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) [99 >= B] (?,1) 3. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [B >= 100] (?,1) 4. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [C >= 1 + A] (?,1) 5. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [A >= C] (?,1) 6. evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) True (?,1) 7. evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) True (?,1) 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) True (?,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)] * 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) [99 >= B] (?,1) 3. evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [B >= 100] (?,1) 4. evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [C >= 1 + A] (?,1) 5. evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [A >= C] (?,1) 6. evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) True (?,1) 7. evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) True (?,1) 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) True (?,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->{2,3},7->{2,3},8->{}] + Applied Processor: FromIts + Details: () * Step 3: Unfold 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) [99 >= B] evalfbb3in(A,B,C) -> evalfreturnin(A,B,C) [B >= 100] evalfbbin(A,B,C) -> evalfbb1in(A,B,C) [C >= 1 + A] evalfbbin(A,B,C) -> evalfbb2in(A,B,C) [A >= C] evalfbb1in(A,B,C) -> evalfbb3in(1 + A,B,C) True evalfbb2in(A,B,C) -> evalfbb3in(A,1 + B,C) True evalfreturnin(A,B,C) -> evalfstop(A,B,C) True 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->{2,3},7->{2,3},8->{}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalfstart.0(A,B,C) -> evalfentryin.1(A,B,C) True evalfentryin.1(A,B,C) -> evalfbb3in.2(0,0,C) True evalfbb3in.2(A,B,C) -> evalfbbin.4(A,B,C) [99 >= B] evalfbb3in.2(A,B,C) -> evalfbbin.5(A,B,C) [99 >= B] evalfbb3in.3(A,B,C) -> evalfreturnin.8(A,B,C) [B >= 100] evalfbbin.4(A,B,C) -> evalfbb1in.6(A,B,C) [C >= 1 + A] evalfbbin.5(A,B,C) -> evalfbb2in.7(A,B,C) [A >= C] evalfbb1in.6(A,B,C) -> evalfbb3in.2(1 + A,B,C) True evalfbb1in.6(A,B,C) -> evalfbb3in.3(1 + A,B,C) True evalfbb2in.7(A,B,C) -> evalfbb3in.2(A,1 + B,C) True evalfbb2in.7(A,B,C) -> evalfbb3in.3(A,1 + B,C) True evalfreturnin.8(A,B,C) -> evalfstop.9(A,B,C) True Signature: {(evalfbb1in.6,3) ;(evalfbb2in.7,3) ;(evalfbb3in.2,3) ;(evalfbb3in.3,3) ;(evalfbbin.4,3) ;(evalfbbin.5,3) ;(evalfentryin.1,3) ;(evalfreturnin.8,3) ;(evalfstart.0,3) ;(evalfstop.9,3)} Rule Graph: [0->{1},1->{2,3},2->{5},3->{6},4->{11},5->{7,8},6->{9,10},7->{2,3},8->{4},9->{2,3},10->{4},11->{}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalfstart.0(A,B,C) -> evalfentryin.1(A,B,C) True evalfentryin.1(A,B,C) -> evalfbb3in.2(0,0,C) True evalfbb3in.2(A,B,C) -> evalfbbin.4(A,B,C) [99 >= B] evalfbb3in.2(A,B,C) -> evalfbbin.5(A,B,C) [99 >= B] evalfbb3in.3(A,B,C) -> evalfreturnin.8(A,B,C) [B >= 100] evalfbbin.4(A,B,C) -> evalfbb1in.6(A,B,C) [C >= 1 + A] evalfbbin.5(A,B,C) -> evalfbb2in.7(A,B,C) [A >= C] evalfbb1in.6(A,B,C) -> evalfbb3in.2(1 + A,B,C) True evalfbb1in.6(A,B,C) -> evalfbb3in.3(1 + A,B,C) True evalfbb2in.7(A,B,C) -> evalfbb3in.2(A,1 + B,C) True evalfbb2in.7(A,B,C) -> evalfbb3in.3(A,1 + B,C) True evalfreturnin.8(A,B,C) -> evalfstop.9(A,B,C) True evalfstop.9(A,B,C) -> exitus616(A,B,C) True evalfstop.9(A,B,C) -> exitus616(A,B,C) True Signature: {(evalfbb1in.6,3) ;(evalfbb2in.7,3) ;(evalfbb3in.2,3) ;(evalfbb3in.3,3) ;(evalfbbin.4,3) ;(evalfbbin.5,3) ;(evalfentryin.1,3) ;(evalfreturnin.8,3) ;(evalfstart.0,3) ;(evalfstop.9,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3},2->{5},3->{6},4->{11},5->{7,8},6->{9,10},7->{2,3},8->{4},9->{2,3},10->{4},11->{12,13}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[2,7,5,9,6,3] c: [2,3,5,6,7,9] * Step 