YES(?,O(1)) * Step 1: ArgumentFilter WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f6(0,C) True (1,1) 1. f6(A,B) -> f6(1 + A,B) [A >= 0 && 49 >= A] (?,1) 2. f6(A,B) -> f14(A,B) [A >= 0 && A >= 50] (?,1) Signature: {(f0,2);(f14,2);(f6,2)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: ArgumentFilter [1] + Details: We remove following argument positions: [1]. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f6(0) True (1,1) 1. f6(A) -> f6(1 + A) [A >= 0 && 49 >= A] (?,1) 2. f6(A) -> f14(A) [A >= 0 && A >= 50] (?,1) Signature: {(f0,2);(f14,2);(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(A) -> f6(0) True (1,1) 1. f6(A) -> f6(1 + A) [A >= 0 && 49 >= A] (?,1) 2. f6(A) -> f14(A) [A >= 0 && A >= 50] (?,1) Signature: {(f0,2);(f14,2);(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(A) -> f6(0) True f6(A) -> f6(1 + A) [A >= 0 && 49 >= A] f6(A) -> f14(A) [A >= 0 && A >= 50] Signature: {(f0,2);(f14,2);(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(A) -> f6(0) True f6(A) -> f6(1 + A) [A >= 0 && 49 >= A] f6(A) -> f14(A) [A >= 0 && A >= 50] f14(A) -> exitus616(A) True Signature: {(exitus616,1);(f0,2);(f14,2);(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(A) -> f6(0) True f6(A) -> f6(1 + A) [A >= 0 && 49 >= A] f6(A) -> f14(A) [A >= 0 && A >= 50] f14(A) -> exitus616(A) True Signature: {(exitus616,1);(f0,2);(f14,2);(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: [A,0.0] f0 ~> f6 [A <= 0*K] f6 ~> f6 [A <= 50*K] f6 ~> f14 [A <= A] f14 ~> exitus616 [A <= A] + Loop: [0.0 <= 49*K + A] f6 ~> f6 [A <= 50*K] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,0.0] f0 ~> f6 [K ~=> A] f6 ~> f6 [K ~=> A] f6 ~> f14 [] f14 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f6 ~> f6 [K ~=> A] + Applied Processor: Lare + Details: f0 ~> exitus616 [K ~=> A,tick ~+> tick,K ~+> 0.0,K ~+> tick,K ~*> 0.0,K ~*> tick] + f6> [K ~=> A,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] YES(?,O(1))