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