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: Unfold 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: Unfold + Details: () * Step 4: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalaaron2start.0(A,B,C) -> evalaaron2entryin.1(A,B,C) True evalaaron2start.0(A,B,C) -> evalaaron2entryin.2(A,B,C) True evalaaron2entryin.1(A,B,C) -> evalaaron2bb6in.3(A,C,B) [A >= 0] evalaaron2entryin.1(A,B,C) -> evalaaron2bb6in.4(A,C,B) [A >= 0] evalaaron2entryin.2(A,B,C) -> evalaaron2returnin.10(A,B,C) [0 >= 1 + A] evalaaron2bb6in.3(A,B,C) -> evalaaron2returnin.10(A,B,C) [A >= 0 && B >= 1 + C] evalaaron2bb6in.4(A,B,C) -> evalaaron2bb3in.5(A,B,C) [A >= 0 && C >= B] evalaaron2bb6in.4(A,B,C) -> evalaaron2bb3in.6(A,B,C) [A >= 0 && C >= B] evalaaron2bb6in.4(A,B,C) -> evalaaron2bb3in.7(A,B,C) [A >= 0 && C >= B] evalaaron2bb3in.5(A,B,C) -> evalaaron2bb4in.8(A,B,C) [-1*B + C >= 0 && A >= 0 && 0 >= 1 + D] evalaaron2bb3in.6(A,B,C) -> evalaaron2bb4in.8(A,B,C) [-1*B + C >= 0 && A >= 0 && D >= 1] evalaaron2bb3in.7(A,B,C) -> evalaaron2bb5in.9(A,B,C) [-1*B + C >= 0 && A >= 0] evalaaron2bb4in.8(A,B,C) -> evalaaron2bb6in.3(A,B,-1 + -1*A + C) [-1*B + C >= 0 && A >= 0] evalaaron2bb4in.8(A,B,C) -> evalaaron2bb6in.4(A,B,-1 + -1*A + C) [-1*B + C >= 0 && A >= 0] evalaaron2bb5in.9(A,B,C) -> evalaaron2bb6in.3(A,1 + A + B,C) [-1*B + C >= 0 && A >= 0] evalaaron2bb5in.9(A,B,C) -> evalaaron2bb6in.4(A,1 + A + B,C) [-1*B + C >= 0 && A >= 0] evalaaron2returnin.10(A,B,C) -> evalaaron2stop.11(A,B,C) True evalaaron2returnin.10(A,B,C) -> evalaaron2stop.12(A,B,C) True evalaaron2stop.11(A,B,C) -> exitus616.13(A,B,C) True evalaaron2stop.12(A,B,C) -> exitus616.13(A,B,C) True Signature: {(evalaaron2bb3in.5,3) ;(evalaaron2bb3in.6,3) ;(evalaaron2bb3in.7,3) ;(evalaaron2bb4in.8,3) ;(evalaaron2bb5in.9,3) ;(evalaaron2bb6in.3,3) ;(evalaaron2bb6in.4,3) ;(evalaaron2entryin.1,3) ;(evalaaron2entryin.2,3) ;(evalaaron2returnin.10,3) ;(evalaaron2start.0,3) ;(evalaaron2stop.11,3) ;(evalaaron2stop.12,3) ;(exitus616.13,3)} Rule Graph: [0->{2,3},1->{4},2->{5},3->{6,7,8},4->{16,17},5->{16,17},6->{9},7->{10},8->{11},9->{12,13},10->{12,13} ,11->{14,15},12->{5},13->{6,7,8},14->{5},15->{6,7,8},16->{18},17->{19},18->{},19->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] | `- p:[6,13,9,10,7,15,11,8] c: [6,7,8,9,10,11,13,15] * Step 5: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: evalaaron2start.0(A,B,C) -> evalaaron2entryin.1(A,B,C) True evalaaron2start.0(A,B,C) -> evalaaron2entryin.2(A,B,C) True evalaaron2entryin.1(A,B,C) -> evalaaron2bb6in.3(A,C,B) [A >= 0] evalaaron2entryin.1(A,B,C) -> evalaaron2bb6in.4(A,C,B) [A >= 0] evalaaron2entryin.2(A,B,C) -> evalaaron2returnin.10(A,B,C) [0 >= 1 + A] evalaaron2bb6in.3(A,B,C) -> evalaaron2returnin.10(A,B,C) [A >= 0 && B >= 1 + C] evalaaron2bb6in.4(A,B,C) -> evalaaron2bb3in.5(A,B,C) [A >= 0 && C >= B] evalaaron2bb6in.4(A,B,C) -> evalaaron2bb3in.6(A,B,C) [A >= 0 && C >= B] evalaaron2bb6in.4(A,B,C) -> evalaaron2bb3in.7(A,B,C) [A >= 0 && C >= B] evalaaron2bb3in.5(A,B,C) -> evalaaron2bb4in.8(A,B,C) [-1*B + C >= 0 && A >= 0 && 0 >= 1 + D] evalaaron2bb3in.6(A,B,C) -> evalaaron2bb4in.8(A,B,C) [-1*B + C >= 0 && A >= 0 && D >= 1] evalaaron2bb3in.7(A,B,C) -> evalaaron2bb5in.9(A,B,C) [-1*B + C >= 0 && A >= 0] evalaaron2bb4in.8(A,B,C) -> evalaaron2bb6in.3(A,B,-1 + -1*A + C) [-1*B + C >= 0 && A >= 0] evalaaron2bb4in.8(A,B,C) -> evalaaron2bb6in.4(A,B,-1 + -1*A + C) [-1*B + C >= 0 && A >= 0] evalaaron2bb5in.9(A,B,C) -> evalaaron2bb6in.3(A,1 + A + B,C) [-1*B + C >= 0 && A >= 0] evalaaron2bb5in.9(A,B,C) -> evalaaron2bb6in.4(A,1 + A + B,C) [-1*B + C >= 0 && A >= 0] evalaaron2returnin.10(A,B,C) -> evalaaron2stop.11(A,B,C) True evalaaron2returnin.10(A,B,C) -> evalaaron2stop.12(A,B,C) True evalaaron2stop.11(A,B,C) -> exitus616.13(A,B,C) True evalaaron2stop.12(A,B,C) -> exitus616.13(A,B,C) True Signature: {(evalaaron2bb3in.5,3) ;(evalaaron2bb3in.6,3) ;(evalaaron2bb3in.7,3) ;(evalaaron2bb4in.8,3) ;(evalaaron2bb5in.9,3) ;(evalaaron2bb6in.3,3) ;(evalaaron2bb6in.4,3) ;(evalaaron2entryin.1,3) ;(evalaaron2entryin.2,3) ;(evalaaron2returnin.10,3) ;(evalaaron2start.0,3) ;(evalaaron2stop.11,3) ;(evalaaron2stop.12,3) ;(exitus616.13,3)} Rule Graph: [0->{2,3},1->{4},2->{5},3->{6,7,8},4->{16,17},5->{16,17},6->{9},7->{10},8->{11},9->{12,13},10->{12,13} ,11->{14,15},12->{5},13->{6,7,8},14->{5},15->{6,7,8},16->{18},17->{19},18->{},19->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] | `- p:[6,13,9,10,7,15,11,8] c: [6,7,8,9,10,11,13,15]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0] evalaaron2start.0 ~> evalaaron2entryin.1 [A <= A, B <= B, C <= C] evalaaron2start.0 ~> evalaaron2entryin.2 [A <= A, B <= B, C <= C] evalaaron2entryin.1 ~> evalaaron2bb6in.3 [A <= A, B <= C, C <= B] evalaaron2entryin.1 ~> evalaaron2bb6in.4 [A <= A, B <= C, C <= B] evalaaron2entryin.2 ~> evalaaron2returnin.10 [A <= A, B <= B, C <= C] evalaaron2bb6in.3 ~> evalaaron2returnin.10 [A <= A, B <= B, C <= C] evalaaron2bb6in.4 ~> evalaaron2bb3in.5 [A <= A, B <= B, C <= C] evalaaron2bb6in.4 ~> evalaaron2bb3in.6 [A <= A, B <= B, C <= C] evalaaron2bb6in.4 ~> evalaaron2bb3in.7 [A <= A, B <= B, C <= C] evalaaron2bb3in.5 ~> evalaaron2bb4in.8 [A <= A, B <= B, C <= C] evalaaron2bb3in.6 ~> evalaaron2bb4in.8 [A <= A, B <= B, C <= C] evalaaron2bb3in.7 ~> evalaaron2bb5in.9 [A <= A, B <= B, C <= C] evalaaron2bb4in.8 ~> evalaaron2bb6in.3 [A <= A, B <= B, C <= K + A + C] evalaaron2bb4in.8 ~> evalaaron2bb6in.4 [A <= A, B <= B, C <= K + A + C] evalaaron2bb5in.9 ~> evalaaron2bb6in.3 [A <= A, B <= K + A + B, C <= C] evalaaron2bb5in.9 ~> evalaaron2bb6in.4 [A <= A, B <= K + A + B, C <= C] evalaaron2returnin.10 ~> evalaaron2stop.11 [A <= A, B <= B, C <= C] evalaaron2returnin.10 ~> evalaaron2stop.12 [A <= A, B <= B, C <= C] evalaaron2stop.11 ~> exitus616.13 [A <= A, B <= B, C <= C] evalaaron2stop.12 ~> exitus616.13 [A <= A, B <= B, C <= C] + Loop: [0.0 <= B + C] evalaaron2bb6in.4 ~> evalaaron2bb3in.5 [A <= A, B <= B, C <= C] evalaaron2bb4in.8 ~> evalaaron2bb6in.4 [A <= A, B <= B, C <= K + A + C] evalaaron2bb3in.5 ~> evalaaron2bb4in.8 [A <= A, B <= B, C <= C] evalaaron2bb3in.6 ~> evalaaron2bb4in.8 [A <= A, B <= B, C <= C] evalaaron2bb6in.4 ~> evalaaron2bb3in.6 [A <= A, B <= B, C <= C] evalaaron2bb5in.9 ~> evalaaron2bb6in.4 [A <= A, B <= K + A + B, C <= C] evalaaron2bb3in.7 ~> evalaaron2bb5in.9 [A <= A, B <= B, C <= C] evalaaron2bb6in.4 ~> evalaaron2bb3in.7 [A <= A, B <= B, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] evalaaron2start.0 ~> evalaaron2entryin.1 [] evalaaron2start.0 ~> evalaaron2entryin.2 [] evalaaron2entryin.1 ~> evalaaron2bb6in.3 [B ~=> C,C ~=> B] evalaaron2entryin.1 ~> evalaaron2bb6in.4 [B ~=> C,C ~=> B] evalaaron2entryin.2 ~> evalaaron2returnin.10 [] evalaaron2bb6in.3 ~> evalaaron2returnin.10 [] evalaaron2bb6in.4 ~> evalaaron2bb3in.5 [] evalaaron2bb6in.4 ~> evalaaron2bb3in.6 [] evalaaron2bb6in.4 ~> evalaaron2bb3in.7 [] evalaaron2bb3in.5 ~> evalaaron2bb4in.8 [] evalaaron2bb3in.6 ~> evalaaron2bb4in.8 [] evalaaron2bb3in.7 ~> evalaaron2bb5in.9 [] evalaaron2bb4in.8 ~> evalaaron2bb6in.3 [A ~+> C,C ~+> C,K ~+> C] evalaaron2bb4in.8 ~> evalaaron2bb6in.4 [A ~+> C,C ~+> C,K ~+> C] evalaaron2bb5in.9 ~> evalaaron2bb6in.3 [A ~+> B,B ~+> B,K ~+> B] evalaaron2bb5in.9 ~> evalaaron2bb6in.4 [A ~+> B,B ~+> B,K ~+> B] evalaaron2returnin.10 ~> evalaaron2stop.11 [] evalaaron2returnin.10 ~> evalaaron2stop.12 [] evalaaron2stop.11 ~> exitus616.13 [] evalaaron2stop.12 ~> exitus616.13 [] + Loop: [B ~+> 0.0,C ~+> 0.0] evalaaron2bb6in.4 ~> evalaaron2bb3in.5 [] evalaaron2bb4in.8 ~> evalaaron2bb6in.4 [A ~+> C,C ~+> C,K ~+> C] evalaaron2bb3in.5 ~> evalaaron2bb4in.8 [] evalaaron2bb3in.6 ~> evalaaron2bb4in.8 [] evalaaron2bb6in.4 ~> evalaaron2bb3in.6 [] evalaaron2bb5in.9 ~> evalaaron2bb6in.4 [A ~+> B,B ~+> B,K ~+> B] evalaaron2bb3in.7 ~> evalaaron2bb5in.9 [] evalaaron2bb6in.4 ~> evalaaron2bb3in.7 [] + Applied Processor: Lare + Details: evalaaron2start.0 ~> exitus616.13 [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 ,A ~*> B ,A ~*> C ,B ~*> B ,B ~*> C ,C ~*> B ,C ~*> C ,K ~*> B ,K ~*> C] + evalaaron2bb4in.8> [A ~+> B ,A ~+> C ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,A ~*> B ,A ~*> C ,B ~*> B ,B ~*> C ,C ~*> B ,C ~*> C ,K ~*> B ,K ~*> C] evalaaron2bb5in.9> [A ~+> B ,A ~+> C ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,A ~*> B ,A ~*> C ,B ~*> B ,B ~*> C ,C ~*> B ,C ~*> C ,K ~*> B ,K ~*> C] YES(?,O(n^1))