YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalDis1start(A,B,C,D) -> evalDis1entryin(A,B,C,D) True (1,1) 1. evalDis1entryin(A,B,C,D) -> evalDis1bb3in(B,A,D,C) True (?,1) 2. evalDis1bb3in(A,B,C,D) -> evalDis1bbin(A,B,C,D) [A >= 1 + B] (?,1) 3. evalDis1bb3in(A,B,C,D) -> evalDis1returnin(A,B,C,D) [B >= A] (?,1) 4. evalDis1bbin(A,B,C,D) -> evalDis1bb1in(A,B,C,D) [-1 + A + -1*B >= 0 && C >= 1 + D] (?,1) 5. evalDis1bbin(A,B,C,D) -> evalDis1bb2in(A,B,C,D) [-1 + A + -1*B >= 0 && D >= C] (?,1) 6. evalDis1bb1in(A,B,C,D) -> evalDis1bb3in(A,B,C,1 + D) [-1 + C + -1*D >= 0 && -1 + A + -1*B >= 0] (?,1) 7. evalDis1bb2in(A,B,C,D) -> evalDis1bb3in(A,1 + B,C,D) [-1*C + D >= 0 && -1 + A + -1*B >= 0] (?,1) 8. evalDis1returnin(A,B,C,D) -> evalDis1stop(A,B,C,D) [-1*A + B >= 0] (?,1) Signature: {(evalDis1bb1in,4) ;(evalDis1bb2in,4) ;(evalDis1bb3in,4) ;(evalDis1bbin,4) ;(evalDis1entryin,4) ;(evalDis1returnin,4) ;(evalDis1start,4) ;(evalDis1stop,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(?,O(n^1)) + Considered Problem: Rules: 0. evalDis1start(A,B,C,D) -> evalDis1entryin(A,B,C,D) True (1,1) 1. evalDis1entryin(A,B,C,D) -> evalDis1bb3in(B,A,D,C) True (?,1) 2. evalDis1bb3in(A,B,C,D) -> evalDis1bbin(A,B,C,D) [A >= 1 + B] (?,1) 3. evalDis1bb3in(A,B,C,D) -> evalDis1returnin(A,B,C,D) [B >= A] (?,1) 4. evalDis1bbin(A,B,C,D) -> evalDis1bb1in(A,B,C,D) [-1 + A + -1*B >= 0 && C >= 1 + D] (?,1) 5. evalDis1bbin(A,B,C,D) -> evalDis1bb2in(A,B,C,D) [-1 + A + -1*B >= 0 && D >= C] (?,1) 6. evalDis1bb1in(A,B,C,D) -> evalDis1bb3in(A,B,C,1 + D) [-1 + C + -1*D >= 0 && -1 + A + -1*B >= 0] (?,1) 7. evalDis1bb2in(A,B,C,D) -> evalDis1bb3in(A,1 + B,C,D) [-1*C + D >= 0 && -1 + A + -1*B >= 0] (?,1) 8. evalDis1returnin(A,B,C,D) -> evalDis1stop(A,B,C,D) [-1*A + B >= 0] (?,1) Signature: {(evalDis1bb1in,4) ;(evalDis1bb2in,4) ;(evalDis1bb3in,4) ;(evalDis1bbin,4) ;(evalDis1entryin,4) ;(evalDis1returnin,4) ;(evalDis1start,4) ;(evalDis1stop,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(?,O(n^1)) + Considered Problem: Rules: evalDis1start(A,B,C,D) -> evalDis1entryin(A,B,C,D) True evalDis1entryin(A,B,C,D) -> evalDis1bb3in(B,A,D,C) True evalDis1bb3in(A,B,C,D) -> evalDis1bbin(A,B,C,D) [A >= 1 + B] evalDis1bb3in(A,B,C,D) -> evalDis1returnin(A,B,C,D) [B >= A] evalDis1bbin(A,B,C,D) -> evalDis1bb1in(A,B,C,D) [-1 + A + -1*B >= 0 && C >= 1 + D] evalDis1bbin(A,B,C,D) -> evalDis1bb2in(A,B,C,D) [-1 + A + -1*B >= 0 && D >= C] evalDis1bb1in(A,B,C,D) -> evalDis1bb3in(A,B,C,1 + D) [-1 + C + -1*D >= 0 && -1 + A + -1*B >= 0] evalDis1bb2in(A,B,C,D) -> evalDis1bb3in(A,1 + B,C,D) [-1*C + D >= 0 && -1 + A + -1*B >= 0] evalDis1returnin(A,B,C,D) -> evalDis1stop(A,B,C,D) [-1*A + B >= 0] Signature: {(evalDis1bb1in,4) ;(evalDis1bb2in,4) ;(evalDis1bb3in,4) ;(evalDis1bbin,4) ;(evalDis1entryin,4) ;(evalDis1returnin,4) ;(evalDis1start,4) ;(evalDis1stop,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: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalDis1start(A,B,C,D) -> evalDis1entryin(A,B,C,D) True evalDis1entryin(A,B,C,D) -> evalDis1bb3in(B,A,D,C) True evalDis1bb3in(A,B,C,D) -> evalDis1bbin(A,B,C,D) [A >= 1 + B] evalDis1bb3in(A,B,C,D) -> evalDis1returnin(A,B,C,D) [B >= A] evalDis1bbin(A,B,C,D) -> evalDis1bb1in(A,B,C,D) [-1 + A + -1*B >= 0 && C >= 1 + D] evalDis1bbin(A,B,C,D) -> evalDis1bb2in(A,B,C,D) [-1 + A + -1*B >= 0 && D >= C] evalDis1bb1in(A,B,C,D) -> evalDis1bb3in(A,B,C,1 + D) [-1 + C + -1*D >= 0 && -1 + A + -1*B >= 0] evalDis1bb2in(A,B,C,D) -> evalDis1bb3in(A,1 + B,C,D) [-1*C + D >= 0 && -1 + A + -1*B >= 0] evalDis1returnin(A,B,C,D) -> evalDis1stop(A,B,C,D) [-1*A + B >= 