21.04/9.94 WORST_CASE(Omega(n^2), O(n^2)) 21.04/9.95 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 21.04/9.95 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 21.04/9.95 21.04/9.95 21.04/9.95 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2). 21.04/9.95 21.04/9.95 (0) CpxIntTrs 21.04/9.95 (1) Koat Proof [FINISHED, 524 ms] 21.04/9.95 (2) BOUNDS(1, n^2) 21.04/9.95 (3) Loat Proof [FINISHED, 8303 ms] 21.04/9.95 (4) BOUNDS(n^2, INF) 21.04/9.95 21.04/9.95 21.04/9.95 ---------------------------------------- 21.04/9.95 21.04/9.95 (0) 21.04/9.95 Obligation: 21.04/9.95 Complexity Int TRS consisting of the following rules: 21.04/9.95 start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, D, H)) :|: 0 >= A + 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H 21.04/9.95 start(A, B, C, D, E, F, G, H) -> Com_1(lbl142(A, B, C, D, 0, F, D - 1, H)) :|: D >= 0 && D <= 0 && B >= C && B <= C && A >= 0 && A <= 0 && E >= F && E <= F && G >= H && G <= H 21.04/9.95 start(A, B, C, D, E, F, G, H) -> Com_1(lbl91(A, I, C, D, 0, F, D, H)) :|: A >= 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H 21.04/9.95 start(A, B, C, D, E, F, G, H) -> Com_1(lbl131(A, B, C, D, 1, F, D, H)) :|: A >= 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F && G >= H && G <= H 21.04/9.95 lbl142(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= 0 && G + 1 >= 0 && G + 1 <= 0 && E >= 0 && E <= 0 && D >= A && D <= A 21.04/9.95 lbl142(A, B, C, D, E, F, G, H) -> Com_1(lbl142(A, B, C, D, 0, F, G - 1, H)) :|: A >= 1 && G >= 0 && G <= 0 && E >= 1 && E <= 1 && D >= A && D <= A 21.04/9.95 lbl142(A, B, C, D, E, F, G, H) -> Com_1(lbl91(A, I, C, D, 0, F, G, H)) :|: E >= 2 && E >= 0 && A >= E && G + 1 >= E && G + 1 <= E && D >= A && D <= A 21.04/9.95 lbl142(A, B, C, D, E, F, G, H) -> Com_1(lbl131(A, B, C, D, 1, F, G, H)) :|: E >= 2 && E >= 0 && A >= E && G + 1 >= E && G + 1 <= E && D >= A && D <= A 21.04/9.95 lbl131(A, B, C, D, E, F, G, H) -> Com_1(lbl142(A, B, C, D, E, F, G - 1, H)) :|: G >= 1 && A >= G && E >= G && E <= G && D >= A && D <= A 21.04/9.95 lbl131(A, B, C, D, E, F, G, H) -> Com_1(lbl91(A, I, C, D, E, F, G, H)) :|: G >= E + 1 && G >= E && E >= 1 && A >= G && D >= A && D <= A 21.04/9.95 lbl131(A, B, C, D, E, F, G, H) -> Com_1(lbl131(A, B, C, D, 1 + E, F, G, H)) :|: G >= E + 1 && G >= E && E >= 1 && A >= G && D >= A && D <= A 21.04/9.95 lbl91(A, B, C, D, E, F, G, H) -> Com_1(lbl131(A, B, C, D, 1 + E, F, G, H)) :|: E >= 0 && G >= E + 1 && A >= G && D >= A && D <= A 21.04/9.95 start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, A, F, F, H, H)) :|: TRUE 21.04/9.95 21.04/9.95 The start-symbols are:[start0_8] 21.04/9.95 21.04/9.95 21.04/9.95 ---------------------------------------- 21.04/9.95 21.04/9.95 (1) Koat Proof (FINISHED) 21.04/9.95 YES(?, 62*ar_0 + 24*ar_0^2 + 41) 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Initial complexity problem: 21.04/9.95 21.04/9.95 1: T: 21.04/9.95 21.04/9.95 (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_3, ar_7)) [ 0 >= ar_0 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\ ar_1 = ar_2 /\ ar_0 = 0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(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 >= 0 /\ ar_6 + 1 = 0 /\ ar_4 = 0 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\ ar_6 = 0 /\ ar_4 = 1 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\ ar_0 >= ar_6 /\ ar_4 = ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\ ar_6 >= ar_4 + 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (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)) 21.04/9.95 21.04/9.95 (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 ] 21.04/9.95 21.04/9.95 start location: koat_start 21.04/9.95 21.04/9.95 leaf cost: 0 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Repeatedly propagating knowledge in problem 1 produces the following problem: 21.04/9.95 21.04/9.95 2: T: 21.04/9.95 21.04/9.95 (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_3, ar_7)) [ 0 >= ar_0 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\ ar_1 = ar_2 /\ ar_0 = 0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(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 >= 0 /\ ar_6 + 1 = 0 /\ ar_4 = 0 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\ ar_6 = 0 /\ ar_4 = 1 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\ ar_0 >= ar_6 /\ ar_4 = ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\ ar_6 >= ar_4 + 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (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)) 21.04/9.95 21.04/9.95 (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 ] 21.04/9.95 21.04/9.95 start location: koat_start 21.04/9.95 21.04/9.95 leaf cost: 0 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 A polynomial rank function with 21.04/9.95 21.04/9.95 Pol(start) = 1 21.04/9.95 21.04/9.95 Pol(stop) = 0 21.04/9.95 21.04/9.95 Pol(lbl142) = 1 21.04/9.95 21.04/9.95 Pol(lbl91) = 1 21.04/9.95 21.04/9.95 Pol(lbl131) = 1 21.04/9.95 21.04/9.95 Pol(start0) = 1 21.04/9.95 21.04/9.95 Pol(koat_start) = 1 21.04/9.95 21.04/9.95 orients all transitions weakly and the transition 21.04/9.95 21.04/9.95 lbl142(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 >= 0 /\ ar_6 + 1 = 0 /\ ar_4 = 0 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 strictly and produces the following problem: 21.04/9.95 21.04/9.95 3: T: 21.04/9.95 21.04/9.95 (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_3, ar_7)) [ 0 >= ar_0 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\ ar_1 = ar_2 /\ ar_0 = 0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) lbl142(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 >= 0 /\ ar_6 + 1 = 0 /\ ar_4 = 0 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\ ar_6 = 0 /\ ar_4 = 1 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\ ar_0 >= ar_6 /\ ar_4 = ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\ ar_6 >= ar_4 + 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (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)) 21.04/9.95 21.04/9.95 (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 ] 21.04/9.95 21.04/9.95 start location: koat_start 21.04/9.95 21.04/9.95 leaf cost: 0 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 A polynomial rank function with 21.04/9.95 21.04/9.95 Pol(start) = 2*V_1 + 2 21.04/9.95 21.04/9.95 Pol(stop) = 2*V_1 - 2*V_4 + 2*V_7 + 2 21.04/9.95 21.04/9.95 Pol(lbl142) = 2*V_5 + 1 21.04/9.95 21.04/9.95 Pol(lbl91) = 2*V_7 + 2 21.04/9.95 21.04/9.95 Pol(lbl131) = 2*V_7 + 2 21.04/9.95 21.04/9.95 Pol(start0) = 2*V_1 + 2 21.04/9.95 21.04/9.95 Pol(koat_start) = 2*V_1 + 2 21.04/9.95 21.04/9.95 orients all transitions weakly and the transitions 21.04/9.95 21.04/9.95 lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\ ar_6 = 0 /\ ar_4 = 1 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\ ar_0 >= ar_6 /\ ar_4 = ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 strictly and produces the following problem: 21.04/9.95 21.04/9.95 4: T: 21.04/9.95 21.04/9.95 (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_3, ar_7)) [ 0 >= ar_0 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\ ar_1 = ar_2 /\ ar_0 = 0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) lbl142(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 >= 0 /\ ar_6 + 1 = 0 /\ ar_4 = 0 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: 2*ar_0 + 2, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\ ar_6 = 0 /\ ar_4 = 1 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: 2*ar_0 + 2, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: 2*ar_0 + 2, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: 2*ar_0 + 2, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\ ar_0 >= ar_6 /\ ar_4 = ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: ?, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\ ar_6 >= ar_4 + 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (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)) 21.04/9.95 21.04/9.95 (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 ] 21.04/9.95 21.04/9.95 start location: koat_start 21.04/9.95 21.04/9.95 leaf cost: 0 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 A polynomial rank function with 21.04/9.95 21.04/9.95 Pol(lbl91) = -2*V_5 + 2*V_7 21.04/9.95 21.04/9.95 Pol(lbl131) = -2*V_5 + 2*V_7 + 1 21.04/9.95 21.04/9.95 and size complexities 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 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 21.04/9.95 21.04/9.95 S("lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\\ ar_6 >= ar_4 + 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-0) = ar_0 21.04/9.95 21.04/9.95 S("lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\\ ar_6 >= ar_4 + 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-1) = ? 21.04/9.95 21.04/9.95 S("lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\\ ar_6 >= ar_4 + 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-2) = ar_2 21.04/9.95 21.04/9.95 S("lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\\ ar_6 >= ar_4 + 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-3) = ar_0 21.04/9.95 21.04/9.95 S("lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\\ ar_6 >= ar_4 + 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-4) = ar_0 21.04/9.95 21.04/9.95 S("lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\\ ar_6 >= ar_4 + 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-5) = ar_5 21.04/9.95 21.04/9.95 S("lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\\ ar_6 >= ar_4 + 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-6) = ar_0 21.04/9.95 21.04/9.95 S("lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\\ ar_6 >= ar_4 + 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-7) = ar_7 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-0) = ar_0 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-1) = ? 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-2) = ar_2 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-3) = ar_0 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-4) = ar_0 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-5) = ar_5 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-6) = ar_0 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-7) = ar_7 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-0) = ar_0 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-1) = ? 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-2) = ar_2 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-3) = ar_0 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-4) = ar_0 + 2 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-5) = ar_5 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-6) = ar_0 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\\ ar_6 >= ar_4 /\\ ar_4 >= 1 /\\ ar_0 >= ar_6 /\\ ar_3 = ar_0 ]", 0-7) = ar_7 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\\ ar_0 >= ar_6 /\\ ar_4 = ar_6 /\\ ar_3 = ar_0 ]", 0-0) = ar_0 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\\ ar_0 >= ar_6 /\\ ar_4 = ar_6 /\\ ar_3 = ar_0 ]", 0-1) = ? 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\\ ar_0 >= ar_6 /\\ ar_4 = ar_6 /\\ ar_3 = ar_0 ]", 0-2) = ar_2 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\\ ar_0 >= ar_6 /\\ ar_4 = ar_6 /\\ ar_3 = ar_0 ]", 0-3) = ar_0 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\\ ar_0 >= ar_6 /\\ ar_4 = ar_6 /\\ ar_3 = ar_0 ]", 0-4) = ar_0 + 2 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\\ ar_0 >= ar_6 /\\ ar_4 = ar_6 /\\ ar_3 = ar_0 ]", 0-5) = ar_5 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\\ ar_0 >= ar_6 /\\ ar_4 = ar_6 /\\ ar_3 = ar_0 ]", 0-6) = ar_0 21.04/9.95 21.04/9.95 S("lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\\ ar_0 >= ar_6 /\\ ar_4 = ar_6 /\\ ar_3 = ar_0 ]", 0-7) = ar_7 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-0) = ar_0 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-1) = ? 