YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True (?,1) 2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [B >= 0 && A + B >= 0 && A >= 0 && 99 >= B] (?,1) 3. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [B >= 0 && A + B >= 0 && A >= 0 && B >= 100] (?,1) 4. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + A] (?,1) 5. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= C] (?,1) 6. evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && 98 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && 99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) [A + -1*C >= 0 && 99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0] (?,1) 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-100 + B >= 0 && -100 + A + B >= 0 && A >= 0] (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbbin,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} 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: [(1,3),(6,3)] * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True (?,1) 2. evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [B >= 0 && A + B >= 0 && A >= 0 && 99 >= B] (?,1) 3. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [B >= 0 && A + B >= 0 && A >= 0 && B >= 100] (?,1) 4. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + A] (?,1) 5. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= C] (?,1) 6. evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) [-1 + C >= 0 (?,1) && -1 + B + C >= 0 && 98 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && 99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) [A + -1*C >= 0 && 99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0] (?,1) 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-100 + B >= 0 && -100 + A + B >= 0 && A >= 0] (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbbin,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Flow Graph: [0->{1},1->{2},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: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [B >= 0 && A + B >= 0 && A >= 0 && 99 >= B] evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [B >= 0 && A + B >= 0 && A >= 0 && B >= 100] evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + A] evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= C] evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) [-1 + C >= 0 && -1 + B + C >= 0 && 98 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && 99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) [A + -1*C >= 0 && 99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-100 + B >= 0 && -100 + A + B >= 0 && A >= 0] Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbbin,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Rule Graph: [0->{1},1->{2},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: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [B >= 0 && A + B >= 0 && A >= 0 && 99 >= B] evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [B >= 0 && A + B >= 0 && A >= 0 && B >= 100] evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + A] evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= C] evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) [-1 + C >= 0 && -1 + B + C >= 0 && 98 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && 99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) [A + -1*C >= 0 && 99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-100 + B >= 0 && -100 + A + B >= 0 && A >= 0] evalfstop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbbin,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2},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: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb3in(0,0,C) True evalfbb3in(A,B,C) -> evalfbbin(A,B,C) [B >= 0 && A + B >= 0 && A >= 0 && 99 >= B] evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [B >= 0 && A + B >= 0 && A >= 0 && B >= 100] evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= 1 + A] evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0 && A >= C] evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) [-1 + C >= 0 && -1 + B + C >= 0 && 98 + -1*B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && 99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) [A + -1*C >= 0 && 99 + -1*B >= 0 && 99 + A + -1*B >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-100 + B >= 0 && -100 + A + B >= 0 && A >= 0] evalfstop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbbin,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2},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,0.0] evalfstart ~> evalfentryin [A <= A, B <= B, C <= C] evalfentryin ~> evalfbb3in [A <= 0*K, B <= 0*K, C <= C] evalfbb3in ~> evalfbbin [A <= A, B <= B, C <= C] evalfbb3in ~> evalfreturnin [A <= A, B <= B, C <= C] evalfbbin ~> evalfbb1in [A <= A, B <= B, C <= C] evalfbbin ~> evalfbb2in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb3in [A <= C, B <= B, C <= C] evalfbb2in ~> evalfbb3in [A <= A, B <= 100*K, C <= C] evalfreturnin ~> evalfstop [A <= A, B <= B, C <= C] evalfstop ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= 99*K + A + B + C] evalfbb3in ~> evalfbbin [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb3in [A <= C, B <= B, C <= C] evalfbbin ~> evalfbb1in [A <= A, B <= B, C <= C] evalfbb2in ~> evalfbb3in [A <= A, B <= 100*K, C <= C] evalfbbin ~> evalfbb2in [A <= A, B <= B, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] evalfstart ~> evalfentryin [] evalfentryin ~> evalfbb3in [K ~=> A,K ~=> B] evalfbb3in ~> evalfbbin [] evalfbb3in ~> evalfreturnin [] evalfbbin ~> evalfbb1in [] evalfbbin ~> evalfbb2in [] evalfbb1in ~> evalfbb3in [C ~=> A] evalfbb2in ~> evalfbb3in [K ~=> B] evalfreturnin ~> evalfstop [] evalfstop ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0,K ~*> 0.0] evalfbb3in ~> evalfbbin [] evalfbb1in ~> evalfbb3in [C ~=> A] evalfbbin ~> evalfbb1in [] evalfbb2in ~> evalfbb3in [K ~=> B] evalfbbin ~> evalfbb2in [] + Applied Processor: Lare + Details: evalfstart ~> exitus616 [C ~=> A ,K ~=> A ,K ~=> B ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,K ~*> 0.0 ,K ~*> tick] + evalfbb3in> [C ~=> A ,K ~=> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~*> 0.0 ,K ~*> tick] YES(?,O(n^1))