YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 1. f4(A,B,C) -> f3(1 + -1*A,B,0) [1 + -1*C >= 0 && -1 + C >= 0 && A >= 1 && C = 1] (?,1) 2. f3(A,B,C) -> f4(-1 + -1*A,B,1) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && 0 >= 1 + A && 0 >= C] (?,1) 3. f3(A,B,C) -> f7(0,D,C) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A = 0] (?,1) 4. f4(A,B,C) -> f7(0,D,C) [1 + -1*C >= 0 && -1 + C >= 0 && A = 0] (?,1) Signature: {(f3,3);(f4,3);(f6,3);(f7,3)} Flow Graph: [0->{1,4},1->{2,3},2->{1,4},3->{},4->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 1. f4(A,B,C) -> f3(1 + -1*A,B,0) [1 + -1*C >= 0 && -1 + C >= 0 && A >= 1 && C = 1] (?,1) 2. f3(A,B,C) -> f4(-1 + -1*A,B,1) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && 0 >= 1 + A && 0 >= C] (?,1) 3. f3(A,B,C) -> f7(0,D,C) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A = 0] (1,1) 4. f4(A,B,C) -> f7(0,D,C) [1 + -1*C >= 0 && -1 + C >= 0 && A = 0] (1,1) Signature: {(f3,3);(f4,3);(f6,3);(f7,3)} Flow Graph: [0->{1,4},1->{2,3},2->{1,4},3->{},4->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 1. f4(A,B,C) -> f3(1 + -1*A,B,0) [1 + -1*C >= 0 && -1 + C >= 0 && A >= 1 && C = 1] (?,1) 2. f3(A,B,C) -> f4(-1 + -1*A,B,1) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && 0 >= 1 + A && 0 >= C] (?,1) 3. f3(A,B,C) -> f7(0,D,C) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A = 0] (1,1) 4. f4(A,B,C) -> f7(0,D,C) [1 + -1*C >= 0 && -1 + C >= 0 && A = 0] (1,1) Signature: {(f3,3);(f4,3);(f6,3);(f7,3)} Flow Graph: [0->{1},1->{2,3},2->{1,4},3->{},4->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 1. f4(A,B,C) -> f3(1 + -1*A,B,0) [1 + -1*C >= 0 && -1 + C >= 0 && A >= 1 && C = 1] (?,1) 2. f3(A,B,C) -> f4(-1 + -1*A,B,1) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && 0 >= 1 + A && 0 >= C] (?,1) 3. f3(A,B,C) -> f7(0,D,C) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A = 0] (?,1) 4. f4(A,B,C) -> f7(0,D,C) [1 + -1*C >= 0 && -1 + C >= 0 && A = 0] (?,1) 5. f3(A,B,C) -> exitus616(A,B,C) True (?,1) 6. f4(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f3,3);(f4,3);(f6,3);(f7,3)} Flow Graph: [0->{1,4,6},1->{2,3,5},2->{1,4,6},3->{},4->{},5->{},6->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 1. f4(A,B,C) -> f3(1 + -1*A,B,0) [1 + -1*C >= 0 && -1 + C >= 0 && A >= 1 && C = 1] (?,1) 2. f3(A,B,C) -> f4(-1 + -1*A,B,1) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && 0 >= 1 + A && 0 >= C] (?,1) 3. f3(A,B,C) -> f7(0,D,C) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A = 0] (?,1) 4. f4(A,B,C) -> f7(0,D,C) [1 + -1*C >= 0 && -1 + C >= 0 && A = 0] (?,1) 5. f3(A,B,C) -> exitus616(A,B,C) True (?,1) 6. f4(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f3,3);(f4,3);(f6,3);(f7,3)} Flow Graph: [0->{1,6},1->{2,3,5},2->{1,4,6},3->{},4->{},5->{},6->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[1,2] c: [2] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 1. f4(A,B,C) -> f3(1 + -1*A,B,0) [1 + -1*C >= 0 && -1 + C >= 0 && A >= 1 && C = 1] (?,1) 2. f3(A,B,C) -> f4(-1 + -1*A,B,1) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && 0 >= 1 + A && 0 >= C] (?,1) 3. f3(A,B,C) -> f7(0,D,C) [-1*C >= 0 && -1*A + -1*C >= 0 && C >= 0 && -1*A + C >= 0 && -1*A >= 0 && A = 0] (?,1) 4. f4(A,B,C) -> f7(0,D,C) [1 + -1*C >= 0 && -1 + C >= 0 && A = 0] (?,1) 5. f3(A,B,C) -> exitus616(A,B,C) True (?,1) 6. f4(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f3,3);(f4,3);(f6,3);(f7,3)} Flow Graph: [0->{1,6},1->{2,3,5},2->{1,4,6},3->{},4->{},5->{},6->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[1,2] c: [2]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0] f6 ~> f4 [A <= A, B <= B, C <= K] f4 ~> f3 [A <= A, B <= B, C <= 0*K] f3 ~> f4 [A <= A, B <= B, C <= K] f3 ~> f7 [A <= 0*K, B <= unknown, C <= C] f4 ~> f7 [A <= 0*K, B <= unknown, C <= C] f3 ~> exitus616 [A <= A, B <= B, C <= C] f4 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A] f4 ~> f3 [A <= A, B <= B, C <= 0*K] f3 ~> f4 [A <= A, B <= B, C <= K] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] f6 ~> f4 [K ~=> C] f4 ~> f3 [K ~=> C] f3 ~> f4 [K ~=> C] f3 ~> f7 [K ~=> A,huge ~=> B] f4 ~> f7 [K ~=> A,huge ~=> B] f3 ~> exitus616 [] f4 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~+> 0.0] f4 ~> f3 [K ~=> C] f3 ~> f4 [K ~=> C] + Applied Processor: LareProcessor + Details: f6 ~> exitus616 [K ~=> C,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick,A ~*> tick,K ~*> tick] f6 ~> f7 [K ~=> A ,K ~=> C ,huge ~=> B ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> tick ,K ~*> tick] + f3> [K ~=> C,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] f4> [K ~=> C,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] YES(?,POLY)