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-2) = ar_2 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-3) = ar_0 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-4) = 1 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-5) = ar_5 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-6) = ar_0 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-7) = ar_7 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-0) = ar_0 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-1) = ? 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-2) = ar_2 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-3) = ar_0 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-4) = 0 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-5) = ar_5 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-6) = ar_0 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\\ ar_4 >= 0 /\\ ar_0 >= ar_4 /\\ ar_6 + 1 = ar_4 /\\ ar_3 = ar_0 ]", 0-7) = ar_7 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\\ ar_6 = 0 /\\ ar_4 = 1 /\\ ar_3 = ar_0 ]", 0-0) = ar_0 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\\ ar_6 = 0 /\\ ar_4 = 1 /\\ ar_3 = ar_0 ]", 0-1) = ? 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\\ ar_6 = 0 /\\ ar_4 = 1 /\\ ar_3 = ar_0 ]", 0-2) = ar_2 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\\ ar_6 = 0 /\\ ar_4 = 1 /\\ ar_3 = ar_0 ]", 0-3) = ar_0 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\\ ar_6 = 0 /\\ ar_4 = 1 /\\ ar_3 = ar_0 ]", 0-4) = 0 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\\ ar_6 = 0 /\\ ar_4 = 1 /\\ ar_3 = ar_0 ]", 0-5) = ar_5 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\\ ar_6 = 0 /\\ ar_4 = 1 /\\ ar_3 = ar_0 ]", 0-6) = 1 21.04/9.95 21.04/9.95 S("lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\\ ar_6 = 0 /\\ ar_4 = 1 /\\ ar_3 = ar_0 ]", 0-7) = ar_7 21.04/9.95 21.04/9.95 S("lbl142(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 >= 0 /\\ ar_6 + 1 = 0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 ]", 0-0) = ar_0 21.04/9.95 21.04/9.95 S("lbl142(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 >= 0 /\\ ar_6 + 1 = 0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 ]", 0-1) = ? 21.04/9.95 21.04/9.95 S("lbl142(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 >= 0 /\\ ar_6 + 1 = 0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 ]", 0-2) = ar_2 21.04/9.95 21.04/9.95 S("lbl142(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 >= 0 /\\ ar_6 + 1 = 0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 ]", 0-3) = ar_0 21.04/9.95 21.04/9.95 S("lbl142(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 >= 0 /\\ ar_6 + 1 = 0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 ]", 0-4) = 0 21.04/9.95 21.04/9.95 S("lbl142(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 >= 0 /\\ ar_6 + 1 = 0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 ]", 0-5) = ar_5 21.04/9.95 21.04/9.95 S("lbl142(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 >= 0 /\\ ar_6 + 1 = 0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 ]", 0-6) = 1 21.04/9.95 21.04/9.95 S("lbl142(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 >= 0 /\\ ar_6 + 1 = 0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 ]", 0-7) = ar_7 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-0) = ar_0 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-1) = ar_2 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-2) = ar_2 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-3) = ar_0 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-4) = 1 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-5) = ar_5 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-6) = ar_0 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-7) = ar_7 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-0) = ar_0 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-1) = ? 