/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 315 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 786 ms] (4) BOUNDS(n^1, 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 >= E && D <= E && F >= G && F <= G && H >= A && H <= A start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 0 >= G + 1 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, 0, C, F, E, F, G, H)) :|: A >= 1 && F >= 0 && F <= 0 && B >= C && B <= C && D >= E && D <= E && G >= 0 && G <= 0 && H >= A && H <= A start(A, B, C, D, E, F, G, H) -> Com_1(lM1(A, 1, C, F - 1, E, F, G, H)) :|: A >= 1 && G >= 1 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A lM1(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= B && G >= B && B >= 1 && D >= 0 && D <= 0 && H >= A && H <= A && F >= G && F <= G lM1(A, B, C, D, E, F, G, H) -> Com_1(lZZ1(A, 0, C, D, E, F, G, H)) :|: D >= 1 && G >= D + A && A >= 1 && D >= 0 && B >= A && B <= A && H >= A && H <= A && F >= G && F <= G lM1(A, B, C, D, E, F, G, H) -> Com_1(lM1(A, 1 + B, C, D - 1, E, F, G, H)) :|: A >= B + 1 && D >= 1 && A >= B && G >= D + B && B >= 1 && D >= 0 && H >= A && H <= A && F >= G && F <= G lZZ1(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 0 >= D && G >= A + D && A >= 2 && D >= 1 && B >= 0 && B <= 0 && H >= A && H <= A && F >= G && F <= G lZZ1(A, B, C, D, E, F, G, H) -> Com_1(lZZ1(A, 0, C, D, E, F, G, H)) :|: D >= 1 && 0 >= A && G >= A + D && A >= 2 && B >= 0 && B <= 0 && H >= A && H <= A && F >= G && F <= G lZZ1(A, B, C, D, E, F, G, H) -> Com_1(lM1(A, 1 + B, C, D - 1, E, F, G, H)) :|: A >= 1 && D >= 1 && G >= A + D && A >= 2 && B >= 0 && B <= 0 && H >= A && H <= A && F >= G && F <= G start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, E, E, G, G, A)) :|: TRUE The start-symbols are:[start0_8] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 6*Ar_6 + 9) 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_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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_6 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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, 0, Ar_2, Ar_5, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_5 = 0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_6 = 0 /\ Ar_7 = Ar_0 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, 1, Ar_2, Ar_5 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_6 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (Comp: ?, Cost: 1) lM1(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 >= Ar_1 /\ Ar_6 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\ Ar_6 >= Ar_3 + Ar_0 /\ Ar_0 >= 1 /\ Ar_3 >= 0 /\ Ar_1 = Ar_0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 /\ Ar_6 >= Ar_3 + Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) lZZ1(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_3 /\ Ar_6 >= Ar_0 + Ar_3 /\ Ar_0 >= 2 /\ Ar_3 >= 1 /\ Ar_1 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\ 0 >= Ar_0 /\ Ar_6 >= Ar_0 + Ar_3 /\ Ar_0 >= 2 /\ Ar_1 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_6 >= Ar_0 + Ar_3 /\ Ar_0 >= 2 /\ Ar_1 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (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_4, Ar_4, Ar_6, Ar_6, Ar_0)) (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: lZZ1(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_3 /\ Ar_6 >= Ar_0 + Ar_3 /\ Ar_0 >= 2 /\ Ar_3 >= 1 /\ Ar_1 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\ 0 >= Ar_0 /\ Ar_6 >= Ar_0 + Ar_3 /\ Ar_0 >= 2 /\ Ar_1 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] We thus obtain the following problem: 2: T: (Comp: ?, Cost: 1) lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_6 >= Ar_0 + Ar_3 /\ Ar_0 >= 2 /\ Ar_1 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 /\ Ar_6 >= Ar_3 + Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\ Ar_6 >= Ar_3 + Ar_0 /\ Ar_0 >= 1 /\ Ar_3 >= 0 /\ Ar_1 = Ar_0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) lM1(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 >= Ar_1 /\ Ar_6 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, 1, Ar_2, Ar_5 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_6 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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, 0, Ar_2, Ar_5, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_5 = 0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_6 = 0 /\ Ar_7 = Ar_0 ] (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_6 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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_4, Ar_4, Ar_6, Ar_6, Ar_0)) (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) lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_6 >= Ar_0 + Ar_3 /\ Ar_0 >= 2 /\ Ar_1 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 /\ Ar_6 >= Ar_3 + Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\ Ar_6 >= Ar_3 + Ar_0 /\ Ar_0 >= 1 /\ Ar_3 >= 0 /\ Ar_1 = Ar_0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) lM1(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 >= Ar_1 /\ Ar_6 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, 1, Ar_2, Ar_5 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_6 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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, 0, Ar_2, Ar_5, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_5 = 0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_6 = 0 /\ Ar_7 = Ar_0 ] (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_6 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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_4, Ar_4, Ar_6, Ar_6, Ar_0)) (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(lZZ1) = 1 Pol(lM1) = 1 Pol(stop) = 0 Pol(start) = 1 Pol(start0) = 1 Pol(koat_start) = 1 orients all transitions weakly and the transition lM1(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 >= Ar_1 /\ Ar_6 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] strictly and produces the following problem: 4: T: (Comp: ?, Cost: 1) lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_6 >= Ar_0 + Ar_3 /\ Ar_0 >= 2 /\ Ar_1 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 /\ Ar_6 >= Ar_3 + Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: ?, Cost: 1) lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\ Ar_6 >= Ar_3 + Ar_0 /\ Ar_0 >= 1 /\ Ar_3 >= 0 /\ Ar_1 = Ar_0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: 1, Cost: 1) lM1(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 >= Ar_1 /\ Ar_6 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, 1, Ar_2, Ar_5 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_6 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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, 0, Ar_2, Ar_5, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_5 = 0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_6 = 0 /\ Ar_7 = Ar_0 ] (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_6 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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_4, Ar_4, Ar_6, Ar_6, Ar_0)) (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(lZZ1) = 2*V_4 Pol(lM1) = 2*V_4 + 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_4, Ar_4, Ar_6, Ar_6, Ar_0))", 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_4, Ar_4, Ar_6, Ar_6, Ar_0))", 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_4, Ar_4, Ar_6, Ar_6, Ar_0))", 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_4, Ar_4, Ar_6, Ar_6, Ar_0))", 0-3) = Ar_4 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_4, Ar_4, Ar_6, Ar_6, Ar_0))", 0-4) = Ar_4 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_4, Ar_4, Ar_6, Ar_6, Ar_0))", 0-5) = Ar_6 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_4, Ar_4, Ar_6, Ar_6, Ar_0))", 0-6) = Ar_6 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_4, Ar_4, Ar_6, Ar_6, Ar_0))", 0-7) = 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_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 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_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 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_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 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_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-3) = Ar_4 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_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-4) = Ar_4 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_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-5) = Ar_6 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_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-6) = Ar_6 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_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-7) = 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_6 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 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_6 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 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_6 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 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_6 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-3) = Ar_4 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_6 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-4) = Ar_4 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_6 