YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f4(0,B,C,D,E) True (1,1) 1. f20(A,B,C,D,E) -> f20(A,1 + B,B,D,E) [-100 + B >= 0 && -200 + A + B >= 0 && -100 + A >= 0 && 199 >= B] (?,1) 2. f20(A,B,C,D,E) -> f31(A,B,C,D,E) [-100 + B >= 0 && -200 + A + B >= 0 && -100 + A >= 0 && B >= 200] (?,1) 3. f4(A,B,C,D,E) -> f4(1 + A,B,C,A,A) [A >= 0 && 99 >= A] (?,1) 4. f4(A,B,C,D,E) -> f20(A,100,C,D,E) [A >= 0 && A >= 100] (?,1) Signature: {(f0,5);(f20,5);(f31,5);(f4,5)} Flow Graph: [0->{3,4},1->{1,2},2->{},3->{3,4},4->{1,2}] + 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,C,D,E) -> f4(0,B,C,D,E) True (1,1) 1. f20(A,B,C,D,E) -> f20(A,1 + B,B,D,E) [-100 + B >= 0 && -200 + A + B >= 0 && -100 + A >= 0 && 199 >= B] (?,1) 2. f20(A,B,C,D,E) -> f31(A,B,C,D,E) [-100 + B >= 0 && -200 + A + B >= 0 && -100 + A >= 0 && B >= 200] (1,1) 3. f4(A,B,C,D,E) -> f4(1 + A,B,C,A,A) [A >= 0 && 99 >= A] (?,1) 4. f4(A,B,C,D,E) -> f20(A,100,C,D,E) [A >= 0 && A >= 100] (1,1) Signature: {(f0,5);(f20,5);(f31,5);(f4,5)} Flow Graph: [0->{3,4},1->{1,2},2->{},3->{3,4},4->{1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4),(4,2)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f4(0,B,C,D,E) True (1,1) 1. f20(A,B,C,D,E) -> f20(A,1 + B,B,D,E) [-100 + B >= 0 && -200 + A + B >= 0 && -100 + A >= 0 && 199 >= B] (?,1) 2. f20(A,B,C,D,E) -> f31(A,B,C,D,E) [-100 + B >= 0 && -200 + A + B >= 0 && -100 + A >= 0 && B >= 200] (1,1) 3. f4(A,B,C,D,E) -> f4(1 + A,B,C,A,A) [A >= 0 && 99 >= A] (?,1) 4. f4(A,B,C,D,E) -> f20(A,100,C,D,E) [A >= 0 && A >= 100] (1,1) Signature: {(f0,5);(f20,5);(f31,5);(f4,5)} Flow Graph: [0->{3},1->{1,2},2->{},3->{3,4},4->{1}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f4(0,B,C,D,E) True (1,1) 1. f20(A,B,C,D,E) -> f20(A,1 + B,B,D,E) [-100 + B >= 0 && -200 + A + B >= 0 && -100 + A >= 0 && 199 >= B] (?,1) 2. f20(A,B,C,D,E) -> f31(A,B,C,D,E) [-100 + B >= 0 && -200 + A + B >= 0 && -100 + A >= 0 && B >= 200] (?,1) 3. f4(A,B,C,D,E) -> f4(1 + A,B,C,A,A) [A >= 0 && 99 >= A] (?,1) 4. f4(A,B,C,D,E) -> f20(A,100,C,D,E) [A >= 0 && A >= 100] (?,1) 5. f20(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f20,5);(f31,5);(f4,5)} Flow Graph: [0->{3,4},1->{1,2,5},2->{},3->{3,4},4->{1,2,5},5->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4),(4,2)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f4(0,B,C,D,E) True (1,1) 1. f20(A,B,C,D,E) -> f20(A,1 + B,B,D,E) [-100 + B >= 0 && -200 + A + B >= 0 && -100 + A >= 0 && 199 >= B] (?,1) 2. f20(A,B,C,D,E) -> f31(A,B,C,D,E) [-100 + B >= 0 && -200 + A + B >= 0 && -100 + A >= 0 && B >= 200] (?,1) 3. f4(A,B,C,D,E) -> f4(1 + A,B,C,A,A) [A >= 0 && 99 >= A] (?,1) 4. f4(A,B,C,D,E) -> f20(A,100,C,D,E) [A >= 0 && A >= 100] (?,1) 5. f20(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f20,5);(f31,5);(f4,5)} Flow Graph: [0->{3},1->{1,2,5},2->{},3->{3,4},4->{1,5},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | +- p:[3] c: [3] | `- p:[1] c: [1] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C,D,E) -> f4(0,B,C,D,E) True (1,1) 1. f20(A,B,C,D,E) -> f20(A,1 + B,B,D,E) [-100 + B >= 0 && -200 + A + B >= 0 && -100 + A >= 0 && 199 >= B] (?,1) 2. f20(A,B,C,D,E) -> f31(A,B,C,D,E) [-100 + B >= 0 && -200 + A + B >= 0 && -100 + A >= 0 && B >= 200] (?,1) 3. f4(A,B,C,D,E) -> f4(1 + A,B,C,A,A) [A >= 0 && 99 >= A] (?,1) 4. f4(A,B,C,D,E) -> f20(A,100,C,D,E) [A >= 0 && A >= 100] (?,1) 5. f20(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f20,5);(f31,5);(f4,5)} Flow Graph: [0->{3},1->{1,2,5},2->{},3->{3,4},4->{1,5},5->{}] ,We construct a looptree: P: [0,1,2,3,4,5] | +- p:[3] c: [3] | `- p:[1] c: [1]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,0.0,0.1] f0 ~> f4 [A <= 0*K, B <= B, C <= C, D <= D, E <= E] f20 ~> f20 [A <= A, B <= 200*K, C <= B, D <= D, E <= E] f20 ~> f31 [A <= A, B <= B, C <= C, D <= D, E <= E] f4 ~> f4 [A <= 100*K, B <= B, C <= C, D <= A, E <= A] f4 ~> f20 [A <= A, B <= 100*K, C <= C, D <= D, E <= E] f20 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E] + Loop: [0.0 <= 100*K + A] f4 ~> f4 [A <= 100*K, B <= B, C <= C, D <= A, E <= A] + Loop: [0.1 <= 200*K + B] f20 ~> f20 [A <= A, B <= 200*K, C <= B, 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,0.0,0.1] f0 ~> f4 [K ~=> A] f20 ~> f20 [B ~=> C,K ~=> B] f20 ~> f31 [] f4 ~> f4 [A ~=> D,A ~=> E,K ~=> A] f4 ~> f20 [K ~=> B] f20 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f4 ~> f4 [A ~=> D,A ~=> E,K ~=> A] + Loop: [B ~+> 0.1,K ~*> 0.1] f20 ~> f20 [B ~=> C,K ~=> B] + Applied Processor: LareProcessor + Details: f0 ~> f31 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> E ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] f0 ~> exitus616 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> E ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] + f4> [A ~=> D ,A ~=> E ,K ~=> A ,K ~=> D ,K ~=> E ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~*> 0.0 ,K ~*> tick] + f20> [B ~=> C,K ~=> B,K ~=> C,B ~+> 0.1,B ~+> tick,tick ~+> tick,K ~*> 0.1,K ~*> tick] YES(?,O(1))