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-2) = ar_2 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-3) = ar_0 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-4) = 0 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-5) = ar_5 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-6) = ar_0 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-7) = ar_7 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\\ ar_1 = ar_2 /\\ ar_0 = 0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-0) = 0 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\\ ar_1 = ar_2 /\\ ar_0 = 0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-1) = ar_2 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\\ ar_1 = ar_2 /\\ ar_0 = 0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-2) = ar_2 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\\ ar_1 = ar_2 /\\ ar_0 = 0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-3) = 0 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\\ ar_1 = ar_2 /\\ ar_0 = 0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-4) = 0 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\\ ar_1 = ar_2 /\\ ar_0 = 0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-5) = ar_5 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\\ ar_1 = ar_2 /\\ ar_0 = 0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-6) = 1 21.04/9.95 21.04/9.95 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\\ ar_1 = ar_2 /\\ ar_0 = 0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-7) = ar_7 21.04/9.95 21.04/9.95 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_3, ar_7)) [ 0 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-0) = ar_0 21.04/9.95 21.04/9.95 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_3, ar_7)) [ 0 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-1) = ar_2 21.04/9.95 21.04/9.95 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_3, ar_7)) [ 0 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-2) = ar_2 21.04/9.95 21.04/9.95 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_3, ar_7)) [ 0 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-3) = ar_0 21.04/9.95 21.04/9.95 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_3, ar_7)) [ 0 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-4) = ar_5 21.04/9.95 21.04/9.95 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_3, ar_7)) [ 0 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-5) = ar_5 21.04/9.95 21.04/9.95 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_3, ar_7)) [ 0 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-6) = ar_0 21.04/9.95 21.04/9.95 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_3, ar_7)) [ 0 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-7) = ar_7 21.04/9.95 21.04/9.95 orients the transitions 21.04/9.95 21.04/9.95 lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\ ar_6 >= ar_4 + 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 weakly and the transitions 21.04/9.95 21.04/9.95 lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\ ar_6 >= ar_4 + 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 strictly and produces the following problem: 21.04/9.95 21.04/9.95 5: T: 21.04/9.95 21.04/9.95 (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_3, ar_7)) [ 0 >= ar_0 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_3 - 1, ar_7)) [ ar_3 = 0 /\ ar_1 = ar_2 /\ ar_0 = 0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_3, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ] 21.04/9.95 21.04/9.95 (Comp: 1, Cost: 1) lbl142(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 >= 0 /\ ar_6 + 1 = 0 /\ ar_4 = 0 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: 