YES(?,POLY) * Step 1: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval1(A,B) -> eval2(A,B) [A >= 1] (?,1) 1. eval2(A,B) -> eval2(A,-1 + B) [-1 + A >= 0 && A >= 1 && B >= 1] (?,1) 2. eval2(A,B) -> eval1(-1 + A,B) [-1 + A >= 0 && A >= 1 && 0 >= B] (?,1) 3. start(A,B) -> eval1(A,B) True (1,1) Signature: {(eval1,2);(eval2,2);(start,2)} Flow Graph: [0->{1,2},1->{1,2},2->{0},3->{0}] + Applied Processor: AddSinks + Details: () * Step 2: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval1(A,B) -> eval2(A,B) [A >= 1] (?,1) 1. eval2(A,B) -> eval2(A,-1 + B) [-1 + A >= 0 && A >= 1 && B >= 1] (?,1) 2. eval2(A,B) -> eval1(-1 + A,B) [-1 + A >= 0 && A >= 1 && 0 >= B] (?,1) 3. start(A,B) -> eval1(A,B) True (1,1) 4. eval1(A,B) -> exitus616(A,B) True (?,1) 5. eval2(A,B) -> exitus616(A,B) True (?,1) Signature: {(eval1,2);(eval2,2);(exitus616,2);(start,2)} Flow Graph: [0->{1,2,5},1->{1,2,5},2->{0,4},3->{0,4},4->{},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0,2,1] c: [2] | `- p:[1] c: [1] * Step 3: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. eval1(A,B) -> eval2(A,B) [A >= 1] (?,1) 1. eval2(A,B) -> eval2(A,-1 + B) [-1 + A >= 0 && A >= 1 && B >= 1] (?,1) 2. eval2(A,B) -> eval1(-1 + A,B) [-1 + A >= 0 && A >= 1 && 0 >= B] (?,1) 3. start(A,B) -> eval1(A,B) True (1,1) 4. eval1(A,B) -> exitus616(A,B) True (?,1) 5. eval2(A,B) -> exitus616(A,B) True (?,1) Signature: {(eval1,2);(eval2,2);(exitus616,2);(start,2)} Flow Graph: [0->{1,2,5},1->{1,2,5},2->{0,4},3->{0,4},4->{},5->{}] ,We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0,2,1] c: [2] | `- p:[1] c: [1]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 4: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,0.0,0.0.0] eval1 ~> eval2 [A <= A, B <= B] eval2 ~> eval2 [A <= A, B <= B] eval2 ~> eval1 [A <= A, B <= B] start ~> eval1 [A <= A, B <= B] eval1 ~> exitus616 [A <= A, B <= B] eval2 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= A] eval1 ~> eval2 [A <= A, B <= B] eval2 ~> eval1 [A <= A, B <= B] eval2 ~> eval2 [A <= A, B <= B] + Loop: [0.0.0 <= B] eval2 ~> eval2 [A <= A, B <= B] + Applied Processor: FlowAbstraction + Details: () * Step 5: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.0.0] eval1 ~> eval2 [] eval2 ~> eval2 [] eval2 ~> eval1 [] start ~> eval1 [] eval1 ~> exitus616 [] eval2 ~> exitus616 [] + Loop: [A ~=> 0.0] eval1 ~> eval2 [] eval2 ~> eval1 [] eval2 ~> eval2 [] + Loop: [B ~=> 0.0.0] eval2 ~> eval2 [] + Applied Processor: LareProcessor + Details: start ~> exitus616 [A ~=> 0.0,B ~=> 0.0.0,A ~+> tick,B ~+> tick,tick ~+> tick,A ~*> tick,B ~*> tick] + eval2> [A ~=> 0.0,B ~=> 0.0.0,A ~+> tick,B ~+> tick,tick ~+> tick,A ~*> tick] eval1> [A ~=> 0.0,B ~=> 0.0.0,A ~+> tick,B ~+> tick,tick ~+> tick,A ~*> tick] + eval2> [B ~=> 0.0.0,B ~+> tick,tick ~+> tick] YES(?,POLY)