/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). (0) CpxIntTrs (1) Koat Proof [FINISHED, 317 ms] (2) BOUNDS(1, n^2) (3) Loat Proof [FINISHED, 689 ms] (4) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 0 >= A && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H start(A, B, C, D, E, F, G, H) -> Com_1(lbl6(A, B, C, D, E, F, G, H)) :|: A >= 1 && A >= C && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H start(A, B, C, D, E, F, G, H) -> Com_1(lbl121(A, B, C, D, 1, F, 0, H)) :|: A >= 1 && C >= A + 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H lbl6(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= 1 && A >= C && G >= H && G <= H && E >= F && E <= F && D >= A && D <= A && B >= C && B <= C lbl121(A, B, C, D, E, F, G, H) -> Com_1(cut(A, B, C, D, E, F, G, H)) :|: G >= C && C >= G + 1 && A + C >= G + 3 && A >= E && E >= 1 && G >= 0 && C >= A + 1 && D >= A && D <= A && B >= C && B <= C lbl121(A, B, C, D, E, F, G, H) -> Com_1(lbl121(A, B, C, D, 1 + E, F, G, H)) :|: A >= E + 1 && C >= G + 1 && A + C >= G + 3 && A >= E && E >= 1 && G >= 0 && C >= A + 1 && D >= A && D <= A && B >= C && B <= C lbl121(A, B, C, D, E, F, G, H) -> Com_1(lbl141(A, B, C, D, 0, F, 1 + G, H)) :|: C >= G + 1 && A + C >= G + 3 && A >= 1 && G >= 0 && C >= A + 1 && E >= A && E <= A && D >= A && D <= A && B >= C && B <= C lbl141(A, B, C, D, E, F, G, H) -> Com_1(cut(A, B, C, D, E, F, G, H)) :|: A >= 2 && C >= A + 1 && C >= 1 && G >= C && G <= C && E >= 0 && E <= 0 && D >= A && D <= A && B >= C && B <= C lbl141(A, B, C, D, E, F, G, H) -> Com_1(lbl121(A, B, C, D, 1 + E, F, G, H)) :|: A >= 1 && C >= G + 1 && A >= 2 && C >= A + 1 && G >= 1 && C >= G && E >= 0 && E <= 0 && D >= A && D <= A && B >= C && B <= C lbl141(A, B, C, D, E, F, G, H) -> Com_1(lbl141(A, B, C, D, 0, F, 1 + G, H)) :|: 0 >= A && C >= G + 1 && A >= 2 && C >= A + 1 && G >= 1 && C >= G && E >= 0 && E <= 0 && D >= A && D <= A && B >= C && B <= C cut(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: C >= A + 1 && A >= 2 && E >= 0 && E <= 0 && G >= C && G <= C && D >= A && D <= A && B >= C && B <= C start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, A, F, F, H, H)) :|: TRUE The start-symbols are:[start0_8] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 8*Ar_2 + 2*Ar_0*Ar_2 + Ar_0 + 11) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= Ar_2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: ?, Cost: 1) lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= Ar_2 /\ Ar_6 = Ar_7 /\ Ar_4 = Ar_5 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_6 >= Ar_2 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= Ar_4 /\ Ar_4 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= Ar_4 /\ Ar_4 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_4 = Ar_0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_2 >= 1 /\ Ar_6 = Ar_2 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_6 >= 1 /\ Ar_2 >= Ar_6 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ 0 >= Ar_0 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_6 >= 1 /\ Ar_2 >= Ar_6 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\ Ar_0 >= 2 /\ Ar_4 = 0 /\ Ar_6 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_6 >= Ar_2 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= Ar_4 /\ Ar_4 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ 0 >= Ar_0 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_6 >= 1 /\ Ar_2 >= Ar_6 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\ Ar_0 >= 2 /\ Ar_4 = 0 /\ Ar_6 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_6 >= 1 /\ Ar_2 >= Ar_6 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_2 >= 1 /\ Ar_6 = Ar_2 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_4 = Ar_0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= Ar_4 /\ Ar_4 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= Ar_2 /\ Ar_6 = Ar_7 /\ Ar_4 = Ar_5 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= Ar_2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: ?, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: ?, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\ Ar_0 >= 2 /\ Ar_4 = 0 /\ Ar_6 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_6 >= 1 /\ Ar_2 >= Ar_6 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_2 >= 1 /\ Ar_6 = Ar_2 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_4 = Ar_0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= Ar_4 /\ Ar_4 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 1, Cost: 1) lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= Ar_2 /\ Ar_6 = Ar_7 /\ Ar_4 = Ar_5 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= Ar_2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(cut) = 1 Pol(stop) = 0 Pol(lbl141) = 2 Pol(lbl121) = 2 Pol(lbl6) = 0 Pol(start) = 2 Pol(start0) = 2 Pol(koat_start) = 2 orients all transitions weakly and