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