YES(?,O(1)) * Step 1: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f8(0,10,0) True (1,1) 1. f8(A,B,C) -> f8(2 + A,B,1 + C) [A + -1*C >= 0 (?,1) && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && B >= 1 + C] 2. f8(A,B,C) -> f6(A,B,C) [A + -1*C >= 0 (?,1) && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && 2*B >= 1 + A && C >= B] 3. f8(A,B,C) -> f6(A,B,C) [A + -1*C >= 0 (?,1) && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && A >= 2*B && C >= B] Signature: {(f0,3);(f6,3);(f8,3)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{},3->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2),(0,3)] * Step 2: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f8(0,10,0) True (1,1) 1. f8(A,B,C) -> f8(2 + A,B,1 + C) [A + -1*C >= 0 (?,1) && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && B >= 1 + C] 2. f8(A,B,C) -> f6(A,B,C) [A + -1*C >= 0 (?,1) && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && 2*B >= 1 + A && C >= B] 3. f8(A,B,C) -> f6(A,B,C) [A + -1*C >= 0 (?,1) && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && A >= 2*B && C >= B] Signature: {(f0,3);(f6,3);(f8,3)} Flow Graph: [0->{1},1->{1,2,3},2->{},3->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A,B,C) -> f8(0,10,0) True f8(A,B,C) -> f8(2 + A,B,1 + C) [A + -1*C >= 0 && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && B >= 1 + C] f8(A,B,C) -> f6(A,B,C) [A + -1*C >= 0 && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && 2*B >= 1 + A && C >= B] f8(A,B,C) -> f6(A,B,C) [A + -1*C >= 0 && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && A >= 2*B && C >= B] Signature: {(f0,3);(f6,3);(f8,3)} Rule Graph: [0->{1},1->{1,2,3},2->{},3->{}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A,B,C) -> f8(0,10,0) True f8(A,B,C) -> f8(2 + A,B,1 + C) [A + -1*C >= 0 && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && B >= 1 + C] f8(A,B,C) -> f6(A,B,C) [A + -1*C >= 0 && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && 2*B >= 1 + A && C >= B] f8(A,B,C) -> f6(A,B,C) [A + -1*C >= 0 && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && A >= 2*B && C >= B] f6(A,B,C) -> exitus616(A,B,C) True f6(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f0,3);(f6,3);(f8,3)} Rule Graph: [0->{1},1->{1,2,3},2->{5},3->{4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[1] c: [1] * Step 5: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f0(A,B,C) -> f8(0,10,0) True f8(A,B,C) -> f8(2 + A,B,1 + C) [A + -1*C >= 0 && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && B >= 1 + C] f8(A,B,C) -> f6(A,B,C) [A + -1*C >= 0 && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && 2*B >= 1 + A && C >= B] f8(A,B,C) -> f6(A,B,C) [A + -1*C >= 0 && C >= 0 && -10 + B + C >= 0 && 10 + -1*B + C >= 0 && A + C >= 0 && 10 + -1*B >= 0 && 10 + A + -1*B >= 0 && -10 + B >= 0 && -10 + A + B >= 0 && A >= 0 && A >= 2*B && C >= B] f6(A,B,C) -> exitus616(A,B,C) True f6(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f0,3);(f6,3);(f8,3)} Rule Graph: [0->{1},1->{1,2,3},2->{5},3->{4}] ,We construct a looptree: P: [0,1,2,3,4,5] | `- p:[1] c: [1]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,0.0] f0 ~> f8 [A <= 0*K, B <= 10*K, C <= 0*K] f8 ~> f8 [A <= A + B, B <= B, C <= 10*K] f8 ~> f6 [A <= A, B <= B, C <= C] f8 ~> f6 [A <= A, B <= B, C <= C] f6 ~> exitus616 [A <= A, B <= B, C <= C] f6 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + B + C] f8 ~> f8 [A <= A + B, B <= B, C <= 10*K] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] f0 ~> f8 [K ~=> A,K ~=> B,K ~=> C] f8 ~> f8 [K ~=> C,A ~+> A,B ~+> A] f8 ~> f6 [] f8 ~> f6 [] f6 ~> exitus616 [] f6 ~> exitus616 [] + Loop: [B ~+> 0.0,C ~+> 0.0,K ~+> 0.0] f8 ~> f8 [K ~=> C,A ~+> A,B ~+> A] + Applied Processor: Lare + Details: f0 ~> exitus616 [K ~=> A ,K ~=> B ,K ~=> C ,tick ~+> tick ,K ~+> A ,K ~+> 0.0 ,K ~+> tick ,K ~*> A ,K ~*> 0.0 ,K ~*> tick] + f8> [K ~=> C ,A ~+> A ,B ~+> A ,B ~+> 0.0 ,B ~+> tick ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,B ~*> A ,C ~*> A ,K ~*> A] YES(?,O(1))