YES(?,PRIMREC) * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. eval1(A,B) -> eval2(1 + A,1) [A >= 0] (?,1) 1. eval2(A,B) -> eval2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] (?,1) 2. eval2(A,B) -> eval1(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + 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: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. eval1(A,B) -> eval2(1 + A,1) [A >= 0] (?,1) 1. eval2(A,B) -> eval2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] (?,1) 2. eval2(A,B) -> eval1(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] (?,1) 3. start(A,B) -> eval1(A,B) True (1,1) Signature: {(eval1,2);(eval2,2);(start,2)} Flow Graph: [0->{1},1->{1,2},2->{0},3->{0}] + Applied Processor: FromIts + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: eval1(A,B) -> eval2(1 + A,1) [A >= 0] eval2(A,B) -> eval2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2(A,B) -> eval1(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] start(A,B) -> eval1(A,B) True Signature: {(eval1,2);(eval2,2);(start,2)} Rule Graph: [0->{1},1->{1,2},2->{0},3->{0}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: eval1.0(A,B) -> eval2.1(1 + A,1) [A >= 0] eval2.1(A,B) -> eval2.1(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2.1(A,B) -> eval2.2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2.2(A,B) -> eval1.0(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] start.3(A,B) -> eval1.0(A,B) True Signature: {(eval1.0,2);(eval2.1,2);(eval2.2,2);(start.3,2)} Rule Graph: [0->{1,2},1->{1,2},2->{3},3->{0},4->{0}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose MAYBE + Considered Problem: Rules: eval1.0(A,B) -> eval2.1(1 + A,1) [A >= 0] eval2.1(A,B) -> eval2.1(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2.1(A,B) -> eval2.2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2.2(A,B) -> eval1.0(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] start.3(A,B) -> eval1.0(A,B) True eval2.1(A,B) -> exitus616(A,B) True eval1.0(A,B) -> exitus616(A,B) True eval2.2(A,B) -> exitus616(A,B) True eval2.1(A,B) -> exitus616(A,B) True Signature: {(eval1.0,2);(eval2.1,2);(eval2.2,2);(exitus616,2);(start.3,2)} Rule Graph: [0->{1,2,5},1->{1,2,8},2->{3,7},3->{0,6},4->{0}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[0,3,2,1] c: [0,2,3] | `- p:[1] c: [1] * Step 6: AbstractSize MAYBE + Considered Problem: (Rules: eval1.0(A,B) -> eval2.1(1 + A,1) [A >= 0] eval2.1(A,B) -> eval2.1(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2.1(A,B) -> eval2.2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2.2(A,B) -> eval1.0(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] start.3(A,B) -> eval1.0(A,B) True eval2.1(A,B) -> exitus616(A,B) True eval1.0(A,B) -> exitus616(A,B) True eval2.2(A,B) -> exitus616(A,B) True eval2.1(A,B) -> exitus616(A,B) True Signature: {(eval1.0,2);(eval2.1,2);(eval2.2,2);(exitus616,2);(start.3,2)} Rule Graph: [0->{1,2,5},1->{1,2,8},2->{3,7},3->{0,6},4->{0}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[0,3,2,1] c: [0,2,3] | `- p:[1] c: [1]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow MAYBE + Considered Problem: Program: Domain: [A,B,0.0,0.0.0] eval1.0 ~> eval2.1 [A <= K + A, B <= K] eval2.1 ~> eval2.1 [A <= A, B <= A + B] eval2.1 ~> eval2.2 [A <= A, B <= A + B] eval2.2 ~> eval1.0 [A <= B, B <= B] start.3 ~> eval1.0 [A <= A, B <= B] eval2.1 ~> exitus616 [A <= A, B <= B] eval1.0 ~> exitus616 [A <= A, B <= B] eval2.2 ~> exitus616 [A <= A, B <= B] eval2.1 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= K + A] eval1.0 ~> eval2.1 [A <= K + A, B <= K] eval2.2 ~> eval1.0 [A <= B, B <= B] eval2.1 ~> eval2.2 [A <= A, B <= A + B] eval2.1 ~> eval2.1 [A <= A, B <= A + B] + Loop: [0.0.0 <= A + B] eval2.1 ~> eval2.1 [A <= A, B <= A + B] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare MAYBE + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.0.0] eval1.0 ~> eval2.1 [K ~=> B,A ~+> A,K ~+> A] eval2.1 ~> eval2.1 [A ~+> B,B ~+> B] eval2.1 ~> eval2.2 [A ~+> B,B ~+> B] eval2.2 ~> eval1.0 [B ~=> A] start.3 ~> eval1.0 [] eval2.1 ~> exitus616 [] eval1.0 ~> exitus616 [] eval2.2 ~> exitus616 [] eval2.1 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~+> 0.0] eval1.0 ~> eval2.1 [K ~=> B,A ~+> A,K ~+> A] eval2.2 ~> eval1.0 [B ~=> A] eval2.1 ~> eval2.2 [A ~+> B,B ~+> B] eval2.1 ~> eval2.1 [A ~+> B,B ~+> B] + Loop: [A ~+> 0.0.0,B ~+> 0.0.0] eval2.1 ~> eval2.1 [A ~+> B,B ~+> B] + Applied Processor: Lare + Details: start.3 ~> exitus616 [K ~=> B ,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 ,K ~^> 0.0.0 ,K ~^> tick] + eval2.2> [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 ~*> 0.0.0 ,A ~*> 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] eval2.1> [K ~=> B ,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 ~*> 0.0.0 ,A ~*> 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] eval1.0> [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 ~*> 0.0.0 ,A ~*> 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] + eval2.1> [A ~+> B ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,A ~*> B ,B ~*> B] YES(?,PRIMREC)