YES(?,O(n^1)) * Step 1: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalaaron2start(A,B,C) -> evalaaron2entryin(A,B,C) True (1,1) 1. evalaaron2entryin(A,B,C) -> evalaaron2bb6in(A,C,B) [A >= 0] (?,1) 2. evalaaron2entryin(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] (?,1) 3. evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [A >= 0 && B >= 1 + C] (?,1) 4. evalaaron2bb6in(A,B,C) -> evalaaron2bb3in(A,B,C) [A >= 0 && C >= B] (?,1) 5. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [-1*B + C >= 0 && A >= 0 && 0 >= 1 + D] (?,1) 6. evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [-1*B + C >= 0 && A >= 0 && D >= 1] (?,1) 7. evalaaron2bb3in(A,B,C) -> evalaaron2bb5in(A,B,C) [-1*B + C >= 0 && A >= 0] (?,1) 8. evalaaron2bb4in(A,B,C) -> evalaaron2bb6in(A,B,-1 + -1*A + C) [-1*B + C >= 0 && A >= 0] (?,1) 9. evalaaron2bb5in(A,B,C) -> evalaaron2bb6in(A,1 + A + B,C) [-1*B + C >= 0 && A >= 0] (?,1) 10. evalaaron2returnin(A,B,C) -> evalaaron2stop(A,B,C) True (?,1) Signature: {(evalaaron2bb3in,3) ;(evalaaron2bb4in,3) ;(evalaaron2bb5in,3) ;(evalaaron2bb6in,3) ;(evalaaron2entryin,3) ;(evalaaron2returnin,3) ;(evalaaron2start,3) ;(evalaaron2stop,3)} Flow Graph: [0->{1,2},1->{3,4},2->{10},3->{10},4->{5,6,7},5->{8},6->{8},7->{9},8->{3,4},9->{3,4},10->{}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalaaron2start(A,B,C) -> evalaaron2entryin(A,B,C) True evalaaron2entryin(A,B,C) -> evalaaron2bb6in(A,C,B) [A >= 0] evalaaron2entryin(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [A >= 0 && B >= 1 + C] evalaaron2bb6in(A,B,C) -> evalaaron2bb3in(A,B,C) [A >= 0 && C >= B] evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [-1*B + C >= 0 && A >= 0 && 0 >= 1 + D] evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [-1*B + C >= 0 && A >= 0 && D >= 1] evalaaron2bb3in(A,B,C) -> evalaaron2bb5in(A,B,C) [-1*B + C >= 0 && A >= 0] evalaaron2bb4in(A,B,C) -> evalaaron2bb6in(A,B,-1 + -1*A + C) [-1*B + C >= 0 && A >= 0] evalaaron2bb5in(A,B,C) -> evalaaron2bb6in(A,1 + A + B,C) [-1*B + C >= 0 && A >= 0] evalaaron2returnin(A,B,C) -> evalaaron2stop(A,B,C) True Signature: {(evalaaron2bb3in,3) ;(evalaaron2bb4in,3) ;(evalaaron2bb5in,3) ;(evalaaron2bb6in,3) ;(evalaaron2entryin,3) ;(evalaaron2returnin,3) ;(evalaaron2start,3) ;(evalaaron2stop,3)} Rule Graph: [0->{1,2},1->{3,4},2->{10},3->{10},4->{5,6,7},5->{8},6->{8},7->{9},8->{3,4},9->{3,4},10->{}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalaaron2start(A,B,C) -> evalaaron2entryin(A,B,C) True evalaaron2entryin(A,B,C) -> evalaaron2bb6in(A,C,B) [A >= 0] evalaaron2entryin(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [A >= 0 && B >= 1 + C] evalaaron2bb6in(A,B,C) -> evalaaron2bb3in(A,B,C) [A >= 0 && C >= B] evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [-1*B + C >= 0 && A >= 0 && 0 >= 1 + D] evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [-1*B + C >= 0 && A >= 0 && D >= 1] evalaaron2bb3in(A,B,C) -> evalaaron2bb5in(A,B,C) [-1*B + C >= 0 && A >= 0] evalaaron2bb4in(A,B,C) -> evalaaron2bb6in(A,B,-1 + -1*A + C) [-1*B + C >= 0 && A >= 0] evalaaron2bb5in(A,B,C) -> evalaaron2bb6in(A,1 + A + B,C) [-1*B + C >= 0 && A >= 0] evalaaron2returnin(A,B,C) -> evalaaron2stop(A,B,C) True evalaaron2stop(A,B,C) -> exitus616(A,B,C) True evalaaron2stop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalaaron2bb3in,3) ;(evalaaron2bb4in,3) ;(evalaaron2bb5in,3) ;(evalaaron2bb6in,3) ;(evalaaron2entryin,3) ;(evalaaron2returnin,3) ;(evalaaron2start,3) ;(evalaaron2stop,3) ;(exitus616,3)} Rule Graph: [0->{1,2},1->{3,4},2->{10},3->{10},4->{5,6,7},5->{8},6->{8},7->{9},8->{3,4},9->{3,4},10->{11,12}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[4,8,5,6,9,7] c: [4,5,6,7,8,9] * Step 4: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: evalaaron2start(A,B,C) -> evalaaron2entryin(A,B,C) True