YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f9(0,D,0) True (1,1) 1. f9(A,B,C) -> f9(A,B,1 + C) [C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A >= 0 && 49 >= C] (?,1) 2. f17(A,B,C) -> f17(1 + A,B,C) [-50 + C >= 0 && -50 + A + C >= 0 && A >= 0 && 49 >= A] (?,1) 3. f17(A,B,C) -> f24(A,B,C) [-50 + C >= 0 && -50 + A + C >= 0 && A >= 0 && A >= 50] (?,1) 4. f9(A,B,C) -> f17(0,B,C) [C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A >= 0 && C >= 50] (?,1) Signature: {(f0,3);(f17,3);(f24,3);(f9,3)} Flow Graph: [0->{1,4},1->{1,4},2->{2,3},3->{},4->{2,3}] + 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,C) -> f9(0,D,0) True (1,1) 1. f9(A,B,C) -> f9(A,B,1 + C) [C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A >= 0 && 49 >= C] (?,1) 2. f17(A,B,C) -> f17(1 + A,B,C) [-50 + C >= 0 && -50 + A + C >= 0 && A >= 0 && 49 >= A] (?,1) 3. f17(A,B,C) -> f24(A,B,C) [-50 + C >= 0 && -50 + A + C >= 0 && A >= 0 && A >= 50] (1,1) 4. f9(A,B,C) -> f17(0,B,C) [C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A >= 0 && C >= 50] (1,1) Signature: {(f0,3);(f17,3);(f24,3);(f9,3)} Flow Graph: [0->{1,4},1->{1,4},2->{2,3},3->{},4->{2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4),(4,3)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f9(0,D,0) True (1,1) 1. f9(A,B,C) -> f9(A,B,1 + C) [C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A >= 0 && 49 >= C] (?,1) 2. f17(A,B,C) -> f17(1 + A,B,C) [-50 + C >= 0 && -50 + A + C >= 0 && A >= 0 && 49 >= A] (?,1) 3. f17(A,B,C) -> f24(A,B,C) [-50 + C >= 0 && -50 + A + C >= 0 && A >= 0 && A >= 50] (1,1) 4. f9(A,B,C) -> f17(0,B,C) [C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A >= 0 && C >= 50] (1,1) Signature: {(f0,3);(f17,3);(f24,3);(f9,3)} Flow Graph: [0->{1},1->{1,4},2->{2,3},3->{},4->{2}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f9(0,D,0) True (1,1) 1. f9(A,B,C) -> f9(A,B,1 + C) [C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A >= 0 && 49 >= C] (?,1) 2. f17(A,B,C) -> f17(1 + A,B,C) [-50 + C >= 0 && -50 + A + C >= 0 && A >= 0 && 49 >= A] (?,1) 3. f17(A,B,C) -> f24(A,B,C) [-50 + C >= 0 && -50 + A + C >= 0 && A >= 0 && A >= 50] (?,1) 4. f9(A,B,C) -> f17(0,B,C) [C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A >= 0 && C >= 50] (?,1) 5. f17(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f0,3);(f17,3);(f24,3);(f9,3)} Flow Graph: [0->{1,4},1->{1,4},2->{2,3,5},3->{},4->{2,3,5},5->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4),(4,3)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f9(0,D,0) True (1,1) 1. f9(A,B,C) -> f9(A,B,1 + C) [C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A >= 0 && 49 >= C] (?,1) 2. f17(A,B,C) -> f17(1 + A,B,C) [-50 + C >= 0 && -50 + A + C >= 0 && A >= 0 && 49 >= A] (?,1) 3. f17(A,B,C) -> f24(A,B,C) [-50 + C >= 0 && -50 + A + C >= 0 && A >= 0 && A >= 50] (?,1) 4. f9(A,B,C) -> f17(0,B,C) [C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A >= 0 && C >= 50] (?,1) 5. f17(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f0,3);(f17,3);(f24,3);(f9,3)} Flow Graph: [0->{1},1->{1,4},2->{2,3,5},3->{},4->{2,5},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | +- p:[1] c: [1] | `- p:[2] c: [2] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C) -> f9(0,D,0) True (1,1) 1. f9(A,B,C) -> f9(A,B,1 + C) [C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A >= 0 && 49 >= C] (?,1) 2. f17(A,B,C) -> f17(1 + A,B,C) [-50 + C >= 0 && -50 + A + C >= 0 && A >= 0 && 49 >= A] (?,1) 3. f17(A,B,C) -> f24(A,B,C) [-50 + C >= 0 && -50 + A + C >= 0 && A >= 0 && A >= 50] (?,1) 4. f9(A,B,C) -> f17(0,B,C) [C >= 0 && A + C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A >= 0 && C >= 50] (?,1) 5. f17(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f0,3);(f17,3);(f24,3);(f9,3)} Flow Graph: [0->{1},1->{1,4},2->{2,3,5},3->{},4->{2,5},5->{}] ,We construct a looptree: P: [0,1,2,3,4,5] | +- p:[1] c: [1] | `- p:[2] c: [2]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,0.0,0.1] f0 ~> f9 [A <= 0*K, B <= unknown, C <= 0*K] f9 ~> f9 [A <= A, B <= B, C <= 50*K] f17 ~> f17 [A <= 50*K, B <= B, C <= C] f17 ~> f24 [A <= A, B <= B, C <= C] f9 ~> f17 [A <= 0*K, B <= B, C <= C] f17 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= 50*K + C] f9 ~> f9 [A <= A, B <= B, C <= 50*K] + Loop: [0.1 <= 50*K + A] f17 ~> f17 [A <= 50*K, B <= B, C <= C] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.1] f0 ~> f9 [K ~=> A,K ~=> C,huge ~=> B] f9 ~> f9 [K ~=> C] f17 ~> f17 [K ~=> A] f17 ~> f24 [] f9 ~> f17 [K ~=> A] f17 ~> exitus616 [] + Loop: [C ~+> 0.0,K ~*> 0.0] f9 ~> f9 [K ~=> C] + Loop: [A ~+> 0.1,K ~*> 0.1] f17 ~> f17 [K ~=> A] + Applied Processor: LareProcessor + Details: f0 ~> f24 [K ~=> A ,K ~=> C ,huge ~=> B ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] f0 ~> exitus616 [K ~=> A ,K ~=> C ,huge ~=> B ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] + f9> [K ~=> C,C ~+> 0.0,C ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + f17> [K ~=> A,A ~+> 0.1,A ~+> tick,tick ~+> tick,K ~*> 0.1,K ~*> tick] YES(?,O(1))