YES(?,POLY) * Step 1: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval1(A,B,C) -> eval2(A,B,C) [A >= 1 + B] (?,1) 1. eval2(A,B,C) -> eval2(A,B,-1 + C) [-1 + A + -1*B >= 0 && A >= 1 + B && C >= 1 + B] (?,1) 2. eval2(A,B,C) -> eval1(-1 + A,B,C) [-1 + A + -1*B >= 0 && A >= 1 + B && B >= C] (?,1) 3. start(A,B,C) -> eval1(A,B,C) True (1,1) Signature: {(eval1,3);(eval2,3);(start,3)} Flow Graph: [0->{1,2},1->{1,2},2->{0},3->{0}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: eval1(A,B,C) -> eval2(A,B,C) [A >= 1 + B] eval2(A,B,C) -> eval2(A,B,-1 + C) [-1 + A + -1*B >= 0 && A >= 1 + B && C >= 1 + B] eval2(A,B,C) -> eval1(-1 + A,B,C) [-1 + A + -1*B >= 0 && A >= 1 + B && B >= C] start(A,B,C) -> eval1(A,B,C) True Signature: {(eval1,3);(eval2,3);(start,3)} Rule Graph: [0->{1,2},1->{1,2},2->{0},3->{0}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: eval1(A,B,C) -> eval2(A,B,C) [A >= 1 + B] eval2(A,B,C) -> eval2(A,B,-1 + C) [-1 + A + -1*B >= 0 && A >= 1 + B && C >= 1 + B] eval2(A,B,C) -> eval1(-1 + A,B,C) [-1 + A + -1*B >= 0 && A >= 1 + B && B >= C] start(A,B,C) -> eval1(A,B,C) True eval2(A,B,C) -> exitus616(A,B,C) True eval1(A,B,C) -> exitus616(A,B,C) True eval2(A,B,C) -> exitus616(A,B,C) True Signature: {(eval1,3);(eval2,3);(exitus616,3);(start,3)} Rule Graph: [0->{1,2,4},1->{1,2,6},2->{0,5},3->{0}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[0,2,1] c: [0,1,2] * Step 4: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: eval1(A,B,C) -> eval2(A,B,C) [A >= 1 + B] eval2(A,B,C) -> eval2(A,B,-1 + C) [-1 + A + -1*B >= 0 && A >= 1 + B && C >= 1 + B] eval2(A,B,C) -> eval1(-1 + A,B,C) [-1 + A + -1*B >= 0 && A >= 1 + B && B >= C] start(A,B,C) -> eval1(A,B,C) True eval2(A,B,C) -> exitus616(A,B,C) True eval1(A,B,C) -> exitus616(A,B,C) True eval2(A,B,C) -> exitus616(A,B,C) True Signature: {(eval1,3);(eval2,3);(exitus616,3);(start,3)} Rule Graph: [0->{1,2,4},1->{1,2,6},2->{0,5},3->{0}] ,We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[0,2,1] c: [0,1,2]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0] eval1 ~> eval2 [A <= A, B <= B, C <= C] eval2 ~> eval2 [A <= A, B <= B, C <= B + C] eval2 ~> eval1 [A <= A + B, B <= B, C <= C] start ~> eval1 [A <= A, B <= B, C <= C] eval2 ~> exitus616 [A <= A, B <= B, C <= C] eval1 ~> exitus616 [A <= A, B <= B, C <= C] eval2 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A + B + C] eval1 ~> eval2 [A <= A, B <= B, C <= C] eval2 ~> eval1 [A <= A + B, B <= B, C <= C] eval2 ~> eval2 [A <= A, B <= B, C <= B + C] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] eval1 ~> eval2 [] eval2 ~> eval2 [B ~+> C,C ~+> C] eval2 ~> eval1 [A ~+> A,B ~+> A] start ~> eval1 [] eval2 ~> exitus616 [] eval1 ~> exitus616 [] eval2 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0,K ~+> 0.0] eval1 ~> eval2 [] eval2 ~> eval1 [A ~+> A,B ~+> A] eval2 ~> eval2 [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 ~+> tick ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> A ,A ~*> C ,A ~*> 0.0 ,A ~*> tick ,B ~*> A ,B ~*> C ,B ~*> 0.0 ,B ~*> tick ,C ~*> A ,C ~*> C ,C ~*> 0.0 ,C ~*> tick ,K ~*> A ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] + eval2> [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,B ~+> C ,B ~+> 0.0 ,B ~+> tick ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> A ,A ~*> C ,B ~*> A ,B ~*> C ,C ~*> A ,C ~*> C ,K ~*> A ,K ~*> C] eval1> [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,B ~+> C ,B ~+> 0.0 ,B ~+> tick ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> A ,A ~*> C ,B ~*> A ,B ~*> C ,C ~*> A ,C ~*> C ,K ~*> A ,K ~*> C] YES(?,POLY)