YES(?,O(n^1)) * Step 1: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = A && E = F] 1. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,1,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 2. start(A,B,C,D,E,F) -> lbl101(A,2,C,D,-1,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] 3. lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A + E >= 0 && A >= 1 && A >= E && B = 1 + A && D = A] 4. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 5. lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,-1 + E,F) [D + -1*E >= 0 (?,1) && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] 6. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) Signature: {(lbl101,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5},2->{3,4,5},3->{},4->{3,4,5},5->{3,4,5},6->{0,1,2}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = A && E = F] start(A,B,C,D,E,F) -> lbl101(A,2,C,D,1,F) [E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] start(A,B,C,D,E,F) -> lbl101(A,2,C,D,-1,F) [E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A + E >= 0 && A >= 1 && A >= E && B = 1 + A && D = A] lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,1 + E,F) [D + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,-1 + E,F) [D + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True Signature: {(lbl101,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{3,4,5},2->{3,4,5},3->{},4->{3,4,5},5->{3,4,5},6->{0,1,2}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = A && E = F] start(A,B,C,D,E,F) -> lbl101(A,2,C,D,1,F) [E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] start(A,B,C,D,E,F) -> lbl101(A,2,C,D,-1,F) [E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A + E >= 0 && A >= 1 && A >= E && B = 1 + A && D = A] lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,1 + E,F) [D + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,-1 + E,F) [D + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True stop(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6);(lbl101,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{9},1->{3,4,5},2->{3,4,5},3->{7,8},4->{3,4,5},5->{3,4,5},6->{0,1,2}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[4,5] c: [4,5] * Step 4: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = A && E = F] start(A,B,C,D,E,F) -> lbl101(A,2,C,D,1,F) [E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] start(A,B,C,D,E,F) -> lbl101(A,2,C,D,-1,F) [E + -1*F >= 0 && -1*E + F >= 0 && A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = A && E = F] lbl101(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [D + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A + E >= 0 && A >= 1 && A >= E && B = 1 + A && D = A] lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,1 + E,F) [D + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] lbl101(A,B,C,D,E,F) -> lbl101(A,1 + B,C,D,-1 + E,F) [D + -1*E >= 0 && -1 + B + -1*E >= 0 && A + -1*E >= 0 && D + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && 1 + A + -1*B >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + A >= 0 && A >= B && B + E >= 1 && 1 + A >= B && B >= 2 && B >= 1 + E && D = A] start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True stop(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6);(lbl101,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{9},1->{3,4,5},2->{3,4,5},3->{7,8},4->{3,4,5},5->{3,4,5},6->{0,1,2}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[4,5] c: [4,5]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0] start ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] start ~> lbl101 [A <= A, B <= 2*K, C <= C, D <= D, E <= K, F <= F] start ~> lbl101 [A <= A, B <= 2*K, C <= C, D <= D, E <= K, F <= F] lbl101 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl101 ~> lbl101 [A <= A, B <= A + D, C <= C, D <= D, E <= A, F <= F] lbl101 ~> lbl101 [A <= A, B <= A + D, C <= C, D <= D, E <= B, F <= F] start0 ~> start [A <= A, B <= C, C <= C, D <= A, E <= F, F <= F] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= K + A + B] lbl101 ~> lbl101 [A <= A, B <= A + D, C <= C, D <= D, E <= A, F <= F] lbl101 ~> lbl101 [A <= A, B <= A + D, C <= C, D <= D, E <= B, F <= F] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0] start ~> stop [] start ~> lbl101 [K ~=> B,K ~=> E] start ~> lbl101 [K ~=> B,K ~=> E] lbl101 ~> stop [] lbl101 ~> lbl101 [A ~=> E,A ~+> B,D ~+> B] lbl101 ~> lbl101 [B ~=> E,A ~+> B,D ~+> B] start0 ~> start [A ~=> D,C ~=> B,F ~=> E] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] lbl101 ~> lbl101 [A ~=> E,A ~+> B,D ~+> B] lbl101 ~> lbl101 [B ~=> E,A ~+> B,D ~+> B] + Applied Processor: Lare + Details: start0 ~> exitus616 [A ~=> D ,A ~=> E ,C ~=> B ,F ~=> E ,K ~=> B ,K ~=> E ,A ~+> B ,A ~+> E ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,A ~*> E ,K ~*> 0.0 ,K ~*> tick] + lbl101> [A ~=> E ,B ~=> E ,A ~+> B ,A ~+> E ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,D ~+> B ,D ~+> E ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick] YES(?,O(n^1))