YES(?,POLY) * Step 1: UnsatPaths 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,A) [B >= 1] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [0 >= B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [C >= A] (?,1) 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [A >= 1 + C] (?,1) 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,-1 + C) True (?,1) 7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) True (?,1) 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) True (?,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: UnsatPaths + Details: We remove following edges from the transition graph: [(2,5)] * Step 2: 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,A) [B >= 1] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [0 >= B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [C >= A] (?,1) 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [A >= 1 + C] (?,1) 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,-1 + C) True (?,1) 7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) True (?,1) 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) True (?,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},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] + Applied Processor: FromIts + 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,A) [B >= 1] evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [0 >= B] evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [C >= A] evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [A >= 1 + C] evalfbb1in(A,B,C) -> evalfbb2in(A,B,-1 + C) True evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) True evalfreturnin(A,B,C) -> evalfstop(A,B,C) True 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},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks 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,A) [B >= 1] evalfbb4in.3(A,B,C) -> evalfreturnin.8(A,B,C) [0 >= B] evalfbb2in.4(A,B,C) -> evalfbb1in.6(A,B,C) [C >= A] evalfbb2in.5(A,B,C) -> evalfbb3in.7(A,B,C) [A >= 1 + C] evalfbb1in.6(A,B,C) -> evalfbb2in.4(A,B,-1 + C) True evalfbb1in.6(A,B,C) -> evalfbb2in.5(A,B,-1 + C) True evalfbb3in.7(A,B,C) -> evalfbb4in.2(A,-1 + B,C) True evalfbb3in.7(A,B,C) -> evalfbb4in.3(A,-1 + B,C) True evalfreturnin.8(A,B,C) -> evalfstop.9(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)} Rule Graph: [0->{1,2},1->{3},2->{4},3->{5},4->{11},5->{7,8},6->{9,10},7->{5},8->{6},9->{3},10->{4},11->{}] + Applied Processor: AddSinks + Details: () * Step 5: 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,A) [B >= 1] evalfbb4in.3(A,B,C) -> evalfreturnin.8(A,B,C) [0 >= B] evalfbb2in.4(A,B,C) -> evalfbb1in.6(A,B,C) [C >= A] evalfbb2in.5(A,B,C) -> evalfbb3in.7(A,B,C) [A >= 1 + C] evalfbb1in.6(A,B,C) -> evalfbb2in.4(A,B,-1 + C) True evalfbb1in.6(A,B,C) -> evalfbb2in.5(A,B,-1 + C) True evalfbb3in.7(A,B,C) -> evalfbb4in.2(A,-1 + B,C) True evalfbb3in.7(A,B,C) -> evalfbb4in.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.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) ;(exitus616,3)} Rule Graph: [0->{1,2},1->{3},2->{4},3->{5},4->{11},5->{7,8},6->{9,10},7->{5},8->{6},9->{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:[3,9,6,8,5,7] c: [3,6,8,9] | `- p:[5,7] c: [5,7] * Step 6: 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,A) [B >= 1] evalfbb4in.3(A,B,C) -> evalfreturnin.8(A,B,C) [0 >= B] evalfbb2in.4(A,B,C) -> evalfbb1in.6(A,B,C) [C >= A] evalfbb2in.5(A,B,C) -> evalfbb3in.7(A,B,C) [A >= 1 + C] evalfbb1in.6(A,B,C) -> evalfbb2in.4(A,B,-1 + C) True evalfbb1in.6(A,B,C) -> evalfbb2in.5(A,B,-1 + C) True evalfbb3in.7(A,B,C) -> evalfbb4in.2(A,-1 + B,C) True evalfbb3in.7(A,B,C) -> evalfbb4in.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.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) ;(exitus616,3)} Rule Graph: [0->{1,2},1->{3},2->{4},3->{5},4->{11},5->{7,8},6->{9,10},7->{5},8->{6},9->{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:[3,9,6,8,5,7] c: [3,6,8,9] | `- p:[5,7] c: [5,7]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: 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 <= A] 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 <= K + C] evalfbb1in.6 ~> evalfbb2in.5 [A <= A, B <= B, C <= K + C] evalfbb3in.7 ~> evalfbb4in.2 [A <= A, B <= K + B, C <= C] evalfbb3in.7 ~> evalfbb4in.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 <= K + B] evalfbb4in.2 ~> evalfbb2in.4 [A <= A, B <= B, C <= A] evalfbb3in.7 ~> evalfbb4in.2 [A <= A, B <= K + B, C <= C] evalfbb2in.5 ~> evalfbb3in.7 [A <= A, B <= B, C <= C] evalfbb1in.6 ~> evalfbb2in.5 [A <= A, B <= B, C <= K + C] evalfbb2in.4 ~> evalfbb1in.6 [A <= A, B <= B, C <= C] evalfbb1in.6 ~> evalfbb2in.4 [A <= A, B <= B, C <= K + C] + Loop: [0.0.0 <= K + A + C] evalfbb2in.4 ~> evalfbb1in.6 [A <= A, B <= B, C <= C] evalfbb1in.6 ~> evalfbb2in.4 [A <= A, B <= B, C <= K + C] + Applied Processor: AbstractFlow + Details: () * Step 8: 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 [A ~=> C] evalfbb4in.3 ~> evalfreturnin.8 [] evalfbb2in.4 ~> evalfbb1in.6 [] evalfbb2in.5 ~> evalfbb3in.7 [] evalfbb1in.6 ~> evalfbb2in.4 [C ~+> C,K ~+> C] evalfbb1in.6 ~> evalfbb2in.5 [C ~+> C,K ~+> C] evalfbb3in.7 ~> evalfbb4in.2 [B ~+> B,K ~+> B] evalfbb3in.7 ~> evalfbb4in.3 [B ~+> B,K ~+> B] evalfreturnin.8 ~> evalfstop.9 [] evalfstop.9 ~> exitus616 [] evalfstop.9 ~> exitus616 [] + Loop: [B ~+> 0.0,K ~+> 0.0] evalfbb4in.2 ~> evalfbb2in.4 [A ~=> C] evalfbb3in.7 ~> evalfbb4in.2 [B ~+> B,K ~+> B] evalfbb2in.5 ~> evalfbb3in.7 [] evalfbb1in.6 ~> evalfbb2in.5 [C ~+> C,K ~+> C] evalfbb2in.4 ~> evalfbb1in.6 [] evalfbb1in.6 ~> evalfbb2in.4 [C ~+> C,K ~+> C] + Loop: [A ~+> 0.0.0,C ~+> 0.0.0,K ~+> 0.0.0] evalfbb2in.4 ~> evalfbb1in.6 [] evalfbb1in.6 ~> evalfbb2in.4 [C ~+> C,K ~+> C] + Applied Processor: Lare + Details: evalfstart.0 ~> exitus616 [A ~=> B ,B ~=> A ,A ~+> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> C ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> B ,A ~*> tick ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> B ,K ~*> C ,K ~*> tick] + evalfbb3in.7> [A ~+> C ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> C ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> B ,B ~*> tick ,K ~*> B ,K ~*> C ,K ~*> tick] + evalfbb1in.6> [A ~+> 0.0.0 ,A ~+> tick ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> C ,C ~*> C ,K ~*> C] YES(?,POLY)