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-5) = Ar_6 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_6 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-6) = Ar_6 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_6 + 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-7) = 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, 0, Ar_2, Ar_5, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_5 = 0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_6 = 0 /\\ Ar_7 = Ar_0 ]", 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, 0, Ar_2, Ar_5, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_5 = 0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_6 = 0 /\\ Ar_7 = Ar_0 ]", 0-1) = 0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, 0, Ar_2, Ar_5, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_5 = 0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_6 = 0 /\\ Ar_7 = Ar_0 ]", 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, 0, Ar_2, Ar_5, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_5 = 0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_6 = 0 /\\ Ar_7 = Ar_0 ]", 0-3) = 0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, 0, Ar_2, Ar_5, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_5 = 0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_6 = 0 /\\ Ar_7 = Ar_0 ]", 0-4) = Ar_4 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, 0, Ar_2, Ar_5, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_5 = 0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_6 = 0 /\\ Ar_7 = Ar_0 ]", 0-5) = 0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, 0, Ar_2, Ar_5, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_5 = 0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_6 = 0 /\\ Ar_7 = Ar_0 ]", 0-6) = 0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, 0, Ar_2, Ar_5, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_5 = 0 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_6 = 0 /\\ Ar_7 = Ar_0 ]", 0-7) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, 1, Ar_2, Ar_5 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_6 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-0) = Ar_0 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, 1, Ar_2, Ar_5 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_6 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-1) = 1 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, 1, Ar_2, Ar_5 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_6 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-2) = Ar_2 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, 1, Ar_2, Ar_5 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_6 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-3) = Ar_6 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, 1, Ar_2, Ar_5 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_6 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-4) = Ar_4 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, 1, Ar_2, Ar_5 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_6 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-5) = Ar_6 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, 1, Ar_2, Ar_5 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_6 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-6) = Ar_6 S("start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, 1, Ar_2, Ar_5 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_6 >= 1 /\\ Ar_1 = Ar_2 /\\ Ar_3 = Ar_4 /\\ Ar_5 = Ar_6 /\\ Ar_7 = Ar_0 ]", 0-7) = Ar_0 S("lM1(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 >= Ar_1 /\\ Ar_6 >= Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-0) = Ar_0 S("lM1(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 >= Ar_1 /\\ Ar_6 >= Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-1) = Ar_6 + 2 S("lM1(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 >= Ar_1 /\\ Ar_6 >= Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-2) = Ar_2 S("lM1(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 >= Ar_1 /\\ Ar_6 >= Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-3) = 0 S("lM1(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 >= Ar_1 /\\ Ar_6 >= Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-4) = Ar_4 S("lM1(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 >= Ar_1 /\\ Ar_6 >= Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-5) = Ar_6 S("lM1(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 >= Ar_1 /\\ Ar_6 >= Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-6) = Ar_6 S("lM1(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 >= Ar_1 /\\ Ar_6 >= Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-7) = Ar_0 