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) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] 1. start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && G >= 1 + E && B = C && D = E && F = G && H = A] 2. start(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [A + -1*H >= 0 (?,1) && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && E >= G && 100 >= A && B = C && D = E && F = G && H = A] 3. lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 (?,1) && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && A + E + G >= 102 + B + D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] 4. lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 (?,1) && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && B >= D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] 5. lbl71(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [E + -1*H >= 0 (?,1) && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && D >= 1 + B && 101 + B + D >= A + E + G && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] 6. start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True (1,1) Signature: {(lbl71,8);(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) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && G >= 1 + E && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && E >= G && 100 >= A && B = C && D = E && F = G && H = A] lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && A + E + G >= 102 + B + D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && B >= D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] lbl71(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && D >= 1 + B && 101 + B + D >= A + E + G && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) True Signature: {(lbl71,8);(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) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && G >= 1 + E && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && E >= G && 100 >= A && B = C && D = E && F = G && H = A] lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && A + E + G >= 102 + B + D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && B >= D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] lbl71(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && D >= 1 + B && 101 + B + D >= A + E + G && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) 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);(lbl71,8);(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) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 101 && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && G >= 1 + E && B = C && D = E && F = G && H = A] start(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [A + -1*H >= 0 && -1*A + H >= 0 && F + -1*G >= 0 && -1*F + G >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && E >= G && 100 >= A && B = C && D = E && F = G && H = A] lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && A + E + G >= 102 + B + D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] lbl71(A,B,C,D,E,F,G,H) -> stop(A,B,C,D,E,F,G,H) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && B >= D && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] lbl71(A,B,C,D,E,F,G,H) -> lbl71(A,H,C,-1 + D,E,1 + H,G,F) [E + -1*H >= 0 && 1 + D + -1*H >= 0 && E + -1*G >= 0 && 1 + B + -1*F >= 0 && -1 + -1*B + F >= 0 && -1 + -1*D + E >= 0 && 100 + -1*A >= 0 && D >= 1 + B && 101 + B + D >= A + E + G && E >= 1 + D && 100 >= A && E >= G && 2 + B + 2*D >= A + E + G && 100 >= B && F = 1 + B && 1 + B + D + H = A + E + G] start0(A,B,C,D,E,F,G,H) -> start(A,C,C,E,E,G,G,A) 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);(lbl71,8);(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 ~> lbl71 [A <= A, B <= H, C <= C, D <= K + E, E <= E, F <= K + H, G <= G, H <= F] lbl71 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl71 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H] lbl71 ~> lbl71 [A <= A, B <= H, C <= C, D <= B + E, E <= E, F <= K + H, G <= G, H <= F] start0 ~> start [A <= A, B <= C, C <= C, D <= E, E <= E, F <= G, G <= G, H <= A] 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 <= 99*K + A + D + G] lbl71 ~> lbl71 [A <= A, B <= H, C <= C, D <= B + E, E <= E, F <= K + H, G <= G, H <= 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,G,H,0.0] start ~> stop [] start ~> stop [] start ~> lbl71 [F ~=> H,H ~=> B,E ~+> D,H ~+> F,K ~+> D,K ~+> F] lbl71 ~> stop [] lbl71 ~> stop [] lbl71 ~> lbl71 [F ~=> H,H ~=> B,B ~+> D,E ~+> D,H ~+> F,K ~+> F] start0 ~> start [A ~=> H,C ~=> B,E ~=> D,G ~=> F] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] + Loop: [A ~+> 0.0,D ~+> 0.0,G ~+> 0.0,K ~*> 0.0] lbl71 ~> lbl71 [F ~=> H,H ~=> B,B ~+> D,E ~+> D,H ~+> F,K ~+> F] + Applied Processor: Lare + Details: start0 ~> exitus616 [A ~=> B ,A ~=> H ,C ~=> B ,E ~=> D ,G ~=> B ,G ~=> F ,G ~=> H ,A ~+> B ,A ~+> D ,A ~+> F ,A ~+> H ,A ~+> 0.0 ,A ~+> tick ,E ~+> D ,E ~+> 0.0 ,E ~+> tick ,G ~+> B ,G ~+> D ,G ~+> F ,G ~+> H ,G ~+> 0.0 ,G ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> D ,K ~+> F ,K ~+> H ,K ~+> 0.0 ,K ~+> tick ,A ~*> F ,A ~*> H ,E ~*> F ,E ~*> H ,G ~*> F ,G ~*> H ,K ~*> B ,K ~*> D ,K ~*> F ,K ~*> H ,K ~*> 0.0 ,K ~*> tick] + lbl71> [F ~=> B ,F ~=> H ,H ~=> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> D ,D ~+> 0.0 ,D ~+> tick ,E ~+> D ,F ~+> B ,F ~+> D ,F ~+> F ,F ~+> H ,G ~+> 0.0 ,G ~+> tick ,H ~+> B ,H ~+> D ,H ~+> F ,H ~+> H ,tick ~+> tick ,K ~+> B ,K ~+> D ,K ~+> F ,K ~+> H ,A ~*> F ,A ~*> H ,D ~*> F ,D ~*> H ,G ~*> F ,G ~*> H ,K ~*> B ,K ~*> D ,K ~*> F ,K ~*> H ,K ~*> 0.0 ,K ~*> tick] YES(?,O(n^1))