evalaaron2entryin(A,B,C) -> evalaaron2bb6in(A,C,B) [A >= 0] evalaaron2entryin(A,B,C) -> evalaaron2returnin(A,B,C) [0 >= 1 + A] evalaaron2bb6in(A,B,C) -> evalaaron2returnin(A,B,C) [A >= 0 && B >= 1 + C] evalaaron2bb6in(A,B,C) -> evalaaron2bb3in(A,B,C) [A >= 0 && C >= B] evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [-1*B + C >= 0 && A >= 0 && 0 >= 1 + D] evalaaron2bb3in(A,B,C) -> evalaaron2bb4in(A,B,C) [-1*B + C >= 0 && A >= 0 && D >= 1] evalaaron2bb3in(A,B,C) -> evalaaron2bb5in(A,B,C) [-1*B + C >= 0 && A >= 0] evalaaron2bb4in(A,B,C) -> evalaaron2bb6in(A,B,-1 + -1*A + C) [-1*B + C >= 0 && A >= 0] evalaaron2bb5in(A,B,C) -> evalaaron2bb6in(A,1 + A + B,C) [-1*B + C >= 0 && A >= 0] evalaaron2returnin(A,B,C) -> evalaaron2stop(A,B,C) True evalaaron2stop(A,B,C) -> exitus616(A,B,C) True evalaaron2stop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalaaron2bb3in,3) ;(evalaaron2bb4in,3) ;(evalaaron2bb5in,3) ;(evalaaron2bb6in,3) ;(evalaaron2entryin,3) ;(evalaaron2returnin,3) ;(evalaaron2start,3) ;(evalaaron2stop,3) ;(exitus616,3)} Rule Graph: [0->{1,2},1->{3,4},2->{10},3->{10},4->{5,6,7},5->{8},6->{8},7->{9},8->{3,4},9->{3,4},10->{11,12}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[4,8,5,6,9,7] c: [4,5,6,7,8,9]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0] evalaaron2start ~> evalaaron2entryin [A <= A, B <= B, C <= C] evalaaron2entryin ~> evalaaron2bb6in [A <= A, B <= C, C <= B] evalaaron2entryin ~> evalaaron2returnin [A <= A, B <= B, C <= C] evalaaron2bb6in ~> evalaaron2returnin [A <= A, B <= B, C <= C] evalaaron2bb6in ~> evalaaron2bb3in [A <= A, B <= B, C <= C] evalaaron2bb3in ~> evalaaron2bb4in [A <= A, B <= B, C <= C] evalaaron2bb3in ~> evalaaron2bb4in [A <= A, B <= B, C <= C] evalaaron2bb3in ~> evalaaron2bb5in [A <= A, B <= B, C <= C] evalaaron2bb4in ~> evalaaron2bb6in [A <= A, B <= B, C <= K + A + C] evalaaron2bb5in ~> evalaaron2bb6in [A <= A, B <= K + A + B, C <= C] evalaaron2returnin ~> evalaaron2stop [A <= A, B <= B, C <= C] evalaaron2stop ~> exitus616 [A <= A, B <= B, C <= C] evalaaron2stop ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= B + C] evalaaron2bb6in ~> evalaaron2bb3in [A <= A, B <= B, C <= C] evalaaron2bb4in ~> evalaaron2bb6in [A <= A, B <= B, C <= K + A + C] evalaaron2bb3in ~> evalaaron2bb4in [A <= A, B <= B, C <= C] evalaaron2bb3in ~> evalaaron2bb4in [A <= A, B <= B, C <= C] evalaaron2bb5in ~> evalaaron2bb6in [A <= A, B <= K + A + B, C <= C] evalaaron2bb3in ~> evalaaron2bb5in [A <= A, B <= B, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] evalaaron2start ~> evalaaron2entryin [] evalaaron2entryin ~> evalaaron2bb6in [B ~=> C,C ~=> B] evalaaron2entryin ~> evalaaron2returnin [] evalaaron2bb6in ~> evalaaron2returnin [] evalaaron2bb6in ~> evalaaron2bb3in [] evalaaron2bb3in ~> evalaaron2bb4in [] evalaaron2bb3in ~> evalaaron2bb4in [] evalaaron2bb3in ~> evalaaron2bb5in [] evalaaron2bb4in ~> evalaaron2bb6in [A ~+> C,C ~+> C,K ~+> C] evalaaron2bb5in ~> evalaaron2bb6in [A ~+> B,B ~+> B,K ~+> B] evalaaron2returnin ~> evalaaron2stop [] evalaaron2stop ~> exitus616 [] evalaaron2stop ~> exitus616 [] + Loop: [B ~+> 0.0,C ~+> 0.0] evalaaron2bb6in ~> evalaaron2bb3in [] evalaaron2bb4in ~> evalaaron2bb6in [A ~+> C,C ~+> C,K ~+> C] evalaaron2bb3in ~> evalaaron2bb4in [] evalaaron2bb3in ~> evalaaron2bb4in [] evalaaron2bb5in ~> evalaaron2bb6in [A ~+> B,B ~+> B,K ~+> B] evalaaron2bb3in ~> evalaaron2bb5in [] + Applied Processor: Lare + Details: evalaaron2start ~> exitus616 [B ~=> C ,C ~=> B ,A ~+> B ,A ~+> C ,B ~+> C ,B ~+> 0.0 ,B ~+> tick ,C ~+> B ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,B ~*> B ,B ~*> C ,C ~*> B ,C ~*> C] + evalaaron2bb6in> [A ~+> B ,A ~+> C ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,B ~*> B ,B ~*> C ,C ~*> B ,C ~*> C] YES(?,O(n^1))