YES(?,POLY) * Step 1: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. l0(A,B) -> l1(A,B) True (1,1) 1. l1(A,B) -> l1(-1 + A,1 + B) [A >= 1] (?,1) 2. l1(A,B) -> l2(A,B) [0 >= A] (?,1) 3. l2(A,B) -> l2(A,-1 + B) [-1*A >= 0 && B >= 1] (?,1) Signature: {(l0,2);(l1,2);(l2,2)} Flow Graph: [0->{1,2},1->{1,2},2->{3},3->{3}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: l0(A,B) -> l1(A,B) True l1(A,B) -> l1(-1 + A,1 + B) [A >= 1] l1(A,B) -> l2(A,B) [0 >= A] l2(A,B) -> l2(A,-1 + B) [-1*A >= 0 && B >= 1] Signature: {(l0,2);(l1,2);(l2,2)} Rule Graph: [0->{1,2},1->{1,2},2->{3},3->{3}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: l0(A,B) -> l1(A,B) True l1(A,B) -> l1(-1 + A,1 + B) [A >= 1] l1(A,B) -> l2(A,B) [0 >= A] l2(A,B) -> l2(A,-1 + B) [-1*A >= 0 && B >= 1] l2(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(l0,2);(l1,2);(l2,2)} Rule Graph: [0->{1,2},1->{1,2},2->{3},3->{3,4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4] | +- p:[1] c: [1] | `- p:[3] c: [3] * Step 4: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: l0(A,B) -> l1(A,B) True l1(A,B) -> l1(-1 + A,1 + B) [A >= 1] l1(A,B) -> l2(A,B) [0 >= A] l2(A,B) -> l2(A,-1 + B) [-1*A >= 0 && B >= 1] l2(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(l0,2);(l1,2);(l2,2)} Rule Graph: [0->{1,2},1->{1,2},2->{3},3->{3,4}] ,We construct a looptree: P: [0,1,2,3,4] | +- p:[1] c: [1] | `- p:[3] c: [3]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,0.0,0.1] l0 ~> l1 [A <= A, B <= B] l1 ~> l1 [A <= A, B <= K + B] l1 ~> l2 [A <= A, B <= B] l2 ~> l2 [A <= A, B <= B] l2 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= K + A] l1 ~> l1 [A <= A, B <= K + B] + Loop: [0.1 <= K + B] l2 ~> l2 [A <= A, B <= B] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.1] l0 ~> l1 [] l1 ~> l1 [B ~+> B,K ~+> B] l1 ~> l2 [] l2 ~> l2 [] l2 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~+> 0.0] l1 ~> l1 [B ~+> B,K ~+> B] + Loop: [B ~+> 0.1,K ~+> 0.1] l2 ~> l2 [] + Applied Processor: Lare + Details: l0 ~> exitus616 [A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.1 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,A ~*> B ,A ~*> 0.1 ,A ~*> tick ,K ~*> B ,K ~*> 0.1 ,K ~*> tick] + l1> [A ~+> 0.0,A ~+> tick,B ~+> B,tick ~+> tick,K ~+> B,K ~+> 0.0,K ~+> tick,A ~*> B,K ~*> B] + l2> [B ~+> 0.1,B ~+> tick,tick ~+> tick,K ~+> 0.1,K ~+> tick] YES(?,POLY)