YES(?,O(n^1)) * Step 1: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalterminatestart(A,B,C) -> evalterminateentryin(A,B,C) True (1,1) 1. evalterminateentryin(A,B,C) -> evalterminatebb1in(B,A,C) True (?,1) 2. evalterminatebb1in(A,B,C) -> evalterminatebbin(A,B,C) [100 >= B && A >= C] (?,1) 3. evalterminatebb1in(A,B,C) -> evalterminatereturnin(A,B,C) [B >= 101] (?,1) 4. evalterminatebb1in(A,B,C) -> evalterminatereturnin(A,B,C) [C >= 1 + A] (?,1) 5. evalterminatebbin(A,B,C) -> evalterminatebb1in(-1 + A,C,1 + B) [A + -1*C >= 0 && 100 + -1*B >= 0] (?,1) 6. evalterminatereturnin(A,B,C) -> evalterminatestop(A,B,C) True (?,1) Signature: {(evalterminatebb1in,3) ;(evalterminatebbin,3) ;(evalterminateentryin,3) ;(evalterminatereturnin,3) ;(evalterminatestart,3) ;(evalterminatestop,3)} Flow Graph: [0->{1},1->{2,3,4},2->{5},3->{6},4->{6},5->{2,3,4},6->{}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalterminatestart(A,B,C) -> evalterminateentryin(A,B,C) True evalterminateentryin(A,B,C) -> evalterminatebb1in(B,A,C) True evalterminatebb1in(A,B,C) -> evalterminatebbin(A,B,C) [100 >= B && A >= C] evalterminatebb1in(A,B,C) -> evalterminatereturnin(A,B,C) [B >= 101] evalterminatebb1in(A,B,C) -> evalterminatereturnin(A,B,C) [C >= 1 + A] evalterminatebbin(A,B,C) -> evalterminatebb1in(-1 + A,C,1 + B) [A + -1*C >= 0 && 100 + -1*B >= 0] evalterminatereturnin(A,B,C) -> evalterminatestop(A,B,C) True Signature: {(evalterminatebb1in,3) ;(evalterminatebbin,3) ;(evalterminateentryin,3) ;(evalterminatereturnin,3) ;(evalterminatestart,3) ;(evalterminatestop,3)} Rule Graph: [0->{1},1->{2,3,4},2->{5},3->{6},4->{6},5->{2,3,4},6->{}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalterminatestart(A,B,C) -> evalterminateentryin(A,B,C) True evalterminateentryin(A,B,C) -> evalterminatebb1in(B,A,C) True evalterminatebb1in(A,B,C) -> evalterminatebbin(A,B,C) [100 >= B && A >= C] evalterminatebb1in(A,B,C) -> evalterminatereturnin(A,B,C) [B >= 101] evalterminatebb1in(A,B,C) -> evalterminatereturnin(A,B,C) [C >= 1 + A] evalterminatebbin(A,B,C) -> evalterminatebb1in(-1 + A,C,1 + B) [A + -1*C >= 0 && 100 + -1*B >= 0] evalterminatereturnin(A,B,C) -> evalterminatestop(A,B,C) True evalterminatestop(A,B,C) -> exitus616(A,B,C) True evalterminatestop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalterminatebb1in,3) ;(evalterminatebbin,3) ;(evalterminateentryin,3) ;(evalterminatereturnin,3) ;(evalterminatestart,3) ;(evalterminatestop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3,4},2->{5},3->{6},4->{6},5->{2,3,4},6->{7,8}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[2,5] c: [2,5] * Step 4: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: evalterminatestart(A,B,C) -> evalterminateentryin(A,B,C) True evalterminateentryin(A,B,C) -> evalterminatebb1in(B,A,C) True evalterminatebb1in(A,B,C) -> evalterminatebbin(A,B,C) [100 >= B && A >= C] evalterminatebb1in(A,B,C) -> evalterminatereturnin(A,B,C) [B >= 101] evalterminatebb1in(A,B,C) -> evalterminatereturnin(A,B,C) [C >= 1 + A] evalterminatebbin(A,B,C) -> evalterminatebb1in(-1 + A,C,1 + B) [A + -1*C >= 0 && 100 + -1*B >= 0] evalterminatereturnin(A,B,C) -> evalterminatestop(A,B,C) True evalterminatestop(A,B,C) -> exitus616(A,B,C) True evalterminatestop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalterminatebb1in,3) ;(evalterminatebbin,3) ;(evalterminateentryin,3) ;(evalterminatereturnin,3) ;(evalterminatestart,3) ;(evalterminatestop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3,4},2->{5},3->{6},4->{6},5->{2,3,4},6->{7,8}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[2,5] c: [2,5]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0] evalterminatestart ~> evalterminateentryin [A <= A, B <= B, C <= C] evalterminateentryin ~> evalterminatebb1in [A <= B, B <= A, C <= C] evalterminatebb1in ~> evalterminatebbin [A <= A, B <= B, C <= C] evalterminatebb1in ~> evalterminatereturnin [A <= A, B <= B, C <= C] evalterminatebb1in ~> evalterminatereturnin [A <= A, B <= B, C <= C] evalterminatebbin ~> evalterminatebb1in [A <= K + A, B <= C, C <= K + B] evalterminatereturnin ~> evalterminatestop [A <= A, B <= B, C <= C] evalterminatestop ~> exitus616 [A <= A, B <= B, C <= C] evalterminatestop ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= 100*K + A + B + C] evalterminatebb1in ~> evalterminatebbin [A <= A, B <= B, C <= C] evalterminatebbin ~> evalterminatebb1in [A <= K + A, B <= C, C <= K + B] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] evalterminatestart ~> evalterminateentryin [] evalterminateentryin ~> evalterminatebb1in [A ~=> B,B ~=> A] evalterminatebb1in ~> evalterminatebbin [] evalterminatebb1in ~> evalterminatereturnin [] evalterminatebb1in ~> evalterminatereturnin [] evalterminatebbin ~> evalterminatebb1in [C ~=> B,A ~+> A,B ~+> C,K ~+> A,K ~+> C] evalterminatereturnin ~> evalterminatestop [] evalterminatestop ~> exitus616 [] evalterminatestop ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0,K ~*> 0.0] evalterminatebb1in ~> evalterminatebbin [] evalterminatebbin ~> evalterminatebb1in [C ~=> B,A ~+> A,B ~+> C,K ~+> A,K ~+> C] + Applied Processor: Lare + Details: evalterminatestart ~> exitus616 [A ~=> B ,B ~=> A ,C ~=> B ,A ~+> B ,A ~+> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,B ~+> 0.0 ,B ~+> tick ,C ~+> B ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> C ,A ~*> A ,A ~*> B ,A ~*> C ,B ~*> A ,B ~*> B ,B ~*> C ,C ~*> A ,C ~*> B ,C ~*> C ,K ~*> A ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] + evalterminatebb1in> [C ~=> B ,A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> C ,B ~+> 0.0 ,B ~+> tick ,C ~+> B ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> C ,A ~*> A ,A ~*> B ,A ~*> C ,B ~*> A ,B ~*> B ,B ~*> C ,C ~*> A ,C ~*> B ,C ~*> C ,K ~*> A ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> tick] YES(?,O(n^1))