YES(?,POLY) * Step 1: TrivialSCCs 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: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: 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 (1,1) 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] (1,1) 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] (1,1) 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 3: AddSinks 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 (1,1) 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] (1,1) 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] (1,1) 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: AddSinks + Details: () * Step 4: 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) 9. evalfreturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8,9},4->{6},5->{7},6->{2,3},7->{2,3},8->{},9->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(6,3)] * Step 5: LooptreeTransformer 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) 9. evalfreturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8,9},4->{6},5->{7},6->{2},7->{2,3},8->{},9->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,6,4,7,5] c: [7] | `- p:[2,6,4] c: [6] * Step 6: SizeAbstraction 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) 9. evalfreturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8,9},4->{6},5->{7},6->{2},7->{2,3},8->{},9->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,6,4,7,5] c: [7] | `- p:[2,6,4] c: [6]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.0.0] evalfstart ~> evalfentryin [A <= A, B <= B, C <= C, D <= D] evalfentryin ~> evalfbb3in [A <= 0*K, B <= 0*K, C <= C, D <= D] evalfbb3in ~> evalfbbin [A <= A, B <= B, C <= C, D <= D] evalfbb3in ~> evalfreturnin [A <= A, B <= B, C <= C, D <= D] evalfbbin ~> evalfbb1in [A <= A, B <= B, C <= C, D <= D] evalfbbin ~> evalfbb2in [A <= A, B <= B, C <= C, D <= D] evalfbb1in ~> evalfbb3in [A <= D, B <= B, C <= C, D <= D] evalfbb2in ~> evalfbb3in [A <= 0*K, B <= C, C <= C, D <= D] evalfreturnin ~> evalfstop [A <= A, B <= B, C <= C, D <= D] evalfreturnin ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= B + C] evalfbb3in ~> evalfbbin [A <= A, B <= B, C <= C, D <= D] evalfbb1in ~> evalfbb3in [A <= D, B <= B, C <= C, D <= D] evalfbbin ~> evalfbb1in [A <= A, B <= B, C <= C, D <= D] evalfbb2in ~> evalfbb3in [A <= 0*K, B <= C, C <= C, D <= D] evalfbbin ~> evalfbb2in [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0.0 <= A + D] evalfbb3in ~> evalfbbin [A <= A, B <= B, C <= C, D <= D] evalfbb1in ~> evalfbb3in [A <= D, B <= B, C <= C, D <= D] evalfbbin ~> evalfbb1in [A <= A, B <= B, C <= C, D <= D] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0,0.0.0] evalfstart ~> evalfentryin [] evalfentryin ~> evalfbb3in [K ~=> A,K ~=> B] evalfbb3in ~> evalfbbin [] evalfbb3in ~> evalfreturnin [] evalfbbin ~> evalfbb1in [] evalfbbin ~> evalfbb2in [] evalfbb1in ~> evalfbb3in [D ~=> A] evalfbb2in ~> evalfbb3in [C ~=> B,K ~=> A] evalfreturnin ~> evalfstop [] evalfreturnin ~> exitus616 [] + Loop: [B ~+> 0.0,C ~+> 0.0] evalfbb3in ~> evalfbbin [] evalfbb1in ~> evalfbb3in [D ~=> A] evalfbbin ~> evalfbb1in [] evalfbb2in ~> evalfbb3in [C ~=> B,K ~=> A] evalfbbin ~> evalfbb2in [] + Loop: [A ~+> 0.0.0,D ~+> 0.0.0] evalfbb3in ~> evalfbbin [] evalfbb1in ~> evalfbb3in [D ~=> A] evalfbbin ~> evalfbb1in [] + Applied Processor: LareProcessor + Details: evalfstart ~> exitus616 [C ~=> B ,D ~=> A ,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 ~*> tick] evalfstart ~> evalfstop [C ~=> B ,D ~=> A ,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 ~*> tick] + evalfbb3in> [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] + evalfbbin> [D ~=> A,A ~+> 0.0.0,A ~+> tick,D ~+> 0.0.0,D ~+> tick,tick ~+> tick] evalfbb3in> [D ~=> A,A ~+> 0.0.0,A ~+> tick,D ~+> 0.0.0,D ~+> tick,tick ~+> tick] YES(?,POLY)