YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C) -> eval(A,B,C) True (1,1) 1. eval(A,B,C) -> eval(A,B,-1 + C) [C >= 1 + B && B >= A] (?,1) 2. eval(A,B,C) -> eval(-1 + A,B,C) [C >= 1 + B && A >= 1 + B] (?,1) 3. eval(A,B,C) -> eval(-1 + A,B,C) [A >= 1 + B] (?,1) Signature: {(eval,3);(start,3)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,2),(1,3)] * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C) -> eval(A,B,C) True (1,1) 1. eval(A,B,C) -> eval(A,B,-1 + C) [C >= 1 + B && B >= A] (?,1) 2. eval(A,B,C) -> eval(-1 + A,B,C) [C >= 1 + B && A >= 1 + B] (?,1) 3. eval(A,B,C) -> eval(-1 + A,B,C) [A >= 1 + B] (?,1) Signature: {(eval,3);(start,3)} Flow Graph: [0->{1,2,3},1->{1},2->{1,2,3},3->{1,2,3}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start(A,B,C) -> eval(A,B,C) True eval(A,B,C) -> eval(A,B,-1 + C) [C >= 1 + B && B >= A] eval(A,B,C) -> eval(-1 + A,B,C) [C >= 1 + B && A >= 1 + B] eval(A,B,C) -> eval(-1 + A,B,C) [A >= 1 + B] Signature: {(eval,3);(start,3)} Rule Graph: [0->{1,2,3},1->{1},2->{1,2,3},3->{1,2,3}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start(A,B,C) -> eval(A,B,C) True eval(A,B,C) -> eval(A,B,-1 + C) [C >= 1 + B && B >= A] eval(A,B,C) -> eval(-1 + A,B,C) [C >= 1 + B && A >= 1 + B] eval(A,B,C) -> eval(-1 + A,B,C) [A >= 1 + B] eval(A,B,C) -> exitus616(A,B,C) True Signature: {(eval,3);(exitus616,3);(start,3)} Rule Graph: [0->{1,2,3},1->{1,4},2->{1,2,3},3->{1,2,3}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4] | +- p:[2,3] c: [2,3] | `- p:[1] c: [1] * Step 5: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: start(A,B,C) -> eval(A,B,C) True eval(A,B,C) -> eval(A,B,-1 + C) [C >= 1 + B && B >= A] eval(A,B,C) -> eval(-1 + A,B,C) [C >= 1 + B && A >= 1 + B] eval(A,B,C) -> eval(-1 + A,B,C) [A >= 1 + B] eval(A,B,C) -> exitus616(A,B,C) True Signature: {(eval,3);(exitus616,3);(start,3)} Rule Graph: [0->{1,2,3},1->{1,4},2->{1,2,3},3->{1,2,3}] ,We construct a looptree: P: [0,1,2,3,4] | +- p:[2,3] c: [2,3] | `- p:[1] c: [1]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0,0.1] start ~> eval [A <= A, B <= B, C <= C] eval ~> eval [A <= A, B <= B, C <= B + C] eval ~> eval [A <= A + B, B <= B, C <= C] eval ~> eval [A <= A + B, B <= B, C <= C] eval ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A + B] eval ~> eval [A <= A + B, B <= B, C <= C] eval ~> eval [A <= A + B, B <= B, C <= C] + Loop: [0.1 <= K + B + C] eval ~> eval [A <= A, B <= B, C <= B + C] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.1] start ~> eval [] eval ~> eval [B ~+> C,C ~+> C] eval ~> eval [A ~+> A,B ~+> A] eval ~> eval [A ~+> A,B ~+> A] eval ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] eval ~> eval [A ~+> A,B ~+> A] eval ~> eval [A ~+> A,B ~+> A] + Loop: [B ~+> 0.1,C ~+> 0.1,K ~+> 0.1] eval ~> eval [B ~+> C,C ~+> C] + Applied Processor: Lare + Details: start ~> exitus616 [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,B ~+> C ,B ~+> 0.0 ,B ~+> 0.1 ,B ~+> tick ,C ~+> C ,C ~+> 0.1 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,A ~*> A ,B ~*> A ,B ~*> C ,C ~*> C ,K ~*> A ,K ~*> C] + eval> [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> A ,B ~*> A ,K ~*> A] + eval> [B ~+> C ,B ~+> 0.1 ,B ~+> tick ,C ~+> C ,C ~+> 0.1 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.1 ,K ~+> tick ,B ~*> C ,C ~*> C ,K ~*> C] YES(?,O(n^1))