YES(?,O(1)) * Step 1: TrivialSCCs 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: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths 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] (1,1) 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: AddSinks 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] (1,1) Signature: {(f0,2);(f14,2);(f6,2)} Flow Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths 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) 3. f6(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f0,2);(f14,2);(f6,2)} 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)] * Step 5: LooptreeTransformer 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) 3. f6(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f0,2);(f14,2);(f6,2)} Flow Graph: [0->{1,3},1->{1,2,3},2->{},3->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3] | `- p:[1] c: [1] * Step 6: SizeAbstraction 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) 3. f6(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f0,2);(f14,2);(f6,2)} Flow Graph: [0->{1,3},1->{1,2,3},2->{},3->{}] ,We construct a looptree: P: [0,1,2,3] | `- p:[1] c: [1]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,0.0] f0 ~> f6 [A <= 0*K, B <= unknown] f6 ~> f6 [A <= 50*K, B <= B] f6 ~> f14 [A <= A, B <= B] f6 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= 50*K + A] f6 ~> f6 [A <= 50*K, B <= B] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0] f0 ~> f6 [K ~=> A,huge ~=> B] f6 ~> f6 [K ~=> A] f6 ~> f14 [] f6 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f6 ~> f6 [K ~=> A] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> A,huge ~=> B,tick ~+> tick,K ~+> 0.0,K ~+> tick,K ~*> 0.0,K ~*> tick] f0 ~> f14 [K ~=> A,huge ~=> B,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))