the transitions lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_2 >= 1 /\ Ar_6 = Ar_2 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\ Ar_0 >= 2 /\ Ar_4 = 0 /\ Ar_6 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] strictly and produces the following problem: 4: T: (Comp: 2, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\ Ar_0 >= 2 /\ Ar_4 = 0 /\ Ar_6 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_6 >= 1 /\ Ar_2 >= Ar_6 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 2, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_2 >= 1 /\ Ar_6 = Ar_2 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_4 = Ar_0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= Ar_4 /\ Ar_4 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 1, Cost: 1) lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= Ar_2 /\ Ar_6 = Ar_7 /\ Ar_4 = Ar_5 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= Ar_2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(lbl141) = 2*V_3 - 2*V_7 + 1 Pol(lbl121) = 2*V_3 - 2*V_7 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-4) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-5) = Ar_5 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-6) = Ar_6 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-7) = Ar_7 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-0) = Ar_0 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-1) = Ar_2 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-2) = Ar_2 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-3) = Ar_0 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-4) = Ar_5 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-5) = Ar_5 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-6) = Ar_7 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-7) = Ar_7 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-0) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-1) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-2) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-3) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-4) = Ar_5 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-5) = Ar_5 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-6) = Ar_7 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-7) = Ar_7 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-0) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-1) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-2) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-3) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-4) = Ar_5 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-5) = Ar_5 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-6) = Ar_7 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-7) = Ar_7 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-0) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-1) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-2) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-3) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-4) = 1 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-5) = Ar_5 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-6) = 0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-7) = Ar_7 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-0) = Ar_0 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-1) = Ar_2 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-2) = Ar_2 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-3) = Ar_0 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-4) = Ar_5 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-5) = Ar_5 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-6) = Ar_7 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-7) = Ar_7 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-0) = Ar_0 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-1) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-2) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-3) = Ar_0 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-4) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-5) = Ar_5 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-6) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-7) = Ar_7 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-0) = Ar_0 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-1) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-2) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-3) = Ar_0 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-4) = 0 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-5) = Ar_5 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-6) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-7) = Ar_7 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-0) = Ar_0 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-1) = Ar_2 