YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f1(A,B,C) -> f1(A,1 + B,C) [-1 + B + -1*C >= 0 && A >= 1 + B] (?,1) 1. f3(A,B,C) -> f1(A,B,C) [B >= 1 + C] (1,1) 2. f1(A,B,C) -> f1(A,B,1 + C) [-1 + B + -1*C >= 0 && B >= 2 + C && B >= A] (?,1) Signature: {(f1,3);(f3,3)} Flow Graph: [0->{0,2},1->{0,2},2->{0,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,0)] * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f1(A,B,C) -> f1(A,1 + B,C) [-1 + B + -1*C >= 0 && A >= 1 + B] (?,1) 1. f3(A,B,C) -> f1(A,B,C) [B >= 1 + C] (1,1) 2. f1(A,B,C) -> f1(A,B,1 + C) [-1 + B + -1*C >= 0 && B >= 2 + C && B >= A] (?,1) Signature: {(f1,3);(f3,3)} Flow Graph: [0->{0,2},1->{0,2},2->{2}] + Applied Processor: AddSinks + Details: () * Step 3: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f1(A,B,C) -> f1(A,1 + B,C) [-1 + B + -1*C >= 0 && A >= 1 + B] (?,1) 1. f3(A,B,C) -> f1(A,B,C) [B >= 1 + C] (1,1) 2. f1(A,B,C) -> f1(A,B,1 + C) [-1 + B + -1*C >= 0 && B >= 2 + C && B >= A] (?,1) 3. f1(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f1,3);(f3,3)} Flow Graph: [0->{0,2,3},1->{0,2,3},2->{0,2,3},3->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,0)] * Step 4: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f1(A,B,C) -> f1(A,1 + B,C) [-1 + B + -1*C >= 0 && A >= 1 + B] (?,1) 1. f3(A,B,C) -> f1(A,B,C) [B >= 1 + C] (1,1) 2. f1(A,B,C) -> f1(A,B,1 + C) [-1 + B + -1*C >= 0 && B >= 2 + C && B >= A] (?,1) 3. f1(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f1,3);(f3,3)} Flow Graph: [0->{0,2,3},1->{0,2,3},2->{2,3},3->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3] | +- p:[0] c: [0] | `- p:[2] c: [2] * Step 5: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. f1(A,B,C) -> f1(A,1 + B,C) [-1 + B + -1*C >= 0 && A >= 1 + B] (?,1) 1. f3(A,B,C) -> f1(A,B,C) [B >= 1 + C] (1,1) 2. f1(A,B,C) -> f1(A,B,1 + C) [-1 + B + -1*C >= 0 && B >= 2 + C && B >= A] (?,1) 3. f1(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f1,3);(f3,3)} Flow Graph: [0->{0,2,3},1->{0,2,3},2->{2,3},3->{}] ,We construct a looptree: P: [0,1,2,3] | +- p:[0] c: [0] | `- p:[2] c: [2]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 6: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0,0.1] f1 ~> f1 [A <= A, B <= K + B, C <= C] f3 ~> f1 [A <= A, B <= B, C <= C] f1 ~> f1 [A <= A, B <= B, C <= B + C] f1 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= A + B] f1 ~> f1 [A <= A, B <= K + B, C <= C] + Loop: [0.1 <= B + C] f1 ~> f1 [A <= A, B <= B, C <= B + C] + Applied Processor: FlowAbstraction + Details: () * Step 7: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.1] f1 ~> f1 [B ~+> B,K ~+> B] f3 ~> f1 [] f1 ~> f1 [B ~+> C,C ~+> C] f1 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0] f1 ~> f1 [B ~+> B,K ~+> B] + Loop: [B ~+> 0.1,C ~+> 0.1] f1 ~> f1 [B ~+> C,C ~+> C] + Applied Processor: LareProcessor + Details: f3 ~> exitus616 [A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> C ,B ~+> 0.0 ,B ~+> 0.1 ,B ~+> tick ,C ~+> C ,C ~+> 0.1 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,A ~*> B ,B ~*> B ,B ~*> C ,C ~*> C ,K ~*> B] + f1> [A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,A ~*> B ,B ~*> B ,K ~*> B] + f1> [B ~+> C,B ~+> 0.1,B ~+> tick,C ~+> C,C ~+> 0.1,C ~+> tick,tick ~+> tick,B ~*> C,C ~*> C] YES(?,O(n^1))