YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalSimpleMultiplestart(A,B,C,D) -> evalSimpleMultipleentryin(A,B,C,D) True (1,1) 1. evalSimpleMultipleentryin(A,B,C,D) -> evalSimpleMultiplebb3in(0,0,C,D) True (?,1) 2. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplebbin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 3. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplereturnin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C] (?,1) 4. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb1in(A,B,C,D) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + A] 5. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb2in(A,B,C,D) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= D] 6. evalSimpleMultiplebb1in(A,B,C,D) -> evalSimpleMultiplebb3in(1 + A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalSimpleMultiplebb2in(A,B,C,D) -> evalSimpleMultiplebb3in(A,1 + B,C,D) [A + -1*D >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 8. evalSimpleMultiplereturnin(A,B,C,D) -> evalSimpleMultiplestop(A,B,C,D) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (?,1) Signature: {(evalSimpleMultiplebb1in,4) ;(evalSimpleMultiplebb2in,4) ;(evalSimpleMultiplebb3in,4) ;(evalSimpleMultiplebbin,4) ;(evalSimpleMultipleentryin,4) ;(evalSimpleMultiplereturnin,4) ;(evalSimpleMultiplestart,4) ;(evalSimpleMultiplestop,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2,3},7->{2,3},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(6,3)] * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalSimpleMultiplestart(A,B,C,D) -> evalSimpleMultipleentryin(A,B,C,D) True (1,1) 1. evalSimpleMultipleentryin(A,B,C,D) -> evalSimpleMultiplebb3in(0,0,C,D) True (?,1) 2. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplebbin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] (?,1) 3. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplereturnin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C] (?,1) 4. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb1in(A,B,C,D) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + A] 5. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb2in(A,B,C,D) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= D] 6. evalSimpleMultiplebb1in(A,B,C,D) -> evalSimpleMultiplebb3in(1 + A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalSimpleMultiplebb2in(A,B,C,D) -> evalSimpleMultiplebb3in(A,1 + B,C,D) [A + -1*D >= 0 (?,1) && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 8. evalSimpleMultiplereturnin(A,B,C,D) -> evalSimpleMultiplestop(A,B,C,D) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (?,1) Signature: {(evalSimpleMultiplebb1in,4) ;(evalSimpleMultiplebb2in,4) ;(evalSimpleMultiplebb3in,4) ;(evalSimpleMultiplebbin,4) ;(evalSimpleMultipleentryin,4) ;(evalSimpleMultiplereturnin,4) ;(evalSimpleMultiplestart,4) ;(evalSimpleMultiplestop,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2},7->{2,3},8->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalSimpleMultiplestart(A,B,C,D) -> evalSimpleMultipleentryin(A,B,C,D) True evalSimpleMultipleentryin(A,B,C,D) -> evalSimpleMultiplebb3in(0,0,C,D) True evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplebbin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplereturnin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C] evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb1in(A,B,C,D) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + A] evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb2in(A,B,C,D) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= D] evalSimpleMultiplebb1in(A,B,C,D) -> evalSimpleMultiplebb3in(1 + A,B,C,D) [-1 + D >= 0 && -2 + C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalSimpleMultiplebb2in(A,B,C,D) -> evalSimpleMultiplebb3in(A,1 + B,C,D) [A + -1*D >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalSimpleMultiplereturnin(A,B,C,D) -> evalSimpleMultiplestop(A,B,C,D) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0] Signature: {(evalSimpleMultiplebb1in,4) ;(evalSimpleMultiplebb2in,4) ;(evalSimpleMultiplebb3in,4) ;(evalSimpleMultiplebbin,4) ;(evalSimpleMultipleentryin,4) ;(evalSimpleMultiplereturnin,4) ;(evalSimpleMultiplestart,4) ;(evalSimpleMultiplestop,4)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2},7->{2,3},8->{}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalSimpleMultiplestart(A,B,C,D) -> evalSimpleMultipleentryin(A,B,C,D) True evalSimpleMultipleentryin(A,B,C,D) -> evalSimpleMultiplebb3in(0,0,C,D) True evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplebbin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplereturnin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C] evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb1in(A,B,C,D) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + A] evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb2in(A,B,C,D) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= D] evalSimpleMultiplebb1in(A,B,C,D) -> evalSimpleMultiplebb3in(1 + A,B,C,D) [-1 + D >= 0 && -2 + C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalSimpleMultiplebb2in(A,B,C,D) -> evalSimpleMultiplebb3in(A,1 + B,C,D) [A + -1*D >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalSimpleMultiplereturnin(A,B,C,D) -> evalSimpleMultiplestop(A,B,C,D) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalSimpleMultiplestop(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(evalSimpleMultiplebb1in,4) ;(evalSimpleMultiplebb2in,4) ;(evalSimpleMultiplebb3in,4) ;(evalSimpleMultiplebbin,4) ;(evalSimpleMultipleentryin,4) ;(evalSimpleMultiplereturnin,4) ;(evalSimpleMultiplestart,4) ;(evalSimpleMultiplestop,4) ;(exitus616,4)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2},7->{2,3},8->{9}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,6,4,7,5] c: [2,4,5,6,7] * Step 5: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: evalSimpleMultiplestart(A,B,C,D) -> evalSimpleMultipleentryin(A,B,C,D) True evalSimpleMultipleentryin(A,B,C,D) -> evalSimpleMultiplebb3in(0,0,C,D) True evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplebbin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + B] evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplereturnin(A,B,C,D) [B >= 0 && A + B >= 0 && A >= 0 && B >= C] evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb1in(A,B,C,D) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + A] evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb2in(A,B,C,D) [-1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= D] evalSimpleMultiplebb1in(A,B,C,D) -> evalSimpleMultiplebb3in(1 + A,B,C,D) [-1 + D >= 0 && -2 + C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalSimpleMultiplebb2in(A,B,C,D) -> evalSimpleMultiplebb3in(A,1 + B,C,D) [A + -1*D >= 0 && -1 + C >= 0 && -1 + B + C >= 0 && -1 + -1*B + C >= 0 && -1 + A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalSimpleMultiplereturnin(A,B,C,D) -> evalSimpleMultiplestop(A,B,C,D) [B + -1*C >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalSimpleMultiplestop(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(evalSimpleMultiplebb1in,4) ;(evalSimpleMultiplebb2in,4) ;(evalSimpleMultiplebb3in,4) ;(evalSimpleMultiplebbin,4) ;(evalSimpleMultipleentryin,4) ;(evalSimpleMultiplereturnin,4) ;(evalSimpleMultiplestart,4) ;(evalSimpleMultiplestop,4) ;(exitus616,4)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2},7->{2,3},8->{9}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,6,4,7,5] c: [2,4,5,6,7]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,0.0] evalSimpleMultiplestart ~> evalSimpleMultipleentryin [A <= A, B <= B, C <= C, D <= D] evalSimpleMultipleentryin ~> evalSimpleMultiplebb3in [A <= 0*K, B <= 0*K, C <= C, D <= D] evalSimpleMultiplebb3in ~> evalSimpleMultiplebbin [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplebb3in ~> evalSimpleMultiplereturnin [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplebbin ~> evalSimpleMultiplebb1in [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplebbin ~> evalSimpleMultiplebb2in [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplebb1in ~> evalSimpleMultiplebb3in [A <= D, B <= B, C <= C, D <= D] evalSimpleMultiplebb2in ~> evalSimpleMultiplebb3in [A <= A, B <= C, C <= C, D <= D] evalSimpleMultiplereturnin ~> evalSimpleMultiplestop [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplestop ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= K + A + B + C + D] evalSimpleMultiplebb3in ~> evalSimpleMultiplebbin [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplebb1in ~> evalSimpleMultiplebb3in [A <= D, B <= B, C <= C, D <= D] evalSimpleMultiplebbin ~> evalSimpleMultiplebb1in [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplebb2in ~> evalSimpleMultiplebb3in [A <= A, B <= C, C <= C, D <= D] evalSimpleMultiplebbin ~> evalSimpleMultiplebb2in [A <= A, B <= B, C <= C, D <= D] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0] evalSimpleMultiplestart ~> evalSimpleMultipleentryin [] evalSimpleMultipleentryin ~> evalSimpleMultiplebb3in [K ~=> A,K ~=> B] evalSimpleMultiplebb3in ~> evalSimpleMultiplebbin [] evalSimpleMultiplebb3in ~> evalSimpleMultiplereturnin [] evalSimpleMultiplebbin ~> evalSimpleMultiplebb1in [] evalSimpleMultiplebbin ~> evalSimpleMultiplebb2in [] evalSimpleMultiplebb1in ~> evalSimpleMultiplebb3in [D ~=> A] evalSimpleMultiplebb2in ~> evalSimpleMultiplebb3in [C ~=> B] evalSimpleMultiplereturnin ~> evalSimpleMultiplestop [] evalSimpleMultiplestop ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0,D ~+> 0.0,K ~+> 0.0] evalSimpleMultiplebb3in ~> evalSimpleMultiplebbin [] evalSimpleMultiplebb1in ~> evalSimpleMultiplebb3in [D ~=> A] evalSimpleMultiplebbin ~> evalSimpleMultiplebb1in [] evalSimpleMultiplebb2in ~> evalSimpleMultiplebb3in [C ~=> B] evalSimpleMultiplebbin ~> evalSimpleMultiplebb2in [] + Applied Processor: Lare + Details: evalSimpleMultiplestart ~> exitus616 [C ~=> B ,D ~=> A ,K ~=> A ,K ~=> B ,C ~+> 0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,K ~*> 0.0 ,K ~*> tick] + evalSimpleMultiplebb3in> [C ~=> B ,D ~=> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,C ~+> 0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick] YES(?,O(n^1))