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-2) = Ar_2 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-3) = Ar_0 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-4) = 0 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-5) = Ar_5 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-6) = Ar_2 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-7) = Ar_7 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-0) = Ar_0 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-1) = Ar_2 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-2) = Ar_2 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-3) = Ar_0 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-4) = 1 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-5) = Ar_5 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-6) = Ar_2 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-7) = Ar_7 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-0) = Ar_0 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-1) = Ar_2 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-2) = Ar_2 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-3) = Ar_0 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-4) = 0 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-5) = Ar_5 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-6) = Ar_2 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-7) = Ar_7 orients the transitions lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_6 >= 1 /\ Ar_2 >= Ar_6 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_4 = Ar_0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= Ar_4 /\ Ar_4 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] weakly and the transitions lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_6 >= 1 /\ Ar_2 >= Ar_6 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_4 = Ar_0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] strictly and produces the following problem: 5: T: (Comp: 2, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\ Ar_0 >= 2 /\ Ar_4 = 0 /\ Ar_6 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 2*Ar_2, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_6 >= 1 /\ Ar_2 >= Ar_6 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 2, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_2 >= 1 /\ Ar_6 = Ar_2 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 2*Ar_2, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_4 = Ar_0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: ?, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= Ar_4 /\ Ar_4 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 1, Cost: 1) lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= Ar_2 /\ Ar_6 = Ar_7 /\ Ar_4 = Ar_5 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= Ar_2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(lbl121) = V_1 - V_5 + 1 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-2) = Ar_2 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-3) = Ar_3 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-4) = Ar_4 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-5) = Ar_5 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-6) = Ar_6 S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ]", 0-7) = Ar_7 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-0) = Ar_0 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-1) = Ar_2 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-2) = Ar_2 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-3) = Ar_0 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-4) = Ar_5 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-5) = Ar_5 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-6) = Ar_7 S("start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7))", 0-7) = Ar_7 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-0) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-1) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-2) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-3) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-4) = Ar_5 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-5) = Ar_5 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-6) = Ar_7 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-7) = Ar_7 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-0) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-1) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-2) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-3) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-4) = Ar_5 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-5) = Ar_5 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-6) = Ar_7 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-7) = Ar_7 