YES(?,O(n^1)) * Step 1: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = A && G = H] 1. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && E >= 1 + C && B = C && D = E && F = A && G = H] 2. start(A,B,C,D,E,F,G,H) -> lbl72(A,-1 + B,C,1 + F,E,D,F,H) [G + -1*H >= 0 (?,1) && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && C >= E && 100 >= A && B = C && D = E && F = A && G = H] 3. lbl72(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*G >= 0 (?,1) && -1 + D + -1*G >= 0 && 201 + -1*D + -1*G >= 0 && 200 + -1*A + -1*G >= 0 && 1 + -1*D + G >= 0 && C + -1*E >= 0 && 101 + -1*D >= 0 && 201 + -1*A + -1*D >= 0 && -1 + -1*B + C >= 0 && 100 + -1*A >= 0 && F >= 101 && 100 >= A && 101 + B + F >= A + C + E && 1 + B >= F && C >= 1 + B && C >= E && 1 + B + F + G = A + C + E && B + D + F = A + C + E] 4. lbl72(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*G >= 0 (?,1) && -1 + D + -1*G >= 0 && 201 + -1*D + -1*G >= 0 && 200 + -1*A + -1*G >= 0 && 1 + -1*D + G >= 0 && C + -1*E >= 0 && 101 + -1*D >= 0 && 201 + -1*A + -1*D >= 0 && -1 + -1*B + C >= 0 && 100 + -1*A >= 0 && A + C + E >= 1 + 2*B + F && 100 >= A && 101 + B + F >= A + C + E && 1 + B >= F && C >= 1 + B && C >= E && 1 + B + F + G = A + C + E && B + D + F = A + C + E] 5. lbl72(A,B,C,D,E,F,G,H) -> lbl72(A,-1 + B,C,1 + F,E,D,F,H) [100 + -1*G >= 0 (?,1) && -1 + D + -1*G >= 0 && 201 + -1*D + -1*G >= 0 && 200 + -1*A + -1*G >= 0 && 1 + -1*D + G >= 0 && C + -1*E >= 0 && 101 + -1*D >= 0 && 201 + -1*A + -1*D >= 0 && -1 + -1*B + C >= 0 && 100 + -1*A >= 0 && 2*B + F >= A + C + E && 100 >= F && 100 >= A && 101 + B + F >= A + C + E && 1 + B >= F && C >= 1 + B && C >= E && 1 + B + F + G = A + C + E && B + D + F = A + C + E] 6. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,A,H,H) True (1,1) Signature: {(lbl72,8);(start,8);(start0,8);(stop,8)} Flow Graph: [0->{},1->{},2->{3,4,5},3->{},4->{},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,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = A && G = H] start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && E >= 1 + C && B = C && D = E && F = A && G = H] start(A,B,C,D,E,F,G,H) -> lbl72(A,-1 + B,C,1 + F,E,D,F,H) [G + -1*H >= 0 && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && C >= E && 100 >= A && B = C && D = E && F = A && G = H] lbl72(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*G >= 0 && -1 + D + -1*G >= 0 && 201 + -1*D + -1*G >= 0 && 200 + -1*A + -1*G >= 0 && 1 + -1*D + G >= 0 && C + -1*E >= 0 && 101 + -1*D >= 0 && 201 + -1*A + -1*D >= 0 && -1 + -1*B + C >= 0 && 100 + -1*A >= 0 && F >= 101 && 100 >= A && 101 + B + F >= A + C + E && 1 + B >= F && C >= 1 + B && C >= E && 1 + B + F + G = A + C + E && B + D + F = A + C + E] lbl72(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*G >= 0 && -1 + D + -1*G >= 0 && 201 + -1*D + -1*G >= 0 && 200 + -1*A + -1*G >= 0 && 1 + -1*D + G >= 0 && C + -1*E >= 0 && 101 + -1*D >= 0 && 201 + -1*A + -1*D >= 0 && -1 + -1*B + C >= 0 && 100 + -1*A >= 0 && A + C + E >= 1 + 2*B + F && 100 >= A && 101 + B + F >= A + C + E && 1 + B >= F && C >= 1 + B && C >= E && 1 + B + F + G = A + C + E && B + D + F = A + C + E] lbl72(A,B,C,D,E,F,G,H) -> lbl72(A,-1 + B,C,1 + F,E,D,F,H) [100 + -1*G >= 0 && -1 + D + -1*G >= 0 && 201 + -1*D + -1*G >= 0 && 200 + -1*A + -1*G >= 0 && 1 + -1*D + G >= 0 && C + -1*E >= 0 && 101 + -1*D >= 0 && 201 + -1*A + -1*D >= 0 && -1 + -1*B + C >= 0 && 100 + -1*A >= 0 && 2*B + F >= A + C + E && 100 >= F && 100 >= A && 101 + B + F >= A + C + E && 1 + B >= F && C >= 1 + B && C >= E && 1 + B + F + G = A + C + E && B + D + F = A + C + E] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,A,H,H) True Signature: {(lbl72,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{},1->{},2->{3,4,5},3->{},4->{},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,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = A && G = H] start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && E >= 1 + C && B = C && D = E && F = A && G = H] start(A,B,C,D,E,F,G,H) -> lbl72(A,-1 + B,C,1 + F,E,D,F,H) [G + -1*H >= 0 && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && C >= E && 100 >= A && B = C && D = E && F = A && G = H] lbl72(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*G >= 0 && -1 + D + -1*G >= 0 && 201 + -1*D + -1*G >= 0 && 200 + -1*A + -1*G >= 0 && 1 + -1*D + G >= 0 && C + -1*E >= 0 && 101 + -1*D >= 0 && 201 + -1*A + -1*D >= 0 && -1 + -1*B + C >= 0 && 100 + -1*A >= 0 && F >= 101 && 100 >= A && 101 + B + F >= A + C + E && 1 + B >= F && C >= 1 + B && C >= E && 1 + B + F + G = A + C + E && B + D + F = A + C + E] lbl72(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*G >= 0 && -1 + D + -1*G >= 0 && 201 + -1*D + -1*G >= 0 && 200 + -1*A + -1*G >= 0 && 1 + -1*D + G >= 0 && C + -1*E >= 0 && 101 + -1*D >= 0 && 201 + -1*A + -1*D >= 0 && -1 + -1*B + C >= 0 && 100 + -1*A >= 0 && A + C + E >= 1 + 2*B + F && 100 >= A && 101 + B + F >= A + C + E && 1 + B >= F && C >= 1 + B && C >= E && 1 + B + F + G = A + C + E && B + D + F = A + C + E] lbl72(A,B,C,D,E,F,G,H) -> lbl72(A,-1 + B,C,1 + F,E,D,F,H) [100 + -1*G >= 0 && -1 + D + -1*G >= 0 && 201 + -1*D + -1*G >= 0 && 200 + -1*A + -1*G >= 0 && 1 + -1*D + G >= 0 && C + -1*E >= 0 && 101 + -1*D >= 0 && 201 + -1*A + -1*D >= 0 && -1 + -1*B + C >= 0 && 100 + -1*A >= 0 && 2*B + F >= A + C + E && 100 >= F && 100 >= A && 101 + B + F >= A + C + E && 1 + B >= F && C >= 1 + B && C >= E && 1 + B + F + G = A + C + E && B + D + F = A + C + E] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,A,H,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True Signature: {(exitus616,8);(lbl72,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{10},1->{9},2->{3,4,5},3->{8},4->{7},5->{3,4,5},6->{0,1,2}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[5] c: [5] * Step 4: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = A && G = H] start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [G + -1*H >= 0 && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && E >= 1 + C && B = C && D = E && F = A && G = H] start(A,B,C,D,E,F,G,H) -> lbl72(A,-1 + B,C,1 + F,E,D,F,H) [G + -1*H >= 0 && -1*G + H >= 0 && A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && C >= E && 100 >= A && B = C && D = E && F = A && G = H] lbl72(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*G >= 0 && -1 + D + -1*G >= 0 && 201 + -1*D + -1*G >= 0 && 200 + -1*A + -1*G >= 0 && 1 + -1*D + G >= 0 && C + -1*E >= 0 && 101 + -1*D >= 0 && 201 + -1*A + -1*D >= 0 && -1 + -1*B + C >= 0 && 100 + -1*A >= 0 && F >= 101 && 100 >= A && 101 + B + F >= A + C + E && 1 + B >= F && C >= 1 + B && C >= E && 1 + B + F + G = A + C + E && B + D + F = A + C + E] lbl72(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [100 + -1*G >= 0 && -1 + D + -1*G >= 0 && 201 + -1*D + -1*G >= 0 && 200 + -1*A + -1*G >= 0 && 1 + -1*D + G >= 0 && C + -1*E >= 0 && 101 + -1*D >= 0 && 201 + -1*A + -1*D >= 0 && -1 + -1*B + C >= 0 && 100 + -1*A >= 0 && A + C + E >= 1 + 2*B + F && 100 >= A && 101 + B + F >= A + C + E && 1 + B >= F && C >= 1 + B && C >= E && 1 + B + F + G = A + C + E && B + D + F = A + C + E] lbl72(A,B,C,D,E,F,G,H) -> lbl72(A,-1 + B,C,1 + F,E,D,F,H) [100 + -1*G >= 0 && -1 + D + -1*G >= 0 && 201 + -1*D + -1*G >= 0 && 200 + -1*A + -1*G >= 0 && 1 + -1*D + G >= 0 && C + -1*E >= 0 && 101 + -1*D >= 0 && 201 + -1*A + -1*D >= 0 && -1 + -1*B + C >= 0 && 100 + -1*A >= 0 && 2*B + F >= A + C + E && 100 >= F && 100 >= A && 101 + B + F >= A + C + E && 1 + B >= F && C >= 1 + B && C >= E && 1 + B + F + G = A + C + E && B + D + F = A + C + E] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,A,H,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True stop(A,B,C,D,E,F,G,H) -> exitus616(A,B,C,D,E,F,G,H) True Signature: {(exitus616,8);(lbl72,8);(start,8);(start0,8);(stop,8)} Rule Graph: [0->{10},1->{9},2->{3,4,5},3->{8},4->{7},5->{3,4,5},6->{0,1,2}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[5] c: [5]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,H,0.0] start ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] start ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] start ~> lbl72 [A <= A, B <= K + C, C <= C, D <= K + F, E <= E, F <= D, G <= F, H <= H] lbl72 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl72 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl72 ~> lbl72 [A <= A, B <= K + B, C <= C, D <= K + F, E <= E, F <= D, G <= F, H <= H] start0 ~> start [A <= A, B <= C, C <= C, D <= E, E <= E, F <= A, G <= H, H <= H] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] + Loop: [0.0 <= 201*K + D + F] lbl72 ~> lbl72 [A <= A, B <= K + B, C <= C, D <= K + F, E <= E, F <= D, G <= F, H <= H] + 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,G,H,0.0] start ~> stop [] start ~> stop [] start ~> lbl72 [D ~=> F,F ~=> G,C ~+> B,F ~+> D,K ~+> B,K ~+> D] lbl72 ~> stop [] lbl72 ~> stop [] lbl72 ~> lbl72 [D ~=> F,F ~=> G,B ~+> B,F ~+> D,K ~+> B,K ~+> D] start0 ~> start [A ~=> F,C ~=> B,E ~=> D,H ~=> G] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] + Loop: [D ~+> 0.0,F ~+> 0.0,K ~*> 0.0] lbl72 ~> lbl72 [D ~=> F,F ~=> G,B ~+> B,F ~+> D,K ~+> B,K ~+> D] + Applied Processor: Lare + Details: start0 ~> exitus616 [A ~=> F ,A ~=> G ,C ~=> B ,E ~=> D ,E ~=> F ,E ~=> G ,H ~=> G ,A ~+> D ,A ~+> F ,A ~+> G ,A ~+> 0.0 ,A ~+> tick ,C ~+> B ,E ~+> D ,E ~+> F ,E ~+> G ,E ~+> 0.0 ,E ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> D ,K ~+> F ,K ~+> G ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,A ~*> D ,A ~*> F ,E ~*> B ,E ~*> D ,E ~*> F ,K ~*> B ,K ~*> D ,K ~*> F ,K ~*> G ,K ~*> 0.0 ,K ~*> tick] + lbl72> [D ~=> F ,D ~=> G ,F ~=> G ,B ~+> B ,D ~+> D ,D ~+> F ,D ~+> G ,D ~+> 0.0 ,D ~+> tick ,F ~+> D ,F ~+> F ,F ~+> G ,F ~+> 0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> D ,K ~+> F ,K ~+> G ,D ~*> B ,D ~*> D ,D ~*> F ,F ~*> B ,F ~*> D ,F ~*> F ,K ~*> B ,K ~*> D ,K ~*> F ,K ~*> G ,K ~*> 0.0 ,K ~*> tick] YES(?,O(n^1))