YES(?,PRIMREC) * Step 1: FromIts MAYBE + Considered Problem: Rules: 0. eval1(A,B) -> eval2(A,1) [A >= 0] (?,1) 1. eval2(A,B) -> eval2(A,2*B) [-1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && A >= 1 + B] (?,1) 2. eval2(A,B) -> eval1(-1 + A,B) [-1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= A] (?,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: FromIts + Details: () * Step 2: AddSinks MAYBE + Considered Problem: Rules: eval1(A,B) -> eval2(A,1) [A >= 0] eval2(A,B) -> eval2(A,2*B) [-1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && A >= 1 + B] eval2(A,B) -> eval1(-1 + A,B) [-1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= A] start(A,B) -> eval1(A,B) True Signature: {(eval1,2);(eval2,2);(start,2)} Rule Graph: [0->{1,2},1->{1,2},2->{0},3->{0}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose MAYBE + Considered Problem: Rules: eval1(A,B) -> eval2(A,1) [A >= 0] eval2(A,B) -> eval2(A,2*B) [-1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && A >= 1 + B] eval2(A,B) -> eval1(-1 + A,B) [-1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= A] start(A,B) -> eval1(A,B) True eval2(A,B) -> exitus616(A,B) True eval1(A,B) -> exitus616(A,B) True eval2(A,B) -> exitus616(A,B) True Signature: {(eval1,2);(eval2,2);(exitus616,2);(start,2)} Rule Graph: [0->{1,2,4},1->{1,2,6},2->{0,5},3->{0}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[0,2,1] c: [0,2] | `- p:[1] c: [1] * Step 4: AbstractSize MAYBE + Considered Problem: (Rules: eval1(A,B) -> eval2(A,1) [A >= 0] eval2(A,B) -> eval2(A,2*B) [-1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && A >= 1 + B] eval2(A,B) -> eval1(-1 + A,B) [-1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= A] start(A,B) -> eval1(A,B) True eval2(A,B) -> exitus616(A,B) True eval1(A,B) -> exitus616(A,B) True eval2(A,B) -> exitus616(A,B) True Signature: {(eval1,2);(eval2,2);(exitus616,2);(start,2)} Rule Graph: [0->{1,2,4},1->{1,2,6},2->{0,5},3->{0}] ,We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[0,2,1] c: [0,2] | `- p:[1] c: [1]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow MAYBE + Considered Problem: Program: Domain: [A,B,0.0,0.0.0] eval1 ~> eval2 [A <= A, B <= K] eval2 ~> eval2 [A <= A, B <= A + B] eval2 ~> eval1 [A <= B, B <= B] start ~> eval1 [A <= A, B <= B] eval2 ~> exitus616 [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 <= K] eval2 ~> eval1 [A <= B, B <= B] eval2 ~> eval2 [A <= A, B <= A + B] + Loop: [0.0.0 <= K + A + B] eval2 ~> eval2 [A <= A, B <= A + B] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare MAYBE + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.0.0] eval1 ~> eval2 [K ~=> B] eval2 ~> eval2 [A ~+> B,B ~+> B] eval2 ~> eval1 [B ~=> A] start ~> eval1 [] eval2 ~> exitus616 [] eval1 ~> exitus616 [] eval2 ~> exitus616 [] + Loop: [A ~=> 0.0] eval1 ~> eval2 [K ~=> B] eval2 ~> eval1 [B ~=> A] eval2 ~> eval2 [A ~+> B,B ~+> B] + Loop: [A ~+> 0.0.0,B ~+> 0.0.0,K ~+> 0.0.0] eval2 ~> eval2 [A ~+> B,B ~+> B] + Applied Processor: Lare + Details: start ~> exitus616 [A ~=> 0.0 ,K ~=> A ,K ~=> B ,K ~=> 0.0 ,A ~+> A ,A ~+> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,A ~*> 0.0 ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> A ,A ~^> B ,A ~^> 0.0 ,A ~^> 0.0.0 ,A ~^> tick ,K ~^> A ,K ~^> B ,K ~^> 0.0.0 ,K ~^> tick] + eval2> [A ~=> 0.0 ,K ~=> A ,K ~=> B ,A ~+> A ,A ~+> B ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> A ,A ~^> B ,A ~^> 0.0.0 ,A ~^> tick] eval1> [A ~=> 0.0 ,K ~=> A ,K ~=> B ,A ~+> A ,A ~+> B ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> A ,A ~^> B ,A ~^> 0.0.0 ,A ~^> tick] + eval2> [A ~+> B ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> B ,B ~*> B ,K ~*> B] YES(?,PRIMREC)