YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f5(A,0,C) [A >= 128] (1,1) 1. f0(A,B,C) -> f7(A,0,D) [127 >= A] (1,1) 2. f7(A,B,C) -> f7(A,1 + B,1 + C) [35 >= B] (?,1) 3. f7(A,B,C) -> f5(A,B,C) [B >= 36] (?,1) Signature: {(f0,3);(f5,3);(f7,3)} Flow Graph: [0->{},1->{2,3},2->{2,3},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) -> f5(A,0,C) [A >= 128] (1,1) 1. f0(A,B,C) -> f7(A,0,D) [127 >= A] (1,1) 2. f7(A,B,C) -> f7(A,1 + B,1 + C) [35 >= B] (?,1) 3. f7(A,B,C) -> f5(A,B,C) [B >= 36] (1,1) Signature: {(f0,3);(f5,3);(f7,3)} Flow Graph: [0->{},1->{2,3},2->{2,3},3->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,3)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f5(A,0,C) [A >= 128] (1,1) 1. f0(A,B,C) -> f7(A,0,D) [127 >= A] (1,1) 2. f7(A,B,C) -> f7(A,1 + B,1 + C) [35 >= B] (?,1) 3. f7(A,B,C) -> f5(A,B,C) [B >= 36] (1,1) Signature: {(f0,3);(f5,3);(f7,3)} Flow Graph: [0->{},1->{2},2->{2,3},3->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f5(A,0,C) [A >= 128] (1,1) 1. f0(A,B,C) -> f7(A,0,D) [127 >= A] (1,1) 2. f7(A,B,C) -> f7(A,1 + B,1 + C) [35 >= B] (?,1) 3. f7(A,B,C) -> f5(A,B,C) [B >= 36] (?,1) 4. f7(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);(f5,3);(f7,3)} Flow Graph: [0->{},1->{2,3,4},2->{2,3,4},3->{},4->{},5->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,3)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f5(A,0,C) [A >= 128] (1,1) 1. f0(A,B,C) -> f7(A,0,D) [127 >= A] (1,1) 2. f7(A,B,C) -> f7(A,1 + B,1 + C) [35 >= B] (?,1) 3. f7(A,B,C) -> f5(A,B,C) [B >= 36] (?,1) 4. f7(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);(f5,3);(f7,3)} Flow Graph: [0->{},1->{2,4},2->{2,3,4},3->{},4->{},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[2] c: [2] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C) -> f5(A,0,C) [A >= 128] (1,1) 1. f0(A,B,C) -> f7(A,0,D) [127 >= A] (1,1) 2. f7(A,B,C) -> f7(A,1 + B,1 + C) [35 >= B] (?,1) 3. f7(A,B,C) -> f5(A,B,C) [B >= 36] (?,1) 4. f7(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);(f5,3);(f7,3)} Flow Graph: [0->{},1->{2,4},2->{2,3,4},3->{},4->{},5->{}] ,We construct a looptree: P: [0,1,2,3,4,5] | `- 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] f0 ~> f5 [A <= A, B <= 0*K, C <= C] f0 ~> f7 [A <= A, B <= 0*K, C <= unknown] f7 ~> f7 [A <= A, B <= K + B, C <= K + C] f7 ~> f5 [A <= A, B <= B, C <= C] f7 ~> exitus616 [A <= A, B <= B, C <= C] f0 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= 36*K + B] f7 ~> f7 [A <= A, B <= K + B, C <= K + C] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] f0 ~> f5 [K ~=> B] f0 ~> f7 [K ~=> B,huge ~=> C] f7 ~> f7 [B ~+> B,C ~+> C,K ~+> B,K ~+> C] f7 ~> f5 [] f7 ~> exitus616 [] f0 ~> exitus616 [] + Loop: [B ~+> 0.0,K ~*> 0.0] f7 ~> f7 [B ~+> B,C ~+> C,K ~+> B,K ~+> C] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> B ,huge ~=> C ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> 0.0 ,K ~+> tick ,huge ~+> C ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] f0 ~> f5 [K ~=> B ,huge ~=> C ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> 0.0 ,K ~+> tick ,huge ~+> C ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] + f7> [B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> C ,tick ~+> tick ,K ~+> B ,K ~+> C ,B ~*> B ,B ~*> C ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] YES(?,O(1))