YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C) -> f1(A,B,2) [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1) 1. f1(A,B,C) -> f1(A,1 + B,C) [A + C >= 1 + 2*B] (?,1) 2. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C] (?,1) Signature: {(f0,3);(f1,3)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,2),(2,1)] * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C) -> f1(A,B,2) [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1) 1. f1(A,B,C) -> f1(A,1 + B,C) [A + C >= 1 + 2*B] (?,1) 2. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C] (?,1) Signature: {(f0,3);(f1,3)} Flow Graph: [0->{1,2},1->{1},2->{2}] + Applied Processor: AddSinks + Details: () * Step 3: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C) -> f1(A,B,2) [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1) 1. f1(A,B,C) -> f1(A,1 + B,C) [A + C >= 1 + 2*B] (?,1) 2. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C] (?,1) 3. f1(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f0,3);(f1,3)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,2),(2,1)] * Step 4: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C) -> f1(A,B,2) [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1) 1. f1(A,B,C) -> f1(A,1 + B,C) [A + C >= 1 + 2*B] (?,1) 2. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C] (?,1) 3. f1(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f0,3);(f1,3)} Flow Graph: [0->{1,2,3},1->{1,3},2->{2,3},3->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3] | +- p:[2] c: [2] | `- p:[1] c: [1] * Step 5: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. f0(A,B,C) -> f1(A,B,2) [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1) 1. f1(A,B,C) -> f1(A,1 + B,C) [A + C >= 1 + 2*B] (?,1) 2. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C] (?,1) 3. f1(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f0,3);(f1,3)} Flow Graph: [0->{1,2,3},1->{1,3},2->{2,3},3->{}] ,We construct a looptree: P: [0,1,2,3] | +- p:[2] c: [2] | `- p:[1] c: [1]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 6: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0,0.1] f0 ~> f1 [A <= A, B <= B, C <= 2*K] f1 ~> f1 [A <= A, B <= K + B, C <= C] f1 ~> f1 [A <= A, B <= K + B, C <= C] f1 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A + 2*B + C] f1 ~> f1 [A <= A, B <= K + B, C <= C] + Loop: [0.1 <= A + 2*B + C] f1 ~> f1 [A <= A, B <= K + B, C <= C] + Applied Processor: FlowAbstraction + Details: () * Step 7: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.1] f0 ~> f1 [K ~=> C] f1 ~> f1 [B ~+> B,K ~+> B] f1 ~> f1 [B ~+> B,K ~+> B] f1 ~> exitus616 [] + Loop: [A ~+> 0.0,C ~+> 0.0,K ~+> 0.0,B ~*> 0.0] f1 ~> f1 [B ~+> B,K ~+> B] + Loop: [A ~+> 0.1,C ~+> 0.1,B ~*> 0.1] f1 ~> f1 [B ~+> B,K ~+> B] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> C ,A ~+> 0.0 ,A ~+> 0.1 ,A ~+> tick ,B ~+> B ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,A ~*> B ,B ~*> B ,B ~*> 0.0 ,B ~*> 0.1 ,B ~*> tick ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] + f1> [A ~+> 0.0 ,A ~+> tick ,B ~+> B ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,B ~*> B ,B ~*> 0.0 ,B ~*> tick ,C ~*> B ,K ~*> B] + f1> [A ~+> 0.1 ,A ~+> tick ,B ~+> B ,C ~+> 0.1 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,A ~*> B ,B ~*> B ,B ~*> 0.1 ,B ~*> tick ,C ~*> B ,K ~*> B] YES(?,POLY)