YES(?,O(1)) * Step 1: ArgumentFilter WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J) -> f5(K,0,0,D,E,F,G,H,I,J) True (1,1) 1. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,1 + B,1 + C,1,E,F,G,H,I,J) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] (?,1) 2. f5(A,B,C,D,E,F,G,H,I,J) -> f5(A,B,1 + C,0,E,F,G,H,I,J) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] (?,1) 3. f5(A,B,C,D,E,F,G,H,I,J) -> f27(A,B,C,D,B,B,K,L,L,L) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && C >= 16] (?,1) Signature: {(f0,10);(f27,10);(f5,10)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}] + Applied Processor: ArgumentFilter [0,3,4,5,6,7,8,9] + Details: We remove following argument positions: [0,3,4,5,6,7,8,9]. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f5(0,0) True (1,1) 1. f5(B,C) -> f5(1 + B,1 + C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] (?,1) 2. f5(B,C) -> f5(B,1 + C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] (?,1) 3. f5(B,C) -> f27(B,C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && C >= 16] (?,1) Signature: {(f0,10);(f27,10);(f5,10)} 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: [(0,3)] * Step 3: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C) -> f5(0,0) True (1,1) 1. f5(B,C) -> f5(1 + B,1 + C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] (?,1) 2. f5(B,C) -> f5(B,1 + C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] (?,1) 3. f5(B,C) -> f27(B,C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && C >= 16] (?,1) Signature: {(f0,10);(f27,10);(f5,10)} Flow Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{}] + Applied Processor: FromIts + Details: () * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(B,C) -> f5(0,0) True f5(B,C) -> f5(1 + B,1 + C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] f5(B,C) -> f5(B,1 + C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] f5(B,C) -> f27(B,C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && C >= 16] Signature: {(f0,10);(f27,10);(f5,10)} Rule Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(B,C) -> f5(0,0) True f5(B,C) -> f5(1 + B,1 + C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] f5(B,C) -> f5(B,1 + C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] f5(B,C) -> f27(B,C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && C >= 16] f27(B,C) -> exitus616(B,C) True Signature: {(exitus616,2);(f0,10);(f27,10);(f5,10)} Rule Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4] | `- p:[1,2] c: [1,2] * Step 6: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f0(B,C) -> f5(0,0) True f5(B,C) -> f5(1 + B,1 + C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] f5(B,C) -> f5(B,1 + C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && 15 >= C] f5(B,C) -> f27(B,C) [C >= 0 && B + C >= 0 && -1*B + C >= 0 && B >= 0 && C >= 16] f27(B,C) -> exitus616(B,C) True Signature: {(exitus616,2);(f0,10);(f27,10);(f5,10)} Rule Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{4}] ,We construct a looptree: P: [0,1,2,3,4] | `- p:[1,2] c: [1,2]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [B,C,0.0] f0 ~> f5 [B <= 0*K, C <= 0*K] f5 ~> f5 [B <= 16*K, C <= 16*K] f5 ~> f5 [B <= B, C <= 16*K] f5 ~> f27 [B <= B, C <= C] f27 ~> exitus616 [B <= B, C <= C] + Loop: [0.0 <= 15*K + B + C] f5 ~> f5 [B <= 16*K, C <= 16*K] f5 ~> f5 [B <= B, C <= 16*K] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,B,C,0.0] f0 ~> f5 [K ~=> B,K ~=> C] f5 ~> f5 [K ~=> B,K ~=> C] f5 ~> f5 [K ~=> C] f5 ~> f27 [] f27 ~> exitus616 [] + Loop: [B ~+> 0.0,C ~+> 0.0,K ~*> 0.0] f5 ~> f5 [K ~=> B,K ~=> C] f5 ~> f5 [K ~=> C] + Applied Processor: Lare + Details: f0 ~> exitus616 [K ~=> B,K ~=> C,tick ~+> tick,K ~+> 0.0,K ~+> tick,K ~*> 0.0,K ~*> tick] + f5> [K ~=> B ,K ~=> C ,B ~+> 0.0 ,B ~+> tick ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~*> 0.0 ,K ~*> tick] YES(?,O(1))