YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B,C,D,E) -> f300(1 + A,B,C,D,E) [100 >= A && B >= 1] (?,1) 1. f300(A,B,C,D,E) -> f3(A,B,0,0,0) [A >= 101] (?,1) 2. f2(A,B,C,D,E) -> f300(1,B,C,D,E) [B >= 1] (1,1) 3. f2(A,B,C,D,E) -> f3(0,B,0,0,0) [0 >= B] (1,1) Signature: {(f2,5);(f3,5);(f300,5)} Flow Graph: [0->{0,1},1->{},2->{0,1},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. f300(A,B,C,D,E) -> f300(1 + A,B,C,D,E) [100 >= A && B >= 1] (?,1) 1. f300(A,B,C,D,E) -> f3(A,B,0,0,0) [A >= 101] (1,1) 2. f2(A,B,C,D,E) -> f300(1,B,C,D,E) [B >= 1] (1,1) 3. f2(A,B,C,D,E) -> f3(0,B,0,0,0) [0 >= B] (1,1) Signature: {(f2,5);(f3,5);(f300,5)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,1)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B,C,D,E) -> f300(1 + A,B,C,D,E) [100 >= A && B >= 1] (?,1) 1. f300(A,B,C,D,E) -> f3(A,B,0,0,0) [A >= 101] (1,1) 2. f2(A,B,C,D,E) -> f300(1,B,C,D,E) [B >= 1] (1,1) 3. f2(A,B,C,D,E) -> f3(0,B,0,0,0) [0 >= B] (1,1) Signature: {(f2,5);(f3,5);(f300,5)} Flow Graph: [0->{0,1},1->{},2->{0},3->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B,C,D,E) -> f300(1 + A,B,C,D,E) [100 >= A && B >= 1] (?,1) 1. f300(A,B,C,D,E) -> f3(A,B,0,0,0) [A >= 101] (?,1) 2. f2(A,B,C,D,E) -> f300(1,B,C,D,E) [B >= 1] (1,1) 3. f2(A,B,C,D,E) -> f3(0,B,0,0,0) [0 >= B] (1,1) 4. f2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (1,1) 5. f300(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f2,5);(f3,5);(f300,5)} Flow Graph: [0->{0,1,5},1->{},2->{0,1,5},3->{},4->{},5->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,1)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B,C,D,E) -> f300(1 + A,B,C,D,E) [100 >= A && B >= 1] (?,1) 1. f300(A,B,C,D,E) -> f3(A,B,0,0,0) [A >= 101] (?,1) 2. f2(A,B,C,D,E) -> f300(1,B,C,D,E) [B >= 1] (1,1) 3. f2(A,B,C,D,E) -> f3(0,B,0,0,0) [0 >= B] (1,1) 4. f2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (1,1) 5. f300(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f2,5);(f3,5);(f300,5)} Flow Graph: [0->{0,1,5},1->{},2->{0,5},3->{},4->{},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0] c: [0] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f300(A,B,C,D,E) -> f300(1 + A,B,C,D,E) [100 >= A && B >= 1] (?,1) 1. f300(A,B,C,D,E) -> f3(A,B,0,0,0) [A >= 101] (?,1) 2. f2(A,B,C,D,E) -> f300(1,B,C,D,E) [B >= 1] (1,1) 3. f2(A,B,C,D,E) -> f3(0,B,0,0,0) [0 >= B] (1,1) 4. f2(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (1,1) 5. f300(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f2,5);(f3,5);(f300,5)} Flow Graph: [0->{0,1,5},1->{},2->{0,5},3->{},4->{},5->{}] ,We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0] c: [0]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,0.0] f300 ~> f300 [A <= K + A, B <= B, C <= C, D <= D, E <= E] f300 ~> f3 [A <= A, B <= B, C <= 0*K, D <= 0*K, E <= 0*K] f2 ~> f300 [A <= K, B <= B, C <= C, D <= D, E <= E] f2 ~> f3 [A <= 0*K, B <= B, C <= 0*K, D <= 0*K, E <= 0*K] f2 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E] f300 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E] + Loop: [0.0 <= 101*K + A] f300 ~> f300 [A <= K + A, B <= B, C <= C, D <= D, E <= E] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,0.0] f300 ~> f300 [A ~+> A,K ~+> A] f300 ~> f3 [K ~=> C,K ~=> D,K ~=> E] f2 ~> f300 [K ~=> A] f2 ~> f3 [K ~=> A,K ~=> C,K ~=> D,K ~=> E] f2 ~> exitus616 [] f300 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f300 ~> f300 [A ~+> A,K ~+> A] + Applied Processor: LareProcessor + Details: f2 ~> exitus616 [K ~=> A,tick ~+> tick,K ~+> A,K ~+> 0.0,K ~+> tick,K ~*> A,K ~*> 0.0,K ~*> tick] f2 ~> f3 [K ~=> A ,K ~=> C ,K ~=> D ,K ~=> E ,tick ~+> tick ,K ~+> A ,K ~+> 0.0 ,K ~+> tick ,K ~*> A ,K ~*> 0.0 ,K ~*> tick] + f300> [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,A ~*> A ,K ~*> A ,K ~*> 0.0 ,K ~*> tick] YES(?,O(1))