexminireturnin ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0,K ~*> 0.0] evalexminibb1in ~> evalexminibbin [] evalexminibbin ~> evalexminibb1in [C ~=> B,A ~+> A,B ~+> C,K ~+> A,K ~+> C] + Applied Processor: LareProcessor + Details: evalexministart ~> exitus616 [A ~=> B ,B ~=> A ,C ~=> B ,A ~+> B ,A ~+> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,B ~+> 0.0 ,B ~+> tick ,C ~+> B ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> C ,A ~*> A ,A ~*> B ,A ~*> C ,B ~*> A ,B ~*> B ,B ~*> C ,C ~*> A ,C ~*> B ,C ~*> C ,K ~*> A ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] evalexministart ~> evalexministop [A ~=> B ,B ~=> A ,C ~=> B ,A ~+> B ,A ~+> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,B ~+> 0.0 ,B ~+> tick ,C ~+> B ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> C ,A ~*> A ,A ~*> B ,A ~*> C ,B ~*> A ,B ~*> B ,B ~*> C ,C ~*> A ,C ~*> B ,C ~*> C ,K ~*> A ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] + evalexminibb1in> [C ~=> B ,A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> C ,B ~+> 0.0 ,B ~+> tick ,C ~+> B ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> C ,A ~*> A ,A ~*> B ,A ~*> C ,B ~*> A ,B ~*> B ,B ~*> C ,C ~*> A ,C ~*> B ,C ~*> C ,K ~*> A ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] YES(?,O(n^1))