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-0) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-1) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-2) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-3) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-4) = 1 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-5) = Ar_5 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-6) = 0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_4 = Ar_5 /\\ Ar_6 = Ar_7 ]", 0-7) = Ar_7 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-0) = Ar_0 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-1) = Ar_2 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-2) = Ar_2 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-3) = Ar_0 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-4) = Ar_5 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-5) = Ar_5 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-6) = Ar_7 S("lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_0 >= Ar_2 /\\ Ar_6 = Ar_7 /\\ Ar_4 = Ar_5 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-7) = Ar_7 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-0) = Ar_0 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-1) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-2) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-3) = Ar_0 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-4) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-5) = Ar_5 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-6) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= Ar_4 /\\ Ar_4 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-7) = Ar_7 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-0) = Ar_0 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-1) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-2) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-3) = Ar_0 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-4) = 0 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-5) = Ar_5 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-6) = Ar_2 S("lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\\ Ar_0 + Ar_2 >= Ar_6 + 3 /\\ Ar_0 >= 1 /\\ Ar_6 >= 0 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_4 = Ar_0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-7) = Ar_7 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-0) = Ar_0 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-1) = Ar_2 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-2) = Ar_2 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-3) = Ar_0 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-4) = 0 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-5) = Ar_5 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-6) = Ar_2 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_2 >= 1 /\\ Ar_6 = Ar_2 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-7) = Ar_7 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-0) = Ar_0 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-1) = Ar_2 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-2) = Ar_2 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-3) = Ar_0 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-4) = 1 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-5) = Ar_5 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-6) = Ar_2 S("lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_2 >= Ar_6 + 1 /\\ Ar_0 >= 2 /\\ Ar_2 >= Ar_0 + 1 /\\ Ar_6 >= 1 /\\ Ar_2 >= Ar_6 /\\ Ar_4 = 0 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-7) = Ar_7 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-0) = Ar_0 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-1) = Ar_2 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-2) = Ar_2 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-3) = Ar_0 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-4) = 0 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-5) = Ar_5 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-6) = Ar_2 S("cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\\ Ar_0 >= 2 /\\ Ar_4 = 0 /\\ Ar_6 = Ar_2 /\\ Ar_3 = Ar_0 /\\ Ar_1 = Ar_2 ]", 0-7) = Ar_7 orients the transitions lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= Ar_4 /\ Ar_4 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] weakly and the transition lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= Ar_4 /\ Ar_4 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] strictly and produces the following problem: 6: T: (Comp: 2, Cost: 1) cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_2 >= Ar_0 + 1 /\ Ar_0 >= 2 /\ Ar_4 = 0 /\ Ar_6 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 2*Ar_2, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_6 >= 1 /\ Ar_2 >= Ar_6 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 2, Cost: 1) lbl141(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(cut(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 