YES(?,O(1)) * Step 1: ArgumentFilter WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f6(C,0) True (1,1) 1. f6(A,B) -> f6(A,1 + B) [B >= 0 && 9 >= B] (?,1) 2. f6(A,B) -> f15(A,B) [B >= 0 && B >= 10] (?,1) Signature: {(f0,2);(f15,2);(f6,2)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: ArgumentFilter [0] + Details: We remove following argument positions: [0]. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B) -> f6(0) True (1,1) 1. f6(B) -> f6(1 + B) [B >= 0 && 9 >= B] (?,1) 2. f6(B) -> f15(B) [B >= 0 && B >= 10] (?,1) Signature: {(f0,2);(f15,2);(f6,2)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 3: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B) -> f6(0) True (1,1) 1. f6(B) -> f6(1 + B) [B >= 0 && 9 >= B] (?,1) 2. f6(B) -> f15(B) [B >= 0 && B >= 10] (?,1) Signature: {(f0,2);(f15,2);(f6,2)} Flow Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: FromIts + Details: () * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(B) -> f6(0) True f6(B) -> f6(1 + B) [B >= 0 && 9 >= B] f6(B) -> f15(B) [B >= 0 && B >= 10] Signature: {(f0,2);(f15,2);(f6,2)} Rule Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(B) -> f6(0) True f6(B) -> f6(1 + B) [B >= 0 && 9 >= B] f6(B) -> f15(B) [B >= 0 && B >= 10] f15(B) -> exitus616(B) True Signature: {(exitus616,1);(f0,2);(f15,2);(f6,2)} Rule Graph: [0->{1},1->{1,2},2->{3}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3] | `- p:[1] c: [1] * Step 6: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f0(B) -> f6(0) True f6(B) -> f6(1 + B) [B >= 0 && 9 >= B] f6(B) -> f15(B) [B >= 0 && B >= 10] f15(B) -> exitus616(B) True Signature: {(exitus616,1);(f0,2);(f15,2);(f6,2)} Rule Graph: [0->{1},1->{1,2},2->{3}] ,We construct a looptree: P: [0,1,2,3] | `- p:[1] c: [1]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [B,0.0] f0 ~> f6 [B <= 0*K] f6 ~> f6 [B <= 10*K] f6 ~> f15 [B <= B] f15 ~> exitus616 [B <= B] + Loop: [0.0 <= 9*K + B] f6 ~> f6 [B <= 10*K] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,B,0.0] f0 ~> f6 [K ~=> B] f6 ~> f6 [K ~=> B] f6 ~> f15 [] f15 ~> exitus616 [] + Loop: [B ~+> 0.0,K ~*> 0.0] f6 ~> f6 [K ~=> B] + Applied Processor: Lare + Details: f0 ~> exitus616 [K ~=> B,tick ~+> tick,K ~+> 0.0,K ~+> tick,K ~*> 0.0,K ~*> tick] + f6> [K ~=> B,B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] YES(?,O(1))