YES(?,POLY) * Step 1: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb4in(1,B,C,D) True (?,1) 2. evalfbb4in(A,B,C,D) -> evalfbb2in(A,B,1,D) [-1 + A >= 0 && B >= A] (?,1) 3. evalfbb4in(A,B,C,D) -> evalfreturnin(A,B,C,D) [-1 + A >= 0 && A >= 1 + B] (?,1) 4. evalfbb2in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= C] 5. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + D] 6. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 7. evalfbb3in(A,B,C,D) -> evalfbb4in(1 + A,B,C,D) [-1 + C + -1*D >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 8. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [-1 + A + -1*B >= 0 && -1 + A >= 0] (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} 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,D) -> evalfentryin(A,B,C,D) True evalfentryin(A,B,C,D) -> evalfbb4in(1,B,C,D) True evalfbb4in(A,B,C,D) -> evalfbb2in(A,B,1,D) [-1 + A >= 0 && B >= A] evalfbb4in(A,B,C,D) -> evalfreturnin(A,B,C,D) [-1 + A >= 0 && A >= 1 + B] evalfbb2in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= C] evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + D] evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,D) [-1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfbb3in(A,B,C,D) -> evalfbb4in(1 + A,B,C,D) [-1 + C + -1*D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [-1 + A + -1*B >= 0 && -1 + A >= 0] Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} 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,D) -> evalfentryin(A,B,C,D) True evalfentryin(A,B,C,D) -> evalfbb4in(1,B,C,D) True evalfbb4in(A,B,C,D) -> evalfbb2in(A,B,1,D) [-1 + A >= 0 && B >= A] evalfbb4in(A,B,C,D) -> evalfreturnin(A,B,C,D) [-1 + A >= 0 && A >= 1 + B] evalfbb2in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= C] evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + D] evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,D) [-1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfbb3in(A,B,C,D) -> evalfbb4in(1 + A,B,C,D) [-1 + C + -1*D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [-1 + A + -1*B >= 0 && -1 + A >= 0] evalfstop(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4) ;(exitus616,4)} 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,D) -> evalfentryin.1(A,B,C,D) True evalfentryin.1(A,B,C,D) -> evalfbb4in.2(1,B,C,D) True evalfentryin.1(A,B,C,D) -> evalfbb4in.3(1,B,C,D) True evalfbb4in.2(A,B,C,D) -> evalfbb2in.4(A,B,1,D) [-1 + A >= 0 && B >= A] evalfbb4in.2(A,B,C,D) -> evalfbb2in.5(A,B,1,D) [-1 + A >= 0 && B >= A] evalfbb4in.3(A,B,C,D) -> evalfreturnin.8(A,B,C,D) [-1 + A >= 0 && A >= 1 + B] evalfbb2in.4(A,B,C,D) -> evalfbb1in.6(A,B,C,D) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= C] evalfbb2in.5(A,B,C,D) -> evalfbb3in.7(A,B,C,D) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + D] evalfbb1in.6(A,B,C,D) -> evalfbb2in.4(A,B,1 + C,D) [-1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfbb1in.6(A,B,C,D) -> evalfbb2in.5(A,B,1 + C,D) [-1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfbb3in.7(A,B,C,D) -> evalfbb4in.2(1 + A,B,C,D) [-1 + C + -1*D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfbb3in.7(A,B,C,D) -> evalfbb4in.3(1 + A,B,C,D) [-1 + C + -1*D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfreturnin.8(A,B,C,D) -> evalfstop.9(A,B,C,D) [-1 + A + -1*B >= 0 && -1 + A >= 0] evalfstop.9(A,B,C,D) -> exitus616.10(A,B,C,D) True Signature: {(evalfbb1in.6,4) ;(evalfbb2in.4,4) ;(evalfbb2in.5,4) ;(evalfbb3in.7,4) ;(evalfbb4in.2,4) ;(evalfbb4in.3,4) ;(evalfentryin.1,4) ;(evalfreturnin.8,4) ;(evalfstart.0,4) ;(evalfstop.9,4) ;(exitus616.10,4)} 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,D) -> evalfentryin.1(A,B,C,D) True evalfentryin.1(A,B,C,D) -> evalfbb4in.2(1,B,C,D) True evalfentryin.1(A,B,C,D) -> evalfbb4in.3(1,B,C,D) True evalfbb4in.2(A,B,C,D) -> evalfbb2in.4(A,B,1,D) [-1 + A >= 0 && B >= A] evalfbb4in.2(A,B,C,D) -> evalfbb2in.5(A,B,1,D) [-1 + A >= 0 && B >= A] evalfbb4in.3(A,B,C,D) -> evalfreturnin.8(A,B,C,D) [-1 + A >= 0 && A >= 1 + B] evalfbb2in.4(A,B,C,D) -> evalfbb1in.6(A,B,C,D) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= C] evalfbb2in.5(A,B,C,D) -> evalfbb3in.7(A,B,C,D) [-1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + D] evalfbb1in.6(A,B,C,D) -> evalfbb2in.4(A,B,1 + C,D) [-1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfbb1in.6(A,B,C,D) -> evalfbb2in.5(A,B,1 + C,D) [-1 + D >= 0 && -2 + C + D >= 0 && -1*C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfbb3in.7(A,B,C,D) -> evalfbb4in.2(1 + A,B,C,D) [-1 + C + -1*D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfbb3in.7(A,B,C,D) -> evalfbb4in.3(1 + A,B,C,D) [-1 + C + -1*D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfreturnin.8(A,B,C,D) -> evalfstop.9(A,B,C,D) [-1 + A + -1*B >= 0 && -1 + A >= 0] evalfstop.9(A,B,C,D) -> exitus616.10(A,B,C,D) True Signature: {(evalfbb1in.6,4) ;(evalfbb2in.4,4) ;(evalfbb2in.5,4) ;(evalfbb3in.7,4) ;(evalfbb4in.2,4) ;(evalfbb4in.3,4) ;(evalfentryin.1,4) ;(evalfreturnin.8,4) ;(evalfstart.0,4) ;(evalfstop.9,4) ;(exitus616.10,4)} 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,D,0.0,0.0.0] evalfstart.0 ~> evalfentryin.1 [A <= A, B <= B, C <= C, D <= D] evalfentryin.1 ~> evalfbb4in.2 [A <= K, B <= B, C <= C, D <= D] evalfentryin.1 ~> evalfbb4in.3 [A <= K, B <= B, C <= C, D <= D] evalfbb4in.2 ~> evalfbb2in.4 [A <= A, B <= B, C <= K, D <= D] evalfbb4in.2 ~> evalfbb2in.5 [A <= A, B <= B, C <= K, D <= D] evalfbb4in.3 ~> evalfreturnin.8 [A <= A, B <= B, C <= C, D <= D] evalfbb2in.4 ~> evalfbb1in.6 [A <= A, B <= B, C <= C, D <= D] evalfbb2in.5 ~> evalfbb3in.7 [A <= A, B <= B, C <= C, D <= D] evalfbb1in.6 ~> evalfbb2in.4 [A <= A, B <= B, C <= C + D, D <= D] evalfbb1in.6 ~> evalfbb2in.5 [A <= A, B <= B, C <= C + D, D <= D] evalfbb3in.7 ~> evalfbb4in.2 [A <= B + C, B <= B, C <= C, D <= D] evalfbb3in.7 ~> evalfbb4in.3 [A <= B + C, B <= B, C <= C, D <= D] evalfreturnin.8 ~> evalfstop.9 [A <= A, B <= B, C <= C, D <= D] evalfstop.9 ~> exitus616.10 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= A + B] evalfbb4in.2 ~> evalfbb2in.4 [A <= A, B <= B, C <= K, D <= D] evalfbb3in.7 ~> evalfbb4in.2 [A <= B + C, B <= B, C <= C, D <= D] evalfbb2in.5 ~> evalfbb3in.7 [A <= A, B <= B, C <= C, D <= D] evalfbb4in.2 ~> evalfbb2in.5 [A <= A, B <= B, C <= K, D <= D] evalfbb1in.6 ~> evalfbb2in.5 [A <= A, B <= B, C <= C + D, D <= D] evalfbb2in.4 ~> evalfbb1in.6 [A <= A, B <= B, C <= C, D <= D] evalfbb1in.6 ~> evalfbb2in.4 [A <= A, B <= B, C <= C + D, D <= D] + Loop: [0.0.0 <= C + D] evalfbb2in.4 ~> evalfbb1in.6 [A <= A, B <= B, C <= C, D <= D] evalfbb1in.6 ~> evalfbb2in.4 [A <= A, B <= B, C <= C + D, D <= D] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0,0.0.0] evalfstart.0 ~> evalfentryin.1 [] evalfentryin.1 ~> evalfbb4in.2 [K ~=> A] evalfentryin.1 ~> evalfbb4in.3 [K ~=> 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 [C ~+> C,D ~+> C] evalfbb1in.6 ~> evalfbb2in.5 [C ~+> C,D ~+> C] evalfbb3in.7 ~> evalfbb4in.2 [B ~+> A,C ~+> A] evalfbb3in.7 ~> evalfbb4in.3 [B ~+> A,C ~+> A] evalfreturnin.8 ~> evalfstop.9 [] evalfstop.9 ~> exitus616.10 [] + Loop: [A ~+> 0.0,B ~+> 0.0] evalfbb4in.2 ~> evalfbb2in.4 [K ~=> C] evalfbb3in.7 ~> evalfbb4in.2 [B ~+> A,C ~+> A] evalfbb2in.5 ~> evalfbb3in.7 [] evalfbb4in.2 ~> evalfbb2in.5 [K ~=> C] evalfbb1in.6 ~> evalfbb2in.5 [C ~+> C,D ~+> C] evalfbb2in.4 ~> evalfbb1in.6 [] evalfbb1in.6 ~> evalfbb2in.4 [C ~+> C,D ~+> C] + Loop: [C ~+> 0.0.0,D ~+> 0.0.0] evalfbb2in.4 ~> evalfbb1in.6 [] evalfbb1in.6 ~> evalfbb2in.4 [C ~+> C,D ~+> C] + Applied Processor: Lare + Details: evalfstart.0 ~> exitus616.10 [K ~=> A ,K ~=> C ,B ~+> A ,B ~+> 0.0 ,B ~+> tick ,C ~+> A ,D ~+> A ,D ~+> C ,D ~+> 0.0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> tick ,D ~*> A ,D ~*> C ,D ~*> tick ,K ~*> A ,K ~*> C ,K ~*> tick] + evalfbb3in.7> [K ~=> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,B ~+> 0.0 ,B ~+> tick ,D ~+> A ,D ~+> C ,D ~+> 0.0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,B ~*> tick ,D ~*> A ,D ~*> C ,D ~*> tick ,K ~*> A ,K ~*> C ,K ~*> tick] + evalfbb1in.6> [C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,D ~+> C ,D ~+> 0.0.0 ,D ~+> tick ,tick ~+> tick ,C ~*> C ,D ~*> C] YES(?,POLY)