2 /\ Ar_2 >= Ar_0 + 1 /\ Ar_2 >= 1 /\ Ar_6 = Ar_2 /\ Ar_4 = 0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 2*Ar_2, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl141(Ar_0, Ar_1, Ar_2, Ar_3, 0, Ar_5, Ar_6 + 1, Ar_7)) [ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_4 = Ar_0 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 2*Ar_0*Ar_2 + 4*Ar_2 + Ar_0 + 2, Cost: 1) lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4 + 1, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_4 + 1 /\ Ar_2 >= Ar_6 + 1 /\ Ar_0 + Ar_2 >= Ar_6 + 3 /\ Ar_0 >= Ar_4 /\ Ar_4 >= 1 /\ Ar_6 >= 0 /\ Ar_2 >= Ar_0 + 1 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 1, Cost: 1) lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= Ar_2 /\ Ar_6 = Ar_7 /\ Ar_4 = Ar_5 /\ Ar_3 = Ar_0 /\ Ar_1 = Ar_2 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl121(Ar_0, Ar_1, Ar_2, Ar_3, 1, Ar_5, 0, Ar_7)) [ Ar_0 >= 1 /\ Ar_2 >= Ar_0 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl6(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_0 >= Ar_2 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_0 /\ Ar_4 = Ar_5 /\ Ar_6 = Ar_7 ] (Comp: 1, Cost: 1) start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start(Ar_0, Ar_2, Ar_2, Ar_0, Ar_5, Ar_5, Ar_7, Ar_7)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(start0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 8*Ar_2 + 2*Ar_0*Ar_2 + Ar_0 + 11 Time: 0.288 sec (SMT: 0.211 sec) ---------------------------------------- (2) BOUNDS(1, n^2) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: start0 0: start -> stop : [ 0>=A && B==C && D==A && E==F && G==H ], cost: 1 1: start -> lbl6 : [ A>=1 && A>=C && B==C && D==A && E==F && G==H ], cost: 1 2: start -> lbl121 : E'=1, G'=0, [ A>=1 && C>=1+A && B==C && D==A && E==F && G==H ], cost: 1 3: lbl6 -> stop : [ A>=1 && A>=C && G==H && E==F && D==A && B==C ], cost: 1 4: lbl121 -> cut : [ G>=C && C>=1+G && C+A>=3+G && A>=E && E>=1 && G>=0 && C>=1+A && D==A && B==C ], cost: 1 5: lbl121 -> lbl121 : E'=1+E, [ A>=1+E && C>=1+G && C+A>=3+G && A>=E && E>=1 && G>=0 && C>=1+A && D==A && B==C ], cost: 1 6: lbl121 -> lbl141 : E'=0, G'=1+G, [ C>=1+G && C+A>=3+G && A>=1 && G>=0 && C>=1+A && E==A && D==A && B==C ], cost: 1 7: lbl141 -> cut : [ A>=2 && C>=1+A && C>=1 && G==C && E==0 && D==A && B==C ], cost: 1 8: lbl141 -> lbl121 : E'=1+E, [ A>=1 && C>=1+G && A>=2 && C>=1+A && G>=1 && C>=G && E==0 && D==A && B==C ], cost: 1 9: lbl141 -> lbl141 : E'=0, G'=1+G, [ 0>=A && C>=1+G && A>=2 && C>=1+A && G>=1 && C>=G && E==0 && D==A && B==C ], cost: 1 10: cut -> stop : [ C>=1+A && A>=2 && E==0 && G==C && D==A && B==C ], cost: 1 11: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 11: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1 Removed unreachable and leaf rules: Start location: start0 2: start -> lbl121 : E'=1, G'=0, [ A>=1 && C>=1+A && B==C && D==A && E==F && G==H ], cost: 1 5: lbl121 -> lbl121 : E'=1+E, [ A>=1+E && C>=1+G && C+A>=3+G && A>=E && E>=1 && G>=0 && C>=1+A && D==A && B==C ], cost: 1 6: lbl121 -> lbl141 : E'=0, G'=1+G, [ C>=1+G && C+A>=3+G && A>=1 && G>=0 && C>=1+A && E==A && D==A && B==C ], cost: 1 8: lbl141 -> lbl121 : E'=1+E, [ A>=1 && C>=1+G && A>=2 && C>=1+A && G>=1 && C>=G && E==0 && D==A && B==C ], cost: 1 9: lbl141 -> lbl141 : E'=0, G'=1+G, [ 0>=A && C>=1+G && A>=2 && C>=1+A && G>=1 && C>=G && E==0 && D==A && B==C ], cost: 1 11: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1 Removed rules with unsatisfiable guard: Start location: start0 2: start -> lbl121 : E'=1, G'=0, [ A>=1 && C>=1+A && B==C && D==A && E==F && G==H ], cost: 1 5: lbl121 -> lbl121 : E'=1+E, [ A>=1+E && C>=1+G && C+A>=3+G && A>=E && E>=1 && G>=0 && C>=1+A && D==A && B==C ], cost: 1 6: lbl121 -> lbl141 : E'=0, G'=1+G, [ C>=1+G && C+A>=3+G && A>=1 && G>=0 && C>=1+A && E==A && D==A && B==C ], cost: 1 8: lbl141 -> lbl121 : E'=1+E, [ A>=1 && C>=1+G && A>=2 && C>=1+A && G>=1 && C>=G && E==0 && D==A && B==C ], cost: 1 11: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1 Simplified all rules, resulting in: Start location: start0 2: start -> lbl121 : E'=1, G'=0, [ A>=1 && C>=1+A && B==C && D==A && E==F && G==H ], cost: 1 5: lbl121 -> lbl121 : E'=1+E, [ A>=1+E && C>=1+G && C+A>=3+G && E>=1 && G>=0 && C>=1+A && D==A && B==C ], cost: 1 6: lbl121 -> lbl141 : E'=0, G'=1+G, [ C>=1+G && C+A>=3+G && A>=1 && G>=0 && C>=1+A && E==A && D==A && B==C ], cost: 1 8: lbl141 -> lbl121 : E'=1+E, [ C>=1+G && A>=2 && C>=1+A && G>=1 && E==0 && D==A && B==C ], cost: 1 11: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 5: lbl121 -> lbl121 : E'=1+E, [ A>=1+E && C>=1+G && C+A>=3+G && E>=1 && G>=0 && C>=1+A && D==A && B==C ], cost: 1 Accelerated rule 5 with metering function A-E, yielding the new rule 12. Removing the simple loops: 5. Accelerated all simple loops using metering functions (where possible): Start