YES(?,POLY) * Step 1: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (?,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [0 >= B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && A >= C] (?,1) 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && C >= 1 + A] (?,1) 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] (?,1) 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-1*B >= 0] (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,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->{4,5},7->{2,3},8->{}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [0 >= B] evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && A >= C] evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && C >= 1 + A] evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-1*B >= 0] Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] + Applied Processor: AddSinks + Details: () * Step 3: Unfold WORST_CASE(?,POLY) + Considered Problem: Rules: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [0 >= B] evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && A >= C] evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && C >= 1 + A] evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-1*B >= 0] evalfstop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{9}] + Applied Processor: Unfold + Details: () * Step 4: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: evalfstart.0(A,B,C) -> evalfentryin.1(A,B,C) True evalfentryin.1(A,B,C) -> evalfbb4in.2(B,A,C) True evalfentryin.1(A,B,C) -> evalfbb4in.3(B,A,C) True evalfbb4in.2(A,B,C) -> evalfbb2in.4(A,B,1) [B >= 1] evalfbb4in.2(A,B,C) -> evalfbb2in.5(A,B,1) [B >= 1] evalfbb4in.3(A,B,C) -> evalfreturnin.8(A,B,C) [0 >= B] evalfbb2in.4(A,B,C) -> evalfbb1in.6(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && A >= C] evalfbb2in.5(A,B,C) -> evalfbb3in.7(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && C >= 1 + A] evalfbb1in.6(A,B,C) -> evalfbb2in.4(A,B,1 + C) [A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] evalfbb1in.6(A,B,C) -> evalfbb2in.5(A,B,1 + C) [A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] evalfbb3in.7(A,B,C) -> evalfbb4in.2(A,-1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] evalfbb3in.7(A,B,C) -> evalfbb4in.3(A,-1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] evalfreturnin.8(A,B,C) -> evalfstop.9(A,B,C) [-1*B >= 0] evalfstop.9(A,B,C) -> exitus616.10(A,B,C) True Signature: {(evalfbb1in.6,3) ;(evalfbb2in.4,3) ;(evalfbb2in.5,3) ;(evalfbb3in.7,3) ;(evalfbb4in.2,3) ;(evalfbb4in.3,3) ;(evalfentryin.1,3) ;(evalfreturnin.8,3) ;(evalfstart.0,3) ;(evalfstop.9,3) ;(exitus616.10,3)} Rule Graph: [0->{1,2},1->{3,4},2->{5},3->{6},4->{7},5->{12},6->{8,9},7->{10,11},8->{6},9->{7},10->{3,4},11->{5} ,12->{13},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:[3,10,7,4,9,6,8] c: [3,4,7,9,10] | `- p:[6,8] c: [6,8] * Step 5: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: evalfstart.0(A,B,C) -> evalfentryin.1(A,B,C) True evalfentryin.1(A,B,C) -> evalfbb4in.2(B,A,C) True evalfentryin.1(A,B,C) -> evalfbb4in.3(B,A,C) True evalfbb4in.2(A,B,C) -> evalfbb2in.4(A,B,1) [B >= 1] evalfbb4in.2(A,B,C) -> evalfbb2in.5(A,B,1) [B >= 1] evalfbb4in.3(A,B,C) -> evalfreturnin.8(A,B,C) [0 >= B] evalfbb2in.4(A,B,C) -> evalfbb1in.6(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && A >= C] evalfbb2in.5(A,B,C) -> evalfbb3in.7(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && C >= 1 + A] evalfbb1in.6(A,B,C) -> evalfbb2in.4(A,B,1 + C) [A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] evalfbb1in.6(A,B,C) -> evalfbb2in.5(A,B,1 + C) [A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] evalfbb3in.7(A,B,C) -> evalfbb4in.2(A,-1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] evalfbb3in.7(A,B,C) -> evalfbb4in.3(A,-1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] evalfreturnin.8(A,B,C) -> evalfstop.9(A,B,C) [-1*B >= 0] evalfstop.9(A,B,C) -> exitus616.10(A,B,C) True Signature: {(evalfbb1in.6,3) ;(evalfbb2in.4,3) ;(evalfbb2in.5,3) ;(evalfbb3in.7,3) ;(evalfbb4in.2,3) ;(evalfbb4in.3,3) ;(evalfentryin.1,3) ;(evalfreturnin.8,3) ;(evalfstart.0,3) ;(evalfstop.9,3) ;(exitus616.10,3)} Rule Graph: [0->{1,2},1->{3,4},2->{5},3->{6},4->{7},5->{12},6->{8,9},7->{10,11},8->{6},9->{7},10->{3,4},11->{5} ,12->{13},13->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[3,10,7,4,9,6,8] c: [3,4,7,9,10] | `- p:[6,8] c: [6,8]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0] evalfstart.0 ~> evalfentryin.1 [A <= A, B <= B, C <= C] evalfentryin.1 ~> evalfbb4in.2 [A <= B, B <= A, C <= C] evalfentryin.1 ~> evalfbb4in.3 [A <= B, B <= A, C <= C] evalfbb4in.2 ~> evalfbb2in.4 [A <= A, B <= B, C <= K] evalfbb4in.2 ~> evalfbb2in.5 [A <= A, B <= B, C <= K] evalfbb4in.3 ~> evalfreturnin.8 [A <= A, B <= B, C <= C] evalfbb2in.4 ~> evalfbb1in.6 [A <= A, B <= B, C <= C] evalfbb2in.5 ~> evalfbb3in.7 [A <= A, B <= B, C <= C] evalfbb1in.6 ~> evalfbb2in.4 [A <= A, B <= B, C <= B + C] evalfbb1in.6 ~> evalfbb2in.5 [A <= A, B <= B, C <= B + C] evalfbb3in.7 ~> evalfbb4in.2 [A <= A, B <= B, C <= C] evalfbb3in.7 ~> evalfbb4in.3 [A <= A, B <= B, C <= C] evalfreturnin.8 ~> evalfstop.9 [A <= A, B <= B, C <= C] evalfstop.9 ~> exitus616.10 [A <= A, B <= B, C <= C] + Loop: [0.0 <= B] evalfbb4in.2 ~> evalfbb2in.4 [A <= A, B <= B, C <= K] evalfbb3in.7 ~> evalfbb4in.2 [A <= A, B <= B, C <= C] evalfbb2in.5 ~> evalfbb3in.7 [A <= A, B <= B, C <= C] evalfbb4in.2 ~> evalfbb2in.5 [A <= A, B <= B, C <= K] evalfbb1in.6 ~> evalfbb2in.5 [A <= A, B <= B, C <= B + C] evalfbb2in.4 ~> evalfbb1in.6 [A <= A, B <= B, C <= C] evalfbb1in.6 ~> evalfbb2in.4 [A <= A, B <= B, C <= B + C] + Loop: [0.0.0 <= A + C] evalfbb2in.4 ~> evalfbb1in.6 [A <= A, B <= B, C <= C] evalfbb1in.6 ~> evalfbb2in.4 [A <= A, B <= B, C <= B + C] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0] evalfstart.0 ~> evalfentryin.1 [] evalfentryin.1 ~> evalfbb4in.2 [A ~=> B,B ~=> A] evalfentryin.1 ~> evalfbb4in.3 [A ~=> B,B ~=> A] evalfbb4in.2 ~> evalfbb2in.4 [K ~=> C] evalfbb4in.2 ~> evalfbb2in.5 [K ~=> C] evalfbb4in.3 ~> evalfreturnin.8 [] evalfbb2in.4 ~> evalfbb1in.6 [] evalfbb2in.5 ~> evalfbb3in.7 [] evalfbb1in.6 ~> evalfbb2in.4 [B ~+> C,C ~+> C] evalfbb1in.6 ~> evalfbb2in.5 [B ~+> C,C ~+> C] evalfbb3in.7 ~> evalfbb4in.2 [] evalfbb3in.7 ~> evalfbb4in.3 [] evalfreturnin.8 ~> evalfstop.9 [] evalfstop.9 ~> exitus616.10 [] + Loop: [B ~=> 0.0] evalfbb4in.2 ~> evalfbb2in.4 [K ~=> C] evalfbb3in.7 ~> evalfbb4in.2 [] evalfbb2in.5 ~> evalfbb3in.7 [] evalfbb4in.2 ~> evalfbb2in.5 [K ~=> C] evalfbb1in.6 ~> evalfbb2in.5 [B ~+> C,C ~+> C] evalfbb2in.4 ~> evalfbb1in.6 [] evalfbb1in.6 ~> evalfbb2in.4 [B ~+> C,C ~+> C] + Loop: [A ~+> 0.0.0,C ~+> 0.0.0] evalfbb2in.4 ~> evalfbb1in.6 [] evalfbb1in.6 ~> evalfbb2in.4 [B ~+> C,C ~+> C] + Applied Processor: Lare + Details: evalfstart.0 ~> exitus616.10 [A ~=> B ,A ~=> 0.0 ,B ~=> A ,K ~=> C ,A ~+> C ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> C ,A ~*> tick ,B ~*> C ,B ~*> tick ,K ~*> C ,K ~*> tick] + evalfbb3in.7> [B ~=> 0.0 ,K ~=> C ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> C ,B ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> C ,A ~*> tick ,B ~*> C ,B ~*> tick ,K ~*> C ,K ~*> tick] + evalfbb1in.6> [A ~+> 0.0.0 ,A ~+> tick ,B ~+> C ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,A ~*> C ,B ~*> C ,C ~*> C] YES(?,POLY)