6: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: evalfstart.0(A,B,C) -> evalfentryin.1(A,B,C) True evalfentryin.1(A,B,C) -> evalfbb3in.2(0,0,C) True evalfbb3in.2(A,B,C) -> evalfbbin.4(A,B,C) [99 >= B] evalfbb3in.2(A,B,C) -> evalfbbin.5(A,B,C) [99 >= B] evalfbb3in.3(A,B,C) -> evalfreturnin.8(A,B,C) [B >= 100] evalfbbin.4(A,B,C) -> evalfbb1in.6(A,B,C) [C >= 1 + A] evalfbbin.5(A,B,C) -> evalfbb2in.7(A,B,C) [A >= C] evalfbb1in.6(A,B,C) -> evalfbb3in.2(1 + A,B,C) True evalfbb1in.6(A,B,C) -> evalfbb3in.3(1 + A,B,C) True evalfbb2in.7(A,B,C) -> evalfbb3in.2(A,1 + B,C) True evalfbb2in.7(A,B,C) -> evalfbb3in.3(A,1 + B,C) True evalfreturnin.8(A,B,C) -> evalfstop.9(A,B,C) True evalfstop.9(A,B,C) -> exitus616(A,B,C) True evalfstop.9(A,B,C) -> exitus616(A,B,C) True Signature: {(evalfbb1in.6,3) ;(evalfbb2in.7,3) ;(evalfbb3in.2,3) ;(evalfbb3in.3,3) ;(evalfbbin.4,3) ;(evalfbbin.5,3) ;(evalfentryin.1,3) ;(evalfreturnin.8,3) ;(evalfstart.0,3) ;(evalfstop.9,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3},2->{5},3->{6},4->{11},5->{7,8},6->{9,10},7->{2,3},8->{4},9->{2,3},10->{4},11->{12,13}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[2,7,5,9,6,3] c: [2,3,5,6,7,9]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0] evalfstart.0 ~> evalfentryin.1 [A <= A, B <= B, C <= C] evalfentryin.1 ~> evalfbb3in.2 [A <= 0*K, B <= 0*K, C <= C] evalfbb3in.2 ~> evalfbbin.4 [A <= A, B <= B, C <= C] evalfbb3in.2 ~> evalfbbin.5 [A <= A, B <= B, C <= C] evalfbb3in.3 ~> evalfreturnin.8 [A <= A, B <= B, C <= C] evalfbbin.4 ~> evalfbb1in.6 [A <= A, B <= B, C <= C] evalfbbin.5 ~> evalfbb2in.7 [A <= A, B <= B, C <= C] evalfbb1in.6 ~> evalfbb3in.2 [A <= K + A, B <= B, C <= C] evalfbb1in.6 ~> evalfbb3in.3 [A <= K + A, B <= B, C <= C] evalfbb2in.7 ~> evalfbb3in.2 [A <= A, B <= K + B, C <= C] evalfbb2in.7 ~> evalfbb3in.3 [A <= A, B <= K + B, C <= C] evalfreturnin.8 ~> evalfstop.9 [A <= A, B <= B, C <= C] evalfstop.9 ~> exitus616 [A <= A, B <= B, C <= C] evalfstop.9 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= 99*K + A + B + C] evalfbb3in.2 ~> evalfbbin.4 [A <= A, B <= B, C <= C] evalfbb1in.6 ~> evalfbb3in.2 [A <= K + A, B <= B, C <= C] evalfbbin.4 ~> evalfbb1in.6 [A <= A, B <= B, C <= C] evalfbb2in.7 ~> evalfbb3in.2 [A <= A, B <= K + B, C <= C] evalfbbin.5 ~> evalfbb2in.7 [A <= A, B <= B, C <= C] evalfbb3in.2 ~> evalfbbin.5 [A <= A, B <= B, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] evalfstart.0 ~> evalfentryin.1 [] evalfentryin.1 ~> evalfbb3in.2 [K ~=> A,K ~=> B] evalfbb3in.2 ~> evalfbbin.4 [] evalfbb3in.2 ~> evalfbbin.5 [] evalfbb3in.3 ~> evalfreturnin.8 [] evalfbbin.4 ~> evalfbb1in.6 [] evalfbbin.5 ~> evalfbb2in.7 [] evalfbb1in.6 ~> evalfbb3in.2 [A ~+> A,K ~+> A] evalfbb1in.6 ~> evalfbb3in.3 [A ~+> A,K ~+> A] evalfbb2in.7 ~> evalfbb3in.2 [B ~+> B,K ~+> B] evalfbb2in.7 ~> evalfbb3in.3 [B ~+> B,K ~+> B] evalfreturnin.8 ~> evalfstop.9 [] evalfstop.9 ~> exitus616 [] evalfstop.9 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0,K ~*> 0.0] evalfbb3in.2 ~> evalfbbin.4 [] evalfbb1in.6 ~> evalfbb3in.2 [A ~+> A,K ~+> A] evalfbbin.4 ~> evalfbb1in.6 [] evalfbb2in.7 ~> evalfbb3in.2 [B ~+> B,K ~+> B] evalfbbin.5 ~> evalfbb2in.7 [] evalfbb3in.2 ~> evalfbbin.5 [] + Applied Processor: Lare + Details: evalfstart.0 ~> exitus616 [K ~=> A ,K ~=> B ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0 ,K ~+> tick ,C ~*> A ,C ~*> B ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] + evalfbb1in.6> [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,A ~*> A ,A ~*> B ,B ~*> A ,B ~*> B ,C ~*> A ,C ~*> B ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] evalfbb2in.7> [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,A ~*> A ,A ~*> B ,B ~*> A ,B ~*> B ,C ~*> A ,C ~*> B ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] YES(?,O(n^1))