YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f4(A,B,C,D,E,F,G) -> f4(A + B,B,C,D,E,F,G) [-1 + -1*B >= 0 && A >= 0] (?,1) 1. f4(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [-1 + -1*B >= 0 && 0 >= 1 + A] (?,1) 2. f5(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,G) [0 >= 1 + B] (1,1) 3. f5(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [B >= 0] (1,1) Signature: {(f4,7);(f5,7);(f6,7)} 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: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f4(A,B,C,D,E,F,G) -> f4(A + B,B,C,D,E,F,G) [-1 + -1*B >= 0 && A >= 0] (?,1) 1. f4(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [-1 + -1*B >= 0 && 0 >= 1 + A] (1,1) 2. f5(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,G) [0 >= 1 + B] (1,1) 3. f5(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [B >= 0] (1,1) Signature: {(f4,7);(f5,7);(f6,7)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f4(A,B,C,D,E,F,G) -> f4(A + B,B,C,D,E,F,G) [-1 + -1*B >= 0 && A >= 0] (?,1) 1. f4(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [-1 + -1*B >= 0 && 0 >= 1 + A] (?,1) 2. f5(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,G) [0 >= 1 + B] (1,1) 3. f5(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [B >= 0] (1,1) 4. f5(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (1,1) 5. f4(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f4,7);(f5,7);(f6,7)} Flow Graph: [0->{0,1,5},1->{},2->{0,1,5},3->{},4->{},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0] c: [0] * Step 4: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. f4(A,B,C,D,E,F,G) -> f4(A + B,B,C,D,E,F,G) [-1 + -1*B >= 0 && A >= 0] (?,1) 1. f4(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [-1 + -1*B >= 0 && 0 >= 1 + A] (?,1) 2. f5(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,G) [0 >= 1 + B] (1,1) 3. f5(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [B >= 0] (1,1) 4. f5(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (1,1) 5. f4(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f4,7);(f5,7);(f6,7)} Flow Graph: [0->{0,1,5},1->{},2->{0,1,5},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 5: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,0.0] f4 ~> f4 [A <= A + B, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f4 ~> f6 [A <= A, B <= B, C <= 0*K, D <= 0*K, E <= 0*K, F <= 0*K, G <= 0*K] f5 ~> f4 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f5 ~> f6 [A <= A, B <= B, C <= 0*K, D <= 0*K, E <= 0*K, F <= 0*K, G <= 0*K] f5 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f4 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.0 <= K + A] f4 ~> f4 [A <= A + B, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,0.0] f4 ~> f4 [A ~+> A,B ~+> A] f4 ~> f6 [K ~=> C,K ~=> D,K ~=> E,K ~=> F,K ~=> G] f5 ~> f4 [] f5 ~> f6 [K ~=> C,K ~=> D,K ~=> E,K ~=> F,K ~=> G] f5 ~> exitus616 [] f4 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~+> 0.0] f4 ~> f4 [A ~+> A,B ~+> A] + Applied Processor: LareProcessor + Details: f5 ~> exitus616 [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> A ,B ~*> A ,K ~*> A] f5 ~> f6 [K ~=> C ,K ~=> D ,K ~=> E ,K ~=> F ,K ~=> G ,A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> A ,B ~*> A ,K ~*> A] + f4> [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> A ,B ~*> A ,K ~*> A] YES(?,O(n^1))