YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f4(A,B,C) -> f5(A,B,1) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && 0 >= A && 0 >= B] (?,1) 1. f0(A,B,C) -> f2(A,B,1) [A >= 1] (1,1) 2. f4(A,B,C) -> f4(A,-1 + B,C) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && B >= 1] (?,1) 3. f0(A,B,C) -> f4(A,B,0) [0 >= A] (1,1) Signature: {(f0,3);(f2,3);(f4,3);(f5,3)} Flow Graph: [0->{},1->{},2->{0,2},3->{0,2}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f4(A,B,C) -> f5(A,B,1) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && 0 >= A && 0 >= B] (1,1) 1. f0(A,B,C) -> f2(A,B,1) [A >= 1] (1,1) 2. f4(A,B,C) -> f4(A,-1 + B,C) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && B >= 1] (?,1) 3. f0(A,B,C) -> f4(A,B,0) [0 >= A] (1,1) Signature: {(f0,3);(f2,3);(f4,3);(f5,3)} Flow Graph: [0->{},1->{},2->{0,2},3->{0,2}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f4(A,B,C) -> f5(A,B,1) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && 0 >= A && 0 >= B] (?,1) 1. f0(A,B,C) -> f2(A,B,1) [A >= 1] (1,1) 2. f4(A,B,C) -> f4(A,-1 + B,C) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && B >= 1] (?,1) 3. f0(A,B,C) -> f4(A,B,0) [0 >= A] (1,1) 4. f4(A,B,C) -> exitus616(A,B,C) True (?,1) 5. f0(A,B,C) -> exitus616(A,B,C) True (1,1) Signature: {(exitus616,3);(f0,3);(f2,3);(f4,3);(f5,3)} Flow Graph: [0->{},1->{},2->{0,2,4},3->{0,2,4},4->{},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[2] c: [2] * Step 4: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. f4(A,B,C) -> f5(A,B,1) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && 0 >= A && 0 >= B] (?,1) 1. f0(A,B,C) -> f2(A,B,1) [A >= 1] (1,1) 2. f4(A,B,C) -> f4(A,-1 + B,C) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && B >= 1] (?,1) 3. f0(A,B,C) -> f4(A,B,0) [0 >= A] (1,1) 4. f4(A,B,C) -> exitus616(A,B,C) True (?,1) 5. f0(A,B,C) -> exitus616(A,B,C) True (1,1) Signature: {(exitus616,3);(f0,3);(f2,3);(f4,3);(f5,3)} Flow Graph: [0->{},1->{},2->{0,2,4},3->{0,2,4},4->{},5->{}] ,We construct a looptree: P: [0,1,2,3,4,5] | `- p:[2] c: [2]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0] f4 ~> f5 [A <= A, B <= B, C <= K] f0 ~> f2 [A <= A, B <= B, C <= K] f4 ~> f4 [A <= A, B <= B, C <= C] f0 ~> f4 [A <= A, B <= B, C <= 0*K] f4 ~> exitus616 [A <= A, B <= B, C <= C] f0 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= B] f4 ~> f4 [A <= A, B <= B, C <= C] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] f4 ~> f5 [K ~=> C] f0 ~> f2 [K ~=> C] f4 ~> f4 [] f0 ~> f4 [K ~=> C] f4 ~> exitus616 [] f0 ~> exitus616 [] + Loop: [B ~=> 0.0] f4 ~> f4 [] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [B ~=> 0.0,K ~=> C,B ~+> tick,tick ~+> tick] f0 ~> f5 [B ~=> 0.0,K ~=> C,B ~+> tick,tick ~+> tick] f0 ~> f2 [K ~=> C] + f4> [B ~=> 0.0,B ~+> tick,tick ~+> tick] YES(?,O(n^1))