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\\ Ar_6 >= Ar_3 + Ar_0 /\\ Ar_0 >= 1 /\\ Ar_3 >= 0 /\\ Ar_1 = Ar_0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-0) = Ar_0 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\\ Ar_6 >= Ar_3 + Ar_0 /\\ Ar_0 >= 1 /\\ Ar_3 >= 0 /\\ Ar_1 = Ar_0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-1) = 0 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\\ Ar_6 >= Ar_3 + Ar_0 /\\ Ar_0 >= 1 /\\ Ar_3 >= 0 /\\ Ar_1 = Ar_0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-2) = Ar_2 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\\ Ar_6 >= Ar_3 + Ar_0 /\\ Ar_0 >= 1 /\\ Ar_3 >= 0 /\\ Ar_1 = Ar_0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-3) = Ar_6 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\\ Ar_6 >= Ar_3 + Ar_0 /\\ Ar_0 >= 1 /\\ Ar_3 >= 0 /\\ Ar_1 = Ar_0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-4) = Ar_4 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\\ Ar_6 >= Ar_3 + Ar_0 /\\ Ar_0 >= 1 /\\ Ar_3 >= 0 /\\ Ar_1 = Ar_0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-5) = Ar_6 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\\ Ar_6 >= Ar_3 + Ar_0 /\\ Ar_0 >= 1 /\\ Ar_3 >= 0 /\\ Ar_1 = Ar_0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-6) = Ar_6 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\\ Ar_6 >= Ar_3 + Ar_0 /\\ Ar_0 >= 1 /\\ Ar_3 >= 0 /\\ Ar_1 = Ar_0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-7) = Ar_0 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 /\\ Ar_6 >= Ar_3 + Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 >= 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-0) = Ar_0 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 /\\ Ar_6 >= Ar_3 + Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 >= 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-1) = Ar_6 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 /\\ Ar_6 >= Ar_3 + Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 >= 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-2) = Ar_2 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 /\\ Ar_6 >= Ar_3 + Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 >= 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-3) = Ar_6 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 /\\ Ar_6 >= Ar_3 + Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 >= 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-4) = Ar_4 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 /\\ Ar_6 >= Ar_3 + Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 >= 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-5) = Ar_6 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 /\\ Ar_6 >= Ar_3 + Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 >= 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-6) = Ar_6 S("lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\\ Ar_3 >= 1 /\\ Ar_0 >= Ar_1 /\\ Ar_6 >= Ar_3 + Ar_1 /\\ Ar_1 >= 1 /\\ Ar_3 >= 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-7) = Ar_0 S("lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_6 >= Ar_0 + Ar_3 /\\ Ar_0 >= 2 /\\ Ar_1 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-0) = Ar_0 S("lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_6 >= Ar_0 + Ar_3 /\\ Ar_0 >= 2 /\\ Ar_1 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-1) = 1 S("lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_6 >= Ar_0 + Ar_3 /\\ Ar_0 >= 2 /\\ Ar_1 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-2) = Ar_2 S("lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_6 >= Ar_0 + Ar_3 /\\ Ar_0 >= 2 /\\ Ar_1 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-3) = Ar_6 S("lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_6 >= Ar_0 + Ar_3 /\\ Ar_0 >= 2 /\\ Ar_1 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-4) = Ar_4 S("lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_6 >= Ar_0 + Ar_3 /\\ Ar_0 >= 2 /\\ Ar_1 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-5) = Ar_6 S("lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_6 >= Ar_0 + Ar_3 /\\ Ar_0 >= 2 /\\ Ar_1 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-6) = Ar_6 S("lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\\ Ar_3 >= 1 /\\ Ar_6 >= Ar_0 + Ar_3 /\\ Ar_0 >= 2 /\\ Ar_1 = 0 /\\ Ar_7 = Ar_0 /\\ Ar_5 = Ar_6 ]", 0-7) = Ar_0 orients the transitions lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_6 >= Ar_0 + Ar_3 /\ Ar_0 >= 2 /\ Ar_1 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\ Ar_6 >= Ar_3 + Ar_0 /\ Ar_0 >= 1 /\ Ar_3 >= 0 /\ Ar_1 = Ar_0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 /\ Ar_6 >= Ar_3 + Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] weakly and the transitions lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_6 >= Ar_0 + Ar_3 /\ Ar_0 >= 2 /\ Ar_1 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\ Ar_6 >= Ar_3 + Ar_0 /\ Ar_0 >= 1 /\ Ar_3 >= 0 /\ Ar_1 = Ar_0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 /\ Ar_6 >= Ar_3 + Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] strictly and produces the following problem: 5: T: (Comp: 2*Ar_6 + 1, Cost: 1) lZZ1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_3 >= 1 /\ Ar_6 >= Ar_0 + Ar_3 /\ Ar_0 >= 2 /\ Ar_1 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: 2*Ar_6 + 1, Cost: 1) lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, Ar_1 + 1, Ar_2, Ar_3 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= Ar_1 + 1 /\ Ar_3 >= 1 /\ Ar_0 >= Ar_1 /\ Ar_6 >= Ar_3 + Ar_1 /\ Ar_1 >= 1 /\ Ar_3 >= 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: 2*Ar_6 + 1, Cost: 1) lM1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lZZ1(Ar_0, 0, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 1 /\ Ar_6 >= Ar_3 + Ar_0 /\ Ar_0 >= 1 /\ Ar_3 >= 0 /\ Ar_1 = Ar_0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: 1, Cost: 1) lM1(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 >= Ar_1 /\ Ar_6 >= Ar_1 /\ Ar_1 >= 1 /\ Ar_3 = 0 /\ Ar_7 = Ar_0 /\ Ar_5 = Ar_6 ] (Comp: 1, Cost: 1) start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lM1(Ar_0, 1, Ar_2, Ar_5 - 1, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_6 >= 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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, 0, Ar_2, Ar_5, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 1 /\ Ar_5 = 0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_6 = 0 /\ Ar_7 = Ar_0 ] (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_6 + 1 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ] (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_4, Ar_4, Ar_6, Ar_6, Ar_0)) (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 6*Ar_6 + 9 Time: 0.271 sec (SMT: 0.206 sec) ---------------------------------------- (2) BOUNDS(1, n^1) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: start0 0: start -> stop : [ 0>=A && B==C && D==E && F==G && H==A ], cost: 1 1: start -> stop : [ 0>=1+G && B==C && D==E && F==G && H==A ], cost: 1 2: start -> stop : B'=0, D'=F, [ A>=1 && F==0 && B==C && D==E && G==0 && H==A ], cost: 1 3: start -> lM1 : B'=1, D'=-1+F, [ A>=1 && G>=1 && B==C && D==E && F==G && H==A ], cost: 1 4: lM1 -> stop : [ A>=B && G>=B && B>=1 && D==0 && H==A && F==G ], cost: 1 5: lM1 -> lZZ1 : B'=0, [ D>=1 && G>=D+A && A>=1 && D>=0 && B==A && H==A && F==G ], cost: 1 6: lM1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1+B && D>=1 && A>=B && G>=D+B && B>=1 && D>=0 && H==A && F==G ], cost: 1 7: lZZ1 -> stop : [ 0>=D && G>=D+A && A>=2 && D>=1 && B==0 && H==A && F==G ], cost: 1 8: lZZ1 -> lZZ1 : B'=0, [ D>=1 && 0>=A && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1 9: lZZ1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1 && D>=1 && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1 10: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 10: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1 Removed unreachable and leaf rules: Start location: start0 3: start -> lM1 : B'=1, D'=-1+F, [ A>=1 && G>=1 && B==C && D==E && F==G && H==A ], cost: 1 5: lM1 -> lZZ1 : B'=0, [ D>=1 && G>=D+A && A>=1 && D>=0 && B==A && H==A && F==G ], cost: 1 6: lM1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1+B && D>=1 && A>=B && G>=D+B && B>=1 && D>=0 && H==A && F==G ], cost: 1 8: lZZ1 -> lZZ1 : B'=0, [ D>=1 && 0>=A && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1 9: lZZ1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1 && D>=1 && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1 10: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1 Removed rules with unsatisfiable guard: Start location: start0 3: start -> lM1 : B'=1, D'=-1+F, [ A>=1 && G>=1 && B==C && D==E && F==G && H==A ], cost: 1 5: lM1 -> lZZ1 : B'=0, [ D>=1 && G>=D+A && A>=1 && D>=0 && B==A && H==A && F==G ], cost: 1 6: lM1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1+B && D>=1 && A>=B && G>=D+B && B>=1 && D>=0 && H==A && F==G ], cost: 1 9: lZZ1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1 && D>=1 && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1 10: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1 Simplified all rules, resulting in: Start location: start0 3: start -> lM1 : B'=1, D'=-1+F, [ A>=1 && G>=1 && B==C && D==E && F==G && H==A ], cost: 1 5: lM1 -> lZZ1 : B'=0, [ D>=1 && G>=D+A && A>=1 && B==A && H==A && F==G ], cost: 1 6: lM1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1+B && D>=1 && G>=D+B && B>=1 && H==A && F==G ], cost: 1 9: lZZ1 -> lM1 : B'=1+B, D'=-1+D, [ D>=1 && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1 10: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 1. Accelerating the following rules: 6: lM1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1+B && D>=1 && G>=D+B && B>=1 && H==A && F==G ], cost: 1 Found no metering function for rule 6. Removing the simple loops:. Accelerated all simple loops using metering functions (where possible): Start location: start0 3: start -> lM1 : B'=1, D'=-1+F, [ A>=1 && G>=1 && B==C && D==E && F==G && H==A ], cost: 1 5: lM1 -> lZZ1 : B'=0, [ D>=1 && G>=D+A && A>=1 && B==A && H==A && F==G ], cost: 1 6: lM1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1+B && D>=1 && G>=D+B && B>=1 && H==A && F==G ], cost: 1 9: lZZ1 -> lM1 : B'=1+B, D'=-1+D, [ D>=1 && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1 10: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: start0 3: start -> lM1 : B'=1, D'=-1+F, [ A>=1 && G>=1 && B==C && D==E && F==G && H==A ], cost: 1 11: start -> lM1 : B'=2, D'=-2+F, [ G>=1 && B==C && D==E && F==G && H==A && A>=2 && -1+F>=1 ], cost: 2 5: lM1 -> lZZ1 : B'=0, [ D>=1 && G>=D+A && A>=1 && B==A && H==A && F==G ], cost: 1 9: lZZ1 -> lM1 : B'=1+B, D'=-1+D, [ D>=1 && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1 12: lZZ1 -> lM1 : B'=2+B, D'=-2+D, [ G>=D+A && A>=2 && B==0 && H==A && F==G && A>=2+B && -1+D>=1 && G>=D+B ], cost: 2 10: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: start0 15: lM1 -> lM1 : B'=1, D'=-1+D, [ D>=1 && G>=D+A && B==A && H==A && F==G && A>=2 ], cost: 2 16: lM1 -> lM1 : B'=2, D'=-2+D, [ G>=D+A && B==A && H==A && F==G && A>=2 && -1+D>=1 && G>=D ], cost: 3 13: start0 -> lM1 : B'=1, D'=-1+G, F'=G, H'=A, [ A>=1 && G>=1 ], cost: 2 14: start0 -> lM1 : B'=2, D'=-2+G, F'=G, H'=A, [ A>=2 && -1+G>=1 ], cost: 3 Accelerating simple loops of location 1. Accelerating the following rules: 15: lM1 -> lM1 : B'=1, D'=-1+D, [ D>=1 && G>=D+A && B==A && H==A && F==G && A>=2 ], cost: 2 16: lM1 -> lM1 : B'=2, D'=-2+D, [ G>=D+A && B==A && H==A && F==G && A>=2 && -1+D>=1 && G>=D ], cost: 3 Accelerated rule 15 with NONTERM (after strengthening guard), yielding the new rule 17. Accelerated rule 16 with metering function meter (where 2*meter==-1+D) (after strengthening guard), yielding the new rule 18. Nested simple loops 15 (outer loop) and 18 (inner loop) with metering function -A+B, resulting in the new rules: 19. Removing the simple loops: 15. Accelerated all simple loops using metering functions (where possible): Start location: start0 16: lM1 -> lM1 : B'=2, D'=-2+D, [ G>=D+A && B==A && H==A && F==G && A>=2 && -1+D>=1 && G>=D ], cost: 3 17: lM1 -> [6] : [ D>=1 && G>=D+A && B==A && H==A && F==G && A>=2 && 1==A ], cost: NONTERM 18: lM1 -> lM1 : B'=2, D'=-2*meter+D, [ G>=D+A && B==A && H==A && F==G && -1+D>=1 && G>=D && 2==A && 2*meter==-1+D && meter>=1 ], cost: 3*meter 19: lM1 -> lM1 : B'=1, D'=D+A+2*meter*(A-B)-B, [ G>=D+A && B==A && H==A && F==G && -1+D>=1 && G>=D && 2==A && 2*meter==-1+D && meter>=1 && G>=-2*meter+D+A && -A+B>=1 ], cost: -2*A-3*meter*(A-B)+2*B 13: start0 -> lM1 : B'=1, D'=-1+G, F'=G, H'=A, [ A>=1 && G>=1 ], cost: 2 14: start0 -> lM1 : B'=2, D'=-2+G, F'=G, H'=A, [ A>=2 && -1+G>=1 ], cost: 3 Chained accelerated rules (with incoming rules): Start location: start0 13: start0 -> lM1 : B'=1, D'=-1+G, F'=G, H'=A, [ A>=1 && G>=1 ], cost: 2 14: start0 -> lM1 : B'=2, D'=-2+G, F'=G, H'=A, [ A>=2 && -1+G>=1 ], cost: 3 20: start0 -> lM1 : B'=2, D'=-4+G, F'=G, H'=A, [ 2-A==0 && -3+G>=1 ], cost: 6 21: start0 -> lM1 : B'=2, D'=-2-2*meter+G, F'=G, H'=A, [ 2-A==0 && -3+G>=1 && 2*meter==-3+G && meter>=1 ], cost: 3+3*meter Removed unreachable locations (and leaf rules with constant cost): Start location: start0 21: start0 -> lM1 : B'=2, D'=-2-2*meter+G, F'=G, H'=A, [ 2-A==0 && -3+G>=1 && 2*meter==-3+G && meter>=1 ], cost: 3+3*meter ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: start0 21: start0 -> lM1 : B'=2, D'=-2-2*meter+G, F'=G, H'=A, [ 2-A==0 && -3+G>=1 && 2*meter==-3+G && meter>=1 ], cost: 3+3*meter Computing asymptotic complexity for rule 21 Solved the limit problem by the following transformations: Created initial limit problem: -1+A (+/+!), 3+3*meter (+), -2-2*meter+G (+/+!), 3-A (+/+!), 4+2*meter-G (+/+!), -3+G (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {meter==n,G==3+2*n,A==2} resulting limit problem: [solved] Solution: meter / n G / 3+2*n A / 2 Resulting cost 3+3*n has complexity: Poly(n^1) Found new complexity Poly(n^1). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: 3+3*n Rule cost: 3+3*meter Rule guard: [ 2-A==0 && -3+G>=1 && 2*meter==-3+G ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)