location: start0 2: start -> lbl121 : E'=1, G'=0, [ A>=1 && C>=1+A && B==C && D==A && E==F && G==H ], cost: 1 6: lbl121 -> lbl141 : E'=0, G'=1+G, [ C>=1+G && C+A>=3+G && A>=1 && G>=0 && C>=1+A && E==A && D==A && B==C ], cost: 1 12: lbl121 -> lbl121 : E'=A, [ A>=1+E && C>=1+G && C+A>=3+G && E>=1 && G>=0 && C>=1+A && D==A && B==C ], cost: A-E 8: lbl141 -> lbl121 : E'=1+E, [ C>=1+G && A>=2 && C>=1+A && G>=1 && E==0 && D==A && B==C ], cost: 1 11: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: start0 2: start -> lbl121 : E'=1, G'=0, [ A>=1 && C>=1+A && B==C && D==A && E==F && G==H ], cost: 1 13: start -> lbl121 : E'=A, G'=0, [ C>=1+A && B==C && D==A && E==F && G==H && A>=2 && C>=1 && C+A>=3 ], cost: A 6: lbl121 -> lbl141 : E'=0, G'=1+G, [ C>=1+G && C+A>=3+G && A>=1 && G>=0 && C>=1+A && E==A && D==A && B==C ], cost: 1 8: lbl141 -> lbl121 : E'=1+E, [ C>=1+G && A>=2 && C>=1+A && G>=1 && E==0 && D==A && B==C ], cost: 1 14: lbl141 -> lbl121 : E'=A, [ C>=1+G && A>=2 && C>=1+A && G>=1 && E==0 && D==A && B==C && A>=2+E && C+A>=3+G ], cost: A-E 11: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: start0 17: lbl121 -> lbl121 : E'=1, G'=1+G, [ C+A>=3+G && G>=0 && C>=1+A && E==A && D==A && B==C && C>=2+G && A>=2 ], cost: 2 18: lbl121 -> lbl121 : E'=A, G'=1+G, [ G>=0 && C>=1+A && E==A && D==A && B==C && C>=2+G && A>=2 && C+A>=4+G ], cost: 1+A 15: start0 -> lbl121 : B'=C, D'=A, E'=1, G'=0, [ A>=1 && C>=1+A ], cost: 2 16: start0 -> lbl121 : B'=C, D'=A, E'=A, G'=0, [ C>=1+A && A>=2 && C>=1 && C+A>=3 ], cost: 1+A Accelerating simple loops of location 2. Accelerating the following rules: 17: lbl121 -> lbl121 : E'=1, G'=1+G, [ C+A>=3+G && G>=0 && C>=1+A && E==A && D==A && B==C && C>=2+G && A>=2 ], cost: 2 18: lbl121 -> lbl121 : E'=A, G'=1+G, [ G>=0 && C>=1+A && E==A && D==A && B==C && C>=2+G && A>=2 && C+A>=4+G ], cost: 1+A Accelerated rule 17 with NONTERM (after strengthening guard), yielding the new rule 19. Accelerated rule 18 with metering function -1+C-G, yielding the new rule 20. Removing the simple loops: 18. Accelerated all simple loops using metering functions (where possible): Start location: start0 17: lbl121 -> lbl121 : E'=1, G'=1+G, [ C+A>=3+G && G>=0 && C>=1+A && E==A && D==A && B==C && C>=2+G && A>=2 ], cost: 2 19: lbl121 -> [8] : [ C+A>=3+G && G>=0 && C>=1+A && E==A && D==A && B==C && C>=2+G && A>=2 && 1==A ], cost: NONTERM 20: lbl121 -> lbl121 : E'=A, G'=-1+C, [ G>=0 && C>=1+A && E==A && D==A && B==C && C>=2+G && A>=2 && C+A>=4+G ], cost: -1+C+A*(-1+C-G)-G 15: start0 -> lbl121 : B'=C, D'=A, E'=1, G'=0, [ A>=1 && C>=1+A ], cost: 2 16: start0 -> lbl121 : B'=C, D'=A, E'=A, G'=0, [ C>=1+A && A>=2 && C>=1 && C+A>=3 ], cost: 1+A Chained accelerated rules (with incoming rules): Start location: start0 15: start0 -> lbl121 : B'=C, D'=A, E'=1, G'=0, [ A>=1 && C>=1+A ], cost: 2 16: start0 -> lbl121 : B'=C, D'=A, E'=A, G'=0, [ C>=1+A && A>=2 && C>=1 && C+A>=3 ], cost: 1+A 21: start0 -> lbl121 : B'=C, D'=A, E'=1, G'=1, [ C>=1+A && A>=2 && C+A>=3 && C>=2 ], cost: 3+A 22: start0 -> lbl121 : B'=C, D'=A, E'=A, G'=-1+C, [ C>=1+A && A>=2 && C>=2 && C+A>=4 ], cost: C+A*(-1+C)+A Removed unreachable locations (and leaf rules with constant cost): Start location: start0 16: start0 -> lbl121 : B'=C, D'=A, E'=A, G'=0, [ C>=1+A && A>=2 && C>=1 && C+A>=3 ], cost: 1+A 21: start0 -> lbl121 : B'=C, D'=A, E'=1, G'=1, [ C>=1+A && A>=2 && C+A>=3 && C>=2 ], cost: 3+A 22: start0 -> lbl121 : B'=C, D'=A, E'=A, G'=-1+C, [ C>=1+A && A>=2 && C>=2 && C+A>=4 ], cost: C+A*(-1+C)+A ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: start0 16: start0 -> lbl121 : B'=C, D'=A, E'=A, G'=0, [ C>=1+A && A>=2 && C>=1 && C+A>=3 ], cost: 1+A 21: start0 -> lbl121 : B'=C, D'=A, E'=1, G'=1, [ C>=1+A && A>=2 && C+A>=3 && C>=2 ], cost: 3+A 22: start0 -> lbl121 : B'=C, D'=A, E'=A, G'=-1+C, [ C>=1+A && A>=2 && C>=2 && C+A>=4 ], cost: C+A*(-1+C)+A Computing asymptotic complexity for rule 16 Solved the limit problem by the following transformations: Created initial limit problem: -1+A (+/+!), C-A (+/+!), 1+A (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==n,A==-1+n} resulting limit problem: [solved] Solution: C / n A / -1+n Resulting cost n has complexity: Poly(n^1) Found new complexity Poly(n^1). Computing asymptotic complexity for rule 22 Solved the limit problem by the following transformations: Created initial limit problem: -1+A (+/+!), C-A (+/+!), C+C*A (+) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {C==3+n,A==2+n} resulting limit problem: [solved] Solution: C / 3+n A / 2+n Resulting cost 9+6*n+n^2 has complexity: Poly(n^2) Found new complexity Poly(n^2). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^2) Cpx degree: 2 Solved cost: 9+6*n+n^2 Rule cost: C+A*(-1+C)+A Rule guard: [ C>=1+A && A>=2 ] WORST_CASE(Omega(n^2),?) ---------------------------------------- (4) BOUNDS(n^2, INF)