YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f4(A,B,C) -> f4(A,1 + B,C) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] 1. f4(A,B,C) -> f4(1 + A,0,C) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 2 + A && B >= A] 2. f0(A,B,C) -> f4(0,0,C) [C >= 1] (1,1) Signature: {(f0,3);(f4,3)} Flow Graph: [0->{0,1},1->{0,1},2->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,1),(2,0)] * Step 2: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f4(A,B,C) -> f4(A,1 + B,C) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] 1. f4(A,B,C) -> f4(1 + A,0,C) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 2 + A && B >= A] 2. f0(A,B,C) -> f4(0,0,C) [C >= 1] (1,1) Signature: {(f0,3);(f4,3)} Flow Graph: [0->{0,1},1->{0},2->{1}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: f4(A,B,C) -> f4(A,1 + B,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] f4(A,B,C) -> f4(1 + A,0,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 2 + A && B >= A] f0(A,B,C) -> f4(0,0,C) [C >= 1] Signature: {(f0,3);(f4,3)} Rule Graph: [0->{0,1},1->{0},2->{1}] + Applied Processor: AddSinks + Details: () * Step 4: Unfold WORST_CASE(?,POLY) + Considered Problem: Rules: f4(A,B,C) -> f4(A,1 + B,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] f4(A,B,C) -> f4(1 + A,0,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 2 + A && B >= A] f0(A,B,C) -> f4(0,0,C) [C >= 1] f4(A,B,C) -> exitus616(A,B,C) True f4(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f0,3);(f4,3)} Rule Graph: [0->{0,1,3},1->{0,4},2->{1}] + Applied Processor: Unfold + Details: () * Step 5: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: f4.0(A,B,C) -> f4.0(A,1 + B,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] f4.0(A,B,C) -> f4.1(A,1 + B,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] f4.0(A,B,C) -> f4.3(A,1 + B,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] f4.1(A,B,C) -> f4.0(1 + A,0,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 2 + A && B >= A] f4.1(A,B,C) -> f4.4(1 + A,0,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 2 + A && B >= A] f0.2(A,B,C) -> f4.1(0,0,C) [C >= 1] f4.3(A,B,C) -> exitus616.5(A,B,C) True f4.4(A,B,C) -> exitus616.5(A,B,C) True Signature: {(exitus616.5,3);(f0.2,3);(f4.0,3);(f4.1,3);(f4.3,3);(f4.4,3)} Rule Graph: [0->{0,1,2},1->{3,4},2->{6},3->{0,1,2},4->{7},5->{3,4},6->{},7->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[0,3,1] c: [1,3] | `- p:[0] c: [0] * Step 6: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: f4.0(A,B,C) -> f4.0(A,1 + B,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] f4.0(A,B,C) -> f4.1(A,1 + B,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] f4.0(A,B,C) -> f4.3(A,1 + B,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] f4.1(A,B,C) -> f4.0(1 + A,0,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 2 + A && B >= A] f4.1(A,B,C) -> f4.4(1 + A,0,C) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 2 + A && B >= A] f0.2(A,B,C) -> f4.1(0,0,C) [C >= 1] f4.3(A,B,C) -> exitus616.5(A,B,C) True f4.4(A,B,C) -> exitus616.5(A,B,C) True Signature: {(exitus616.5,3);(f0.2,3);(f4.0,3);(f4.1,3);(f4.3,3);(f4.4,3)} Rule Graph: [0->{0,1,2},1->{3,4},2->{6},3->{0,1,2},4->{7},5->{3,4},6->{},7->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[0,3,1] c: [1,3] | `- p:[0] c: [0]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0] f4.0 ~> f4.0 [A <= A, B <= C, C <= C] f4.0 ~> f4.1 [A <= A, B <= C, C <= C] f4.0 ~> f4.3 [A <= A, B <= C, C <= C] f4.1 ~> f4.0 [A <= C, B <= 0*K, C <= C] f4.1 ~> f4.4 [A <= C, B <= 0*K, C <= C] f0.2 ~> f4.1 [A <= 0*K, B <= 0*K, C <= C] f4.3 ~> exitus616.5 [A <= A, B <= B, C <= C] f4.4 ~> exitus616.5 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A + C] f4.0 ~> f4.0 [A <= A, B <= C, C <= C] f4.1 ~> f4.0 [A <= C, B <= 0*K, C <= C] f4.0 ~> f4.1 [A <= A, B <= C, C <= C] + Loop: [0.0.0 <= K + A + B] f4.0 ~> f4.0 [A <= A, B <= C, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0] f4.0 ~> f4.0 [C ~=> B] f4.0 ~> f4.1 [C ~=> B] f4.0 ~> f4.3 [C ~=> B] f4.1 ~> f4.0 [C ~=> A,K ~=> B] f4.1 ~> f4.4 [C ~=> A,K ~=> B] f0.2 ~> f4.1 [K ~=> A,K ~=> B] f4.3 ~> exitus616.5 [] f4.4 ~> exitus616.5 [] + Loop: [A ~+> 0.0,C ~+> 0.0,K ~+> 0.0] f4.0 ~> f4.0 [C ~=> B] f4.1 ~> f4.0 [C ~=> A,K ~=> B] f4.0 ~> f4.1 [C ~=> B] + Loop: [A ~+> 0.0.0,B ~+> 0.0.0,K ~+> 0.0.0] f4.0 ~> f4.0 [C ~=> B] + Applied Processor: Lare + Details: f0.2 ~> exitus616.5 [C ~=> A ,C ~=> B ,K ~=> A ,K ~=> B ,C ~+> 0.0 ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,C ~*> 0.0 ,C ~*> 0.0.0 ,C ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] + f4.0> [C ~=> A ,C ~=> B ,K ~=> B ,A ~+> 0.0 ,A ~+> tick ,C ~+> 0.0 ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,C ~*> 0.0.0 ,C ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] f4.1> [C ~=> A ,C ~=> B ,A ~+> 0.0 ,A ~+> tick ,C ~+> 0.0 ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,C ~*> 0.0.0 ,C ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + f4.0> [C ~=> B ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] YES(?,POLY)