YES(?,POLY) * Step 1: UnsatRules WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval(A,B,C) -> eval(-1 + A,B,C) [A >= 1 + B] (?,1) 1. eval(A,B,C) -> eval(-1 + A,B,C) [C >= 1 + B && A >= 1 + B] (?,1) 2. eval(A,B,C) -> eval(A,B,-1 + C) [A >= 1 + B && B >= A && C >= 1 + B] (?,1) 3. eval(A,B,C) -> eval(A,B,-1 + C) [C >= 1 + B && B >= A] (?,1) 4. eval(A,B,C) -> eval(A,B,C) [A >= 1 + B && B >= A && B >= C] (?,1) 5. eval(A,B,C) -> eval(A,B,C) [C >= 1 + B && B >= A && B >= C] (?,1) 6. start(A,B,C) -> eval(A,B,C) True (1,1) Signature: {(eval,3);(start,3)} Flow Graph: [0->{0,1,2,3,4,5},1->{0,1,2,3,4,5},2->{0,1,2,3,4,5},3->{0,1,2,3,4,5},4->{0,1,2,3,4,5},5->{0,1,2,3,4,5} ,6->{0,1,2,3,4,5}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [2,4,5] * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval(A,B,C) -> eval(-1 + A,B,C) [A >= 1 + B] (?,1) 1. eval(A,B,C) -> eval(-1 + A,B,C) [C >= 1 + B && A >= 1 + B] (?,1) 3. eval(A,B,C) -> eval(A,B,-1 + C) [C >= 1 + B && B >= A] (?,1) 6. start(A,B,C) -> eval(A,B,C) True (1,1) Signature: {(eval,3);(start,3)} Flow Graph: [0->{0,1,3},1->{0,1,3},3->{0,1,3},6->{0,1,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,0),(3,1)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval(A,B,C) -> eval(-1 + A,B,C) [A >= 1 + B] (?,1) 1. eval(A,B,C) -> eval(-1 + A,B,C) [C >= 1 + B && A >= 1 + B] (?,1) 3. eval(A,B,C) -> eval(A,B,-1 + C) [C >= 1 + B && B >= A] (?,1) 6. start(A,B,C) -> eval(A,B,C) True (1,1) Signature: {(eval,3);(start,3)} Flow Graph: [0->{0,1,3},1->{0,1,3},3->{3},6->{0,1,3}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval(A,B,C) -> eval(-1 + A,B,C) [A >= 1 + B] (?,1) 1. eval(A,B,C) -> eval(-1 + A,B,C) [C >= 1 + B && A >= 1 + B] (?,1) 3. eval(A,B,C) -> eval(A,B,-1 + C) [C >= 1 + B && B >= A] (?,1) 6. start(A,B,C) -> eval(A,B,C) True (1,1) 7. eval(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(eval,3);(exitus616,3);(start,3)} Flow Graph: [0->{0,1,3,7},1->{0,1,3,7},3->{0,1,3,7},6->{0,1,3,7},7->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,0),(3,1)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval(A,B,C) -> eval(-1 + A,B,C) [A >= 1 + B] (?,1) 1. eval(A,B,C) -> eval(-1 + A,B,C) [C >= 1 + B && A >= 1 + B] (?,1) 3. eval(A,B,C) -> eval(A,B,-1 + C) [C >= 1 + B && B >= A] (?,1) 6. start(A,B,C) -> eval(A,B,C) True (1,1) 7. eval(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(eval,3);(exitus616,3);(start,3)} Flow Graph: [0->{0,1,3,7},1->{0,1,3,7},3->{3,7},6->{0,1,3,7},7->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,3,6,7] | +- p:[0,1] c: [1] | | | `- p:[0] c: [0] | `- p:[3] c: [3] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. eval(A,B,C) -> eval(-1 + A,B,C) [A >= 1 + B] (?,1) 1. eval(A,B,C) -> eval(-1 + A,B,C) [C >= 1 + B && A >= 1 + B] (?,1) 3. eval(A,B,C) -> eval(A,B,-1 + C) [C >= 1 + B && B >= A] (?,1) 6. start(A,B,C) -> eval(A,B,C) True (1,1) 7. eval(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(eval,3);(exitus616,3);(start,3)} Flow Graph: [0->{0,1,3,7},1->{0,1,3,7},3->{3,7},6->{0,1,3,7},7->{}] ,We construct a looptree: P: [0,1,3,6,7] | +- p:[0,1] c: [1] | | | `- p:[0] c: [0] | `- p:[3] c: [3]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0,0.1] eval ~> eval [A <= A + B, B <= B, C <= C] eval ~> eval [A <= A + B, B <= B, C <= C] eval ~> eval [A <= A, B <= B, C <= B + C] start ~> eval [A <= A, B <= B, C <= C] eval ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= A + B] eval ~> eval [A <= A + B, B <= B, C <= C] eval ~> eval [A <= A + B, B <= B, C <= C] + Loop: [0.0.0 <= A + B] eval ~> eval [A <= A + B, B <= B, C <= C] + Loop: [0.1 <= B + C] eval ~> eval [A <= A, B <= B, C <= B + C] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0,0.1] eval ~> eval [A ~+> A,B ~+> A] eval ~> eval [A ~+> A,B ~+> A] eval ~> eval [B ~+> C,C ~+> C] start ~> eval [] eval ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0] eval ~> eval [A ~+> A,B ~+> A] eval ~> eval [A ~+> A,B ~+> A] + Loop: [A ~+> 0.0.0,B ~+> 0.0.0] eval ~> eval [A ~+> A,B ~+> A] + Loop: [B ~+> 0.1,C ~+> 0.1] eval ~> eval [B ~+> C,C ~+> C] + Applied Processor: LareProcessor + Details: start ~> exitus616 [A ~+> A ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> A ,B ~+> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> 0.1 ,B ~+> tick ,C ~+> C ,C ~+> 0.1 ,C ~+> tick ,tick ~+> tick ,A ~*> A ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> A ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,C ~*> C ,A ~^> A ,B ~^> A] + eval> [A ~+> A ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> A ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,A ~*> A ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> A ,B ~*> 0.0.0 ,B ~*> tick ,A ~^> A ,B ~^> A] + eval> [A ~+> A ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> A ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,A ~*> A ,B ~*> A] + eval> [B ~+> C ,B ~+> 0.1 ,B ~+> tick ,C ~+> C ,C ~+> 0.1 ,C ~+> tick ,tick ~+> tick ,B ~*> C ,C ~*> C] YES(?,POLY)