YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalDis2start(A,B,C) -> evalDis2entryin(A,B,C) True (1,1) 1. evalDis2entryin(A,B,C) -> evalDis2bb3in(B,C,A) True (?,1) 2. evalDis2bb3in(A,B,C) -> evalDis2bbin(A,B,C) [A >= 1 + C] (?,1) 3. evalDis2bb3in(A,B,C) -> evalDis2returnin(A,B,C) [C >= A] (?,1) 4. evalDis2bbin(A,B,C) -> evalDis2bb1in(A,B,C) [-1 + A + -1*C >= 0 && B >= 1 + C] (?,1) 5. evalDis2bbin(A,B,C) -> evalDis2bb2in(A,B,C) [-1 + A + -1*C >= 0 && C >= B] (?,1) 6. evalDis2bb1in(A,B,C) -> evalDis2bb3in(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + A + -1*C >= 0] (?,1) 7. evalDis2bb2in(A,B,C) -> evalDis2bb3in(A,1 + B,C) [-1 + A + -1*C >= 0 && -1*B + C >= 0 && -1 + A + -1*B >= 0] (?,1) 8. evalDis2returnin(A,B,C) -> evalDis2stop(A,B,C) [-1*A + C >= 0] (?,1) Signature: {(evalDis2bb1in,3) ;(evalDis2bb2in,3) ;(evalDis2bb3in,3) ;(evalDis2bbin,3) ;(evalDis2entryin,3) ;(evalDis2returnin,3) ;(evalDis2start,3) ;(evalDis2stop,3)} 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. evalDis2start(A,B,C) -> evalDis2entryin(A,B,C) True (1,1) 1. evalDis2entryin(A,B,C) -> evalDis2bb3in(B,C,A) True (1,1) 2. evalDis2bb3in(A,B,C) -> evalDis2bbin(A,B,C) [A >= 1 + C] (?,1) 3. evalDis2bb3in(A,B,C) -> evalDis2returnin(A,B,C) [C >= A] (1,1) 4. evalDis2bbin(A,B,C) -> evalDis2bb1in(A,B,C) [-1 + A + -1*C >= 0 && B >= 1 + C] (?,1) 5. evalDis2bbin(A,B,C) -> evalDis2bb2in(A,B,C) [-1 + A + -1*C >= 0 && C >= B] (?,1) 6. evalDis2bb1in(A,B,C) -> evalDis2bb3in(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + A + -1*C >= 0] (?,1) 7. evalDis2bb2in(A,B,C) -> evalDis2bb3in(A,1 + B,C) [-1 + A + -1*C >= 0 && -1*B + C >= 0 && -1 + A + -1*B >= 0] (?,1) 8. evalDis2returnin(A,B,C) -> evalDis2stop(A,B,C) [-1*A + C >= 0] (1,1) Signature: {(evalDis2bb1in,3) ;(evalDis2bb2in,3) ;(evalDis2bb3in,3) ;(evalDis2bbin,3) ;(evalDis2entryin,3) ;(evalDis2returnin,3) ;(evalDis2start,3) ;(evalDis2stop,3)} 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: [(7,3)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalDis2start(A,B,C) -> evalDis2entryin(A,B,C) True (1,1) 1. evalDis2entryin(A,B,C) -> evalDis2bb3in(B,C,A) True (1,1) 2. evalDis2bb3in(A,B,C) -> evalDis2bbin(A,B,C) [A >= 1 + C] (?,1) 3. evalDis2bb3in(A,B,C) -> evalDis2returnin(A,B,C) [C >= A] (1,1) 4. evalDis2bbin(A,B,C) -> evalDis2bb1in(A,B,C) [-1 + A + -1*C >= 0 && B >= 1 + C] (?,1) 5. evalDis2bbin(A,B,C) -> evalDis2bb2in(A,B,C) [-1 + A + -1*C >= 0 && C >= B] (?,1) 6. evalDis2bb1in(A,B,C) -> evalDis2bb3in(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + A + -1*C >= 0] (?,1) 7. evalDis2bb2in(A,B,C) -> evalDis2bb3in(A,1 + B,C) [-1 + A + -1*C >= 0 && -1*B + C >= 0 && -1 + A + -1*B >= 0] (?,1) 8. evalDis2returnin(A,B,C) -> evalDis2stop(A,B,C) [-1*A + C >= 0] (1,1) Signature: {(evalDis2bb1in,3) ;(evalDis2bb2in,3) ;(evalDis2bb3in,3) ;(evalDis2bbin,3) ;(evalDis2entryin,3) ;(evalDis2returnin,3) ;(evalDis2start,3) ;(evalDis2stop,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2,3},7->{2},8->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalDis2start(A,B,C) -> evalDis2entryin(A,B,C) True (1,1) 1. evalDis2entryin(A,B,C) -> evalDis2bb3in(B,C,A) True (?,1) 2. evalDis2bb3in(A,B,C) -> evalDis2bbin(A,B,C) [A >= 1 + C] (?,1) 3. evalDis2bb3in(A,B,C) -> evalDis2returnin(A,B,C) [C >= A] (?,1) 4. evalDis2bbin(A,B,C) -> evalDis2bb1in(A,B,C) [-1 + A + -1*C >= 0 && B >= 1 + C] (?,1) 5. evalDis2bbin(A,B,C) -> evalDis2bb2in(A,B,C) [-1 + A + -1*C >= 0 && C >= B] (?,1) 6. evalDis2bb1in(A,B,C) -> evalDis2bb3in(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + A + -1*C >= 0] (?,1) 7. evalDis2bb2in(A,B,C) -> evalDis2bb3in(A,1 + B,C) [-1 + A + -1*C >= 0 && -1*B + C >= 0 && -1 + A + -1*B >= 0] (?,1) 8. evalDis2returnin(A,B,C) -> evalDis2stop(A,B,C) [-1*A + C >= 0] (?,1) 9. evalDis2returnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalDis2bb1in,3) ;(evalDis2bb2in,3) ;(evalDis2bb3in,3) ;(evalDis2bbin,3) ;(evalDis2entryin,3) ;(evalDis2returnin,3) ;(evalDis2start,3) ;(evalDis2stop,3) ;(exitus616,3)} 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: [(7,3)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalDis2start(A,B,C) -> evalDis2entryin(A,B,C) True (1,1) 1. evalDis2entryin(A,B,C) -> evalDis2bb3in(B,C,A) True (?,1) 2. evalDis2bb3in(A,B,C) -> evalDis2bbin(A,B,C) [A >= 1 + C] (?,1) 3. evalDis2bb3in(A,B,C) -> evalDis2returnin(A,B,C) [C >= A] (?,1) 4. evalDis2bbin(A,B,C) -> evalDis2bb1in(A,B,C) [-1 + A + -1*C >= 0 && B >= 1 + C] (?,1) 5. evalDis2bbin(A,B,C) -> evalDis2bb2in(A,B,C) [-1 + A + -1*C >= 0 && C >= B] (?,1) 6. evalDis2bb1in(A,B,C) -> evalDis2bb3in(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + A + -1*C >= 0] (?,1) 7. evalDis2bb2in(A,B,C) -> evalDis2bb3in(A,1 + B,C) [-1 + A + -1*C >= 0 && -1*B + C >= 0 && -1 + A + -1*B >= 0] (?,1) 8. evalDis2returnin(A,B,C) -> evalDis2stop(A,B,C) [-1*A + C >= 0] (?,1) 9. evalDis2returnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalDis2bb1in,3) ;(evalDis2bb2in,3) ;(evalDis2bb3in,3) ;(evalDis2bbin,3) ;(evalDis2entryin,3) ;(evalDis2returnin,3) ;(evalDis2start,3) ;(evalDis2stop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8,9},4->{6},5->{7},6->{2,3},7->{2},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. evalDis2start(A,B,C) -> evalDis2entryin(A,B,C) True (1,1) 1. evalDis2entryin(A,B,C) -> evalDis2bb3in(B,C,A) True (?,1) 2. evalDis2bb3in(A,B,C) -> evalDis2bbin(A,B,C) [A >= 1 + C] (?,1) 3. evalDis2bb3in(A,B,C) -> evalDis2returnin(A,B,C) [C >= A] (?,1) 4. evalDis2bbin(A,B,C) -> evalDis2bb1in(A,B,C) [-1 + A + -1*C >= 0 && B >= 1 + C] (?,1) 5. evalDis2bbin(A,B,C) -> evalDis2bb2in(A,B,C) [-1 + A + -1*C >= 0 && C >= B] (?,1) 6. evalDis2bb1in(A,B,C) -> evalDis2bb3in(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + A + -1*C >= 0] (?,1) 7. evalDis2bb2in(A,B,C) -> evalDis2bb3in(A,1 + B,C) [-1 + A + -1*C >= 0 && -1*B + C >= 0 && -1 + A + -1*B >= 0] (?,1) 8. evalDis2returnin(A,B,C) -> evalDis2stop(A,B,C) [-1*A + C >= 0] (?,1) 9. evalDis2returnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalDis2bb1in,3) ;(evalDis2bb2in,3) ;(evalDis2bb3in,3) ;(evalDis2bbin,3) ;(evalDis2entryin,3) ;(evalDis2returnin,3) ;(evalDis2start,3) ;(evalDis2stop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8,9},4->{6},5->{7},6->{2,3},7->{2},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,0.0,0.0.0] evalDis2start ~> evalDis2entryin [A <= A, B <= B, C <= C] evalDis2entryin ~> evalDis2bb3in [A <= B, B <= C, C <= A] evalDis2bb3in ~> evalDis2bbin [A <= A, B <= B, C <= C] evalDis2bb3in ~> evalDis2returnin [A <= A, B <= B, C <= C] evalDis2bbin ~> evalDis2bb1in [A <= A, B <= B, C <= C] evalDis2bbin ~> evalDis2bb2in [A <= A, B <= B, C <= C] evalDis2bb1in ~> evalDis2bb3in [A <= A, B <= B, C <= K + C] evalDis2bb2in ~> evalDis2bb3in [A <= A, B <= A + B, C <= C] evalDis2returnin ~> evalDis2stop [A <= A, B <= B, C <= C] evalDis2returnin ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= A + B] evalDis2bb3in ~> evalDis2bbin [A <= A, B <= B, C <= C] evalDis2bb1in ~> evalDis2bb3in [A <= A, B <= B, C <= K + C] evalDis2bbin ~> evalDis2bb1in [A <= A, B <= B, C <= C] evalDis2bb2in ~> evalDis2bb3in [A <= A, B <= A + B, C <= C] evalDis2bbin ~> evalDis2bb2in [A <= A, B <= B, C <= C] + Loop: [0.0.0 <= A + C] evalDis2bb3in ~> evalDis2bbin [A <= A, B <= B, C <= C] evalDis2bb1in ~> evalDis2bb3in [A <= A, B <= B, C <= K + C] evalDis2bbin ~> evalDis2bb1in [A <= A, B <= B, C <= C] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0] evalDis2start ~> evalDis2entryin [] evalDis2entryin ~> evalDis2bb3in [A ~=> C,B ~=> A,C ~=> B] evalDis2bb3in ~> evalDis2bbin [] evalDis2bb3in ~> evalDis2returnin [] evalDis2bbin ~> evalDis2bb1in [] evalDis2bbin ~> evalDis2bb2in [] evalDis2bb1in ~> evalDis2bb3in [C ~+> C,K ~+> C] evalDis2bb2in ~> evalDis2bb3in [A ~+> B,B ~+> B] evalDis2returnin ~> evalDis2stop [] evalDis2returnin ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0] evalDis2bb3in ~> evalDis2bbin [] evalDis2bb1in ~> evalDis2bb3in [C ~+> C,K ~+> C] evalDis2bbin ~> evalDis2bb1in [] evalDis2bb2in ~> evalDis2bb3in [A ~+> B,B ~+> B] evalDis2bbin ~> evalDis2bb2in [] + Loop: [A ~+> 0.0.0,C ~+> 0.0.0] evalDis2bb3in ~> evalDis2bbin [] evalDis2bb1in ~> evalDis2bb3in [C ~+> C,K ~+> C] evalDis2bbin ~> evalDis2bb1in [] + Applied Processor: LareProcessor + Details: evalDis2start ~> exitus616 [A ~=> C ,B ~=> A ,C ~=> B ,A ~+> C ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> B ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> C ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> B ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,C ~*> B ,C ~*> C ,C ~*> tick ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick ,B ~^> C ,C ~^> C] evalDis2start ~> evalDis2stop [A ~=> C ,B ~=> A ,C ~=> B ,A ~+> C ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> B ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> C ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> B ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,C ~*> B ,C ~*> C ,C ~*> tick ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick ,B ~^> C ,C ~^> C] + evalDis2bb3in> [A ~+> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> B ,A ~*> C ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> B ,B ~*> C ,B ~*> tick ,C ~*> C ,C ~*> 0.0.0 ,C ~*> tick ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> C ,B ~^> C] + evalDis2bbin> [A ~+> 0.0.0 ,A ~+> tick ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> C ,A ~*> C ,C ~*> C ,K ~*> C] evalDis2bb3in> [A ~+> 0.0.0 ,A ~+> tick ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> C ,A ~*> C ,C ~*> C ,K ~*> C] YES(?,POLY)