YES(?,POLY) * Step 1: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval1(A,B) -> eval2(A,0) [A >= 0] (?,1) 1. eval2(A,B) -> eval2(A,1 + B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] (?,1) 2. eval2(A,B) -> eval1(-1 + A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 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 WORST_CASE(?,POLY) + Considered Problem: Rules: eval1(A,B) -> eval2(A,0) [A >= 0] eval2(A,B) -> eval2(A,1 + B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] eval2(A,B) -> eval1(-1 + A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 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: Unfold WORST_CASE(?,POLY) + Considered Problem: Rules: eval1(A,B) -> eval2(A,0) [A >= 0] eval2(A,B) -> eval2(A,1 + B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] eval2(A,B) -> eval1(-1 + A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 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: Unfold + Details: () * Step 4: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: eval1.0(A,B) -> eval2.1(A,0) [A >= 0] eval1.0(A,B) -> eval2.2(A,0) [A >= 0] eval1.0(A,B) -> eval2.4(A,0) [A >= 0] eval2.1(A,B) -> eval2.1(A,1 + B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] eval2.1(A,B) -> eval2.2(A,1 + B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] eval2.1(A,B) -> eval2.6(A,1 + B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] eval2.2(A,B) -> eval1.0(-1 + A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && B >= A] eval2.2(A,B) -> eval1.5(-1 + A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && B >= A] start.3(A,B) -> eval1.0(A,B) True eval2.4(A,B) -> exitus616.7(A,B) True eval1.5(A,B) -> exitus616.7(A,B) True eval2.6(A,B) -> exitus616.7(A,B) True Signature: {(eval1.0,2);(eval1.5,2);(eval2.1,2);(eval2.2,2);(eval2.4,2);(eval2.6,2);(exitus616.7,2);(start.3,2)} Rule Graph: [0->{3,4,5},1->{6,7},2->{9},3->{3,4,5},4->{6,7},5->{11},6->{0,1,2},7->{10},8->{0,1,2},9->{},10->{},11->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[0,6,1,4,3] c: [0,1,4,6] | `- p:[3] c: [3] * Step 5: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: eval1.0(A,B) -> eval2.1(A,0) [A >= 0] eval1.0(A,B) -> eval2.2(A,0) [A >= 0] eval1.0(A,B) -> eval2.4(A,0) [A >= 0] eval2.1(A,B) -> eval2.1(A,1 + B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] eval2.1(A,B) -> eval2.2(A,1 + B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] eval2.1(A,B) -> eval2.6(A,1 + B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= 1 + B] eval2.2(A,B) -> eval1.0(-1 + A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && B >= A] eval2.2(A,B) -> eval1.5(-1 + A,B) [A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && B >= A] start.3(A,B) -> eval1.0(A,B) True eval2.4(A,B) -> exitus616.7(A,B) True eval1.5(A,B) -> exitus616.7(A,B) True eval2.6(A,B) -> exitus616.7(A,B) True Signature: {(eval1.0,2);(eval1.5,2);(eval2.1,2);(eval2.2,2);(eval2.4,2);(eval2.6,2);(exitus616.7,2);(start.3,2)} Rule Graph: [0->{3,4,5},1->{6,7},2->{9},3->{3,4,5},4->{6,7},5->{11},6->{0,1,2},7->{10},8->{0,1,2},9->{},10->{},11->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[0,6,1,4,3] c: [0,1,4,6] | `- p:[3] c: [3]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,0.0,0.0.0] eval1.0 ~> eval2.1 [A <= A, B <= 0*K] eval1.0 ~> eval2.2 [A <= A, B <= 0*K] eval1.0 ~> eval2.4 [A <= A, B <= 0*K] eval2.1 ~> eval2.1 [A <= A, B <= A] eval2.1 ~> eval2.2 [A <= A, B <= A] eval2.1 ~> eval2.6 [A <= A, B <= A] eval2.2 ~> eval1.0 [A <= K + B, B <= B] eval2.2 ~> eval1.5 [A <= K + B, B <= B] start.3 ~> eval1.0 [A <= A, B <= B] eval2.4 ~> exitus616.7 [A <= A, B <= B] eval1.5 ~> exitus616.7 [A <= A, B <= B] eval2.6 ~> exitus616.7 [A <= A, B <= B] + Loop: [0.0 <= A] eval1.0 ~> eval2.1 [A <= A, B <= 0*K] eval2.2 ~> eval1.0 [A <= K + B, B <= B] eval1.0 ~> eval2.2 [A <= A, B <= 0*K] eval2.1 ~> eval2.2 [A <= A, B <= A] eval2.1 ~> eval2.1 [A <= A, B <= A] + Loop: [0.0.0 <= K + A + B] eval2.1 ~> eval2.1 [A <= A, B <= A] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.0.0] eval1.0 ~> eval2.1 [K ~=> B] eval1.0 ~> eval2.2 [K ~=> B] eval1.0 ~> eval2.4 [K ~=> B] eval2.1 ~> eval2.1 [A ~=> B] eval2.1 ~> eval2.2 [A ~=> B] eval2.1 ~> eval2.6 [A ~=> B] eval2.2 ~> eval1.0 [B ~+> A,K ~+> A] eval2.2 ~> eval1.5 [B ~+> A,K ~+> A] start.3 ~> eval1.0 [] eval2.4 ~> exitus616.7 [] eval1.5 ~> exitus616.7 [] eval2.6 ~> exitus616.7 [] + Loop: [A ~=> 0.0] eval1.0 ~> eval2.1 [K ~=> B] eval2.2 ~> eval1.0 [B ~+> A,K ~+> A] eval1.0 ~> eval2.2 [K ~=> B] eval2.1 ~> eval2.2 [A ~=> B] eval2.1 ~> eval2.1 [A ~=> B] + Loop: [A ~+> 0.0.0,B ~+> 0.0.0,K ~+> 0.0.0] eval2.1 ~> eval2.1 [A ~=> B] + Applied Processor: Lare + Details: start.3 ~> exitus616.7 [A ~=> B ,A ~=> 0.0 ,K ~=> B ,A ~+> A ,A ~+> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> A ,B ~+> 0.0.0 ,B ~+> 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 ,B ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] + eval2.1> [A ~=> B ,A ~=> 0.0 ,K ~=> B ,A ~+> A ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0.0 ,K ~*> tick] eval2.2> [A ~=> B ,A ~=> 0.0 ,K ~=> B ,A ~+> A ,A ~+> B ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,A ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0.0 ,K ~*> tick] eval1.0> [A ~=> B ,A ~=> 0.0 ,K ~=> B ,A ~+> A ,A ~+> B ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,A ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0.0 ,K ~*> tick] + eval2.1> [A ~=> B ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] YES(?,POLY)