0] evalDis1stop(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(evalDis1bb1in,4) ;(evalDis1bb2in,4) ;(evalDis1bb3in,4) ;(evalDis1bbin,4) ;(evalDis1entryin,4) ;(evalDis1returnin,4) ;(evalDis1start,4) ;(evalDis1stop,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: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,6,4,7,5] c: [2,4,5,6,7] * Step 5: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: evalDis1start(A,B,C,D) -> evalDis1entryin(A,B,C,D) True evalDis1entryin(A,B,C,D) -> evalDis1bb3in(B,A,D,C) True evalDis1bb3in(A,B,C,D) -> evalDis1bbin(A,B,C,D) [A >= 1 + B] evalDis1bb3in(A,B,C,D) -> evalDis1returnin(A,B,C,D) [B >= A] evalDis1bbin(A,B,C,D) -> evalDis1bb1in(A,B,C,D) [-1 + A + -1*B >= 0 && C >= 1 + D] evalDis1bbin(A,B,C,D) -> evalDis1bb2in(A,B,C,D) [-1 + A + -1*B >= 0 && D >= C] evalDis1bb1in(A,B,C,D) -> evalDis1bb3in(A,B,C,1 + D) [-1 + C + -1*D >= 0 && -1 + A + -1*B >= 0] evalDis1bb2in(A,B,C,D) -> evalDis1bb3in(A,1 + B,C,D) [-1*C + D >= 0 && -1 + A + -1*B >= 0] evalDis1returnin(A,B,C,D) -> evalDis1stop(A,B,C,D) [-1*A + B >= 0] evalDis1stop(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(evalDis1bb1in,4) ;(evalDis1bb2in,4) ;(evalDis1bb3in,4) ;(evalDis1bbin,4) ;(evalDis1entryin,4) ;(evalDis1returnin,4) ;(evalDis1start,4) ;(evalDis1stop,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}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,6,4,7,5] c: [2,4,5,6,7]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,0.0] evalDis1start ~> evalDis1entryin [A <= A, B <= B, C <= C, D <= D] evalDis1entryin ~> evalDis1bb3in [A <= B, B <= A, C <= D, D <= C] evalDis1bb3in ~> evalDis1bbin [A <= A, B <= B, C <= C, D <= D] evalDis1bb3in ~> evalDis1returnin [A <= A, B <= B, C <= C, D <= D] evalDis1bbin ~> evalDis1bb1in [A <= A, B <= B, C <= C, D <= D] evalDis1bbin ~> evalDis1bb2in [A <= A, B <= B, C <= C, D <= D] evalDis1bb1in ~> evalDis1bb3in [A <= A, B <= B, C <= C, D <= C + D] evalDis1bb2in ~> evalDis1bb3in [A <= A, B <= A + B, C <= C, D <= D] evalDis1returnin ~> evalDis1stop [A <= A, B <= B, C <= C, D <= D] evalDis1stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= K + A + B + C + D] evalDis1bb3in ~> evalDis1bbin [A <= A, B <= B, C <= C, D <= D] evalDis1bb1in ~> evalDis1bb3in [A <= A, B <= B, C <= C, D <= C + D] evalDis1bbin ~> evalDis1bb1in [A <= A, B <= B, C <= C, D <= D] evalDis1bb2in ~> evalDis1bb3in [A <= A, B <= A + B, C <= C, D <= D] evalDis1bbin ~> evalDis1bb2in [A <= A, B <= B, C <= C, D <= D] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0] evalDis1start ~> evalDis1entryin [] evalDis1entryin ~> evalDis1bb3in [A ~=> B,B ~=> A,C ~=> D,D ~=> C] evalDis1bb3in ~> evalDis1bbin [] evalDis1bb3in ~> evalDis1returnin [] evalDis1bbin ~> evalDis1bb1in [] evalDis1bbin ~> evalDis1bb2in [] evalDis1bb1in ~> evalDis1bb3in [C ~+> D,D ~+> D] evalDis1bb2in ~> evalDis1bb3in [A ~+> B,B ~+> B] evalDis1returnin ~> evalDis1stop [] evalDis1stop ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0,D ~+> 0.0,K ~+> 0.0] evalDis1bb3in ~> evalDis1bbin [] evalDis1bb1in ~> evalDis1bb3in [C ~+> D,D ~+> D] evalDis1bbin ~> evalDis1bb1in [] evalDis1bb2in ~> evalDis1bb3in [A ~+> B,B ~+> B] evalDis1bbin ~> evalDis1bb2in [] + Applied Processor: Lare + Details: evalDis1start ~> exitus616 [A ~=> B ,B ~=> A ,C ~=> D ,D ~=> C ,A ~+> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> D ,C ~+> 0.0 ,C ~+> tick ,D ~+> D ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,A ~*> D ,B ~*> B ,B ~*> D ,C ~*> B ,C ~*> D ,D ~*> B ,D ~*> D ,K ~*> B ,K ~*> D] + evalDis1bb3in> [A ~+> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> D ,C ~+> 0.0 ,C ~+> tick ,D ~+> D ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,A ~*> D ,B ~*> B ,B ~*> D ,C ~*> B ,C ~*> D ,D ~*> B ,D ~*> D ,K ~*> B ,K ~*> D] YES(?,O(n^1))