2*ar_0 + 2, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6 - 1, ar_7)) [ ar_0 >= 1 /\ ar_6 = 0 /\ ar_4 = 1 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: 2*ar_0 + 2, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: 2*ar_0 + 2, Cost: 1) lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7)) [ ar_4 >= 2 /\ ar_4 >= 0 /\ ar_0 >= ar_4 /\ ar_6 + 1 = ar_4 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: 2*ar_0 + 2, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl142(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 - 1, ar_7)) [ ar_6 >= 1 /\ ar_0 >= ar_6 /\ ar_4 = ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: 8*ar_0^2 + 18*ar_0 + 9, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl91(ar_0, i, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: 8*ar_0^2 + 18*ar_0 + 9, Cost: 1) lbl131(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_6 >= ar_4 + 1 /\ ar_6 >= ar_4 /\ ar_4 >= 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (Comp: 8*ar_0^2 + 18*ar_0 + 9, Cost: 1) lbl91(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl131(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_4 >= 0 /\ ar_6 >= ar_4 + 1 /\ ar_0 >= ar_6 /\ ar_3 = ar_0 ] 21.04/9.95 21.04/9.95 (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)) 21.04/9.95 21.04/9.95 (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 ] 21.04/9.95 21.04/9.95 start location: koat_start 21.04/9.95 21.04/9.95 leaf cost: 0 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Complexity upper bound 62*ar_0 + 24*ar_0^2 + 41 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Time: 0.514 sec (SMT: 0.385 sec) 21.04/9.95 21.04/9.95 21.04/9.95 ---------------------------------------- 21.04/9.95 21.04/9.95 (2) 21.04/9.95 BOUNDS(1, n^2) 21.04/9.95 21.04/9.95 ---------------------------------------- 21.04/9.95 21.04/9.95 (3) Loat Proof (FINISHED) 21.04/9.95 21.04/9.95 21.04/9.95 ### Pre-processing the ITS problem ### 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Initial linear ITS problem 21.04/9.95 21.04/9.95 Start location: start0 21.04/9.95 21.04/9.95 0: start -> stop : G'=D, [ 0>=1+A && B==C && D==A && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 1: start -> lbl142 : E'=0, G'=-1+D, [ D==0 && B==C && A==0 && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 2: start -> lbl91 : B'=free, E'=0, G'=D, [ A>=1 && B==C && D==A && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 3: start -> lbl131 : E'=1, G'=D, [ A>=1 && B==C && D==A && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 4: lbl142 -> stop : [ A>=0 && 1+G==0 && E==0 && D==A ], cost: 1 21.04/9.95 21.04/9.95 5: lbl142 -> lbl142 : E'=0, G'=-1+G, [ A>=1 && G==0 && E==1 && D==A ], cost: 1 21.04/9.95 21.04/9.95 6: lbl142 -> lbl91 : B'=free_1, E'=0, [ E>=2 && E>=0 && A>=E && 1+G==E && D==A ], cost: 1 21.04/9.95 21.04/9.95 7: lbl142 -> lbl131 : E'=1, [ E>=2 && E>=0 && A>=E && 1+G==E && D==A ], cost: 1 21.04/9.95 21.04/9.95 8: lbl131 -> lbl142 : G'=-1+G, [ G>=1 && A>=G && E==G && D==A ], cost: 1 21.04/9.95 21.04/9.95 9: lbl131 -> lbl91 : B'=free_2, [ G>=1+E && G>=E && E>=1 && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 10: lbl131 -> lbl131 : E'=1+E, [ G>=1+E && G>=E && E>=1 && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 11: lbl91 -> lbl131 : E'=1+E, [ E>=0 && G>=1+E && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 12: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Removed unreachable and leaf rules: 21.04/9.95 21.04/9.95 Start location: start0 21.04/9.95 21.04/9.95 1: start -> lbl142 : E'=0, G'=-1+D, [ D==0 && B==C && A==0 && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 2: start -> lbl91 : B'=free, E'=0, G'=D, [ A>=1 && B==C && D==A && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 3: start -> lbl131 : E'=1, G'=D, [ A>=1 && B==C && D==A && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 5: lbl142 -> lbl142 : E'=0, G'=-1+G, [ A>=1 && G==0 && E==1 && D==A ], cost: 1 21.04/9.95 21.04/9.95 6: lbl142 -> lbl91 : B'=free_1, E'=0, [ E>=2 && E>=0 && A>=E && 1+G==E && D==A ], cost: 1 21.04/9.95 21.04/9.95 7: lbl142 -> lbl131 : E'=1, [ E>=2 && E>=0 && A>=E && 1+G==E && D==A ], cost: 1 21.04/9.95 21.04/9.95 8: lbl131 -> lbl142 : G'=-1+G, [ G>=1 && A>=G && E==G && D==A ], cost: 1 21.04/9.95 21.04/9.95 9: lbl131 -> lbl91 : B'=free_2, [ G>=1+E && G>=E && E>=1 && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 10: lbl131 -> lbl131 : E'=1+E, [ G>=1+E && G>=E && E>=1 && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 11: lbl91 -> lbl131 : E'=1+E, [ E>=0 && G>=1+E && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 12: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Simplified all rules, resulting in: 21.04/9.95 21.04/9.95 Start location: start0 21.04/9.95 21.04/9.95 1: start -> lbl142 : E'=0, G'=-1+D, [ D==0 && B==C && A==0 && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 2: start -> lbl91 : B'=free, E'=0, G'=D, [ A>=1 && B==C && D==A && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 3: start -> lbl131 : E'=1, G'=D, [ A>=1 && B==C && D==A && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 5: lbl142 -> lbl142 : E'=0, G'=-1+G, [ A>=1 && G==0 && E==1 && D==A ], cost: 1 21.04/9.95 21.04/9.95 6: lbl142 -> lbl91 : B'=free_1, E'=0, [ E>=2 && A>=E && 1+G==E && D==A ], cost: 1 21.04/9.95 21.04/9.95 7: lbl142 -> lbl131 : E'=1, [ E>=2 && A>=E && 1+G==E && D==A ], cost: 1 21.04/9.95 21.04/9.95 8: lbl131 -> lbl142 : G'=-1+G, [ G>=1 && A>=G && E==G && D==A ], cost: 1 21.04/9.95 21.04/9.95 9: lbl131 -> lbl91 : B'=free_2, [ G>=1+E && E>=1 && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 10: lbl131 -> lbl131 : E'=1+E, [ G>=1+E && E>=1 && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 11: lbl91 -> lbl131 : E'=1+E, [ E>=0 && G>=1+E && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 12: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 ### Simplification by acceleration and chaining ### 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Accelerating simple loops of location 1. 21.04/9.95 21.04/9.95 Accelerating the following rules: 21.04/9.95 21.04/9.95 5: lbl142 -> lbl142 : E'=0, G'=-1+G, [ A>=1 && G==0 && E==1 && D==A ], cost: 1 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Accelerated rule 5 with metering function meter (where 2*meter==G+E), yielding the new rule 13. 21.04/9.95 21.04/9.95 Removing the simple loops: 5. 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Accelerating simple loops of location 2. 21.04/9.95 21.04/9.95 Accelerating the following rules: 21.04/9.95 21.04/9.95 10: lbl131 -> lbl131 : E'=1+E, [ G>=1+E && E>=1 && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Accelerated rule 10 with metering function G-E, yielding the new rule 14. 21.04/9.95 21.04/9.95 Removing the simple loops: 10. 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Accelerated all simple loops using metering functions (where possible): 21.04/9.95 21.04/9.95 Start location: start0 21.04/9.95 21.04/9.95 1: start -> lbl142 : E'=0, G'=-1+D, [ D==0 && B==C && A==0 && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 2: start -> lbl91 : B'=free, E'=0, G'=D, [ A>=1 && B==C && D==A && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 3: start -> lbl131 : E'=1, G'=D, [ A>=1 && B==C && D==A && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 6: lbl142 -> lbl91 : B'=free_1, E'=0, [ E>=2 && A>=E && 1+G==E && D==A ], cost: 1 21.04/9.95 21.04/9.95 7: lbl142 -> lbl131 : E'=1, [ E>=2 && A>=E && 1+G==E && D==A ], cost: 1 21.04/9.95 21.04/9.95 13: lbl142 -> lbl142 : E'=0, G'=G-meter, [ A>=1 && G==0 && E==1 && D==A && 2*meter==G+E && meter>=1 ], cost: meter 21.04/9.95 21.04/9.95 8: lbl131 -> lbl142 : G'=-1+G, [ G>=1 && A>=G && E==G && D==A ], cost: 1 21.04/9.95 21.04/9.95 9: lbl131 -> lbl91 : B'=free_2, [ G>=1+E && E>=1 && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 14: lbl131 -> lbl131 : E'=G, [ G>=1+E && E>=1 && A>=G && D==A ], cost: G-E 21.04/9.95 21.04/9.95 11: lbl91 -> lbl131 : E'=1+E, [ E>=0 && G>=1+E && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 12: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Chained accelerated rules (with incoming rules): 21.04/9.95 21.04/9.95 Start location: start0 21.04/9.95 21.04/9.95 1: start -> lbl142 : E'=0, G'=-1+D, [ D==0 && B==C && A==0 && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 2: start -> lbl91 : B'=free, E'=0, G'=D, [ A>=1 && B==C && D==A && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 3: start -> lbl131 : E'=1, G'=D, [ A>=1 && B==C && D==A && E==F && G==H ], cost: 1 21.04/9.95 21.04/9.95 15: start -> lbl131 : E'=D, G'=D, [ A>=1 && B==C && D==A && E==F && G==H && D>=2 ], cost: D 21.04/9.95 21.04/9.95 6: lbl142 -> lbl91 : B'=free_1, E'=0, [ E>=2 && A>=E && 1+G==E && D==A ], cost: 1 21.04/9.95 21.04/9.95 7: lbl142 -> lbl131 : E'=1, [ E>=2 && A>=E && 1+G==E && D==A ], cost: 1 21.04/9.95 21.04/9.95 16: lbl142 -> lbl131 : E'=G, [ E>=2 && A>=E && 1+G==E && D==A && G>=2 && A>=G ], cost: G 21.04/9.95 21.04/9.95 8: lbl131 -> lbl142 : G'=-1+G, [ G>=1 && A>=G && E==G && D==A ], cost: 1 21.04/9.95 21.04/9.95 9: lbl131 -> lbl91 : B'=free_2, [ G>=1+E && E>=1 && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 11: lbl91 -> lbl131 : E'=1+E, [ E>=0 && G>=1+E && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 17: lbl91 -> lbl131 : E'=G, [ E>=0 && A>=G && D==A && G>=2+E ], cost: G-E 21.04/9.95 21.04/9.95 12: start0 -> start : B'=C, D'=A, E'=F, G'=H, [], cost: 1 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Eliminated locations (on tree-shaped paths): 21.04/9.95 21.04/9.95 Start location: start0 21.04/9.95 21.04/9.95 6: lbl142 -> lbl91 : B'=free_1, E'=0, [ E>=2 && A>=E && 1+G==E && D==A ], cost: 1 21.04/9.95 21.04/9.95 7: lbl142 -> lbl131 : E'=1, [ E>=2 && A>=E && 1+G==E && D==A ], cost: 1 21.04/9.95 21.04/9.95 16: lbl142 -> lbl131 : E'=G, [ E>=2 && A>=E && 1+G==E && D==A && G>=2 && A>=G ], cost: G 21.04/9.95 21.04/9.95 8: lbl131 -> lbl142 : G'=-1+G, [ G>=1 && A>=G && E==G && D==A ], cost: 1 21.04/9.95 21.04/9.95 9: lbl131 -> lbl91 : B'=free_2, [ G>=1+E && E>=1 && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 11: lbl91 -> lbl131 : E'=1+E, [ E>=0 && G>=1+E && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 17: lbl91 -> lbl131 : E'=G, [ E>=0 && A>=G && D==A && G>=2+E ], cost: G-E 21.04/9.95 21.04/9.95 18: start0 -> lbl142 : B'=C, D'=A, E'=0, G'=-1+A, [ A==0 ], cost: 2 21.04/9.95 21.04/9.95 19: start0 -> lbl91 : B'=free, D'=A, E'=0, G'=A, [ A>=1 ], cost: 2 21.04/9.95 21.04/9.95 20: start0 -> lbl131 : B'=C, D'=A, E'=1, G'=A, [ A>=1 ], cost: 2 21.04/9.95 21.04/9.95 21: start0 -> lbl131 : B'=C, D'=A, E'=A, G'=A, [ A>=2 ], cost: 1+A 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Eliminated location lbl142 (as a last resort): 21.04/9.95 21.04/9.95 Start location: start0 21.04/9.95 21.04/9.95 9: lbl131 -> lbl91 : B'=free_2, [ G>=1+E && E>=1 && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 22: lbl131 -> lbl91 : B'=free_1, E'=0, G'=-1+G, [ G>=1 && A>=G && E==G && D==A && E>=2 && A>=E && G==E ], cost: 2 21.04/9.95 21.04/9.95 23: lbl131 -> lbl131 : E'=1, G'=-1+G, [ G>=1 && A>=G && E==G && D==A && E>=2 && A>=E && G==E ], cost: 2 21.04/9.95 21.04/9.95 24: lbl131 -> lbl131 : E'=-1+G, G'=-1+G, [ A>=G && E==G && D==A && E>=2 && A>=E && G==E && -1+G>=2 ], cost: G 21.04/9.95 21.04/9.95 11: lbl91 -> lbl131 : E'=1+E, [ E>=0 && G>=1+E && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 17: lbl91 -> lbl131 : E'=G, [ E>=0 && A>=G && D==A && G>=2+E ], cost: G-E 21.04/9.95 21.04/9.95 19: start0 -> lbl91 : B'=free, D'=A, E'=0, G'=A, [ A>=1 ], cost: 2 21.04/9.95 21.04/9.95 20: start0 -> lbl131 : B'=C, D'=A, E'=1, G'=A, [ A>=1 ], cost: 2 21.04/9.95 21.04/9.95 21: start0 -> lbl131 : B'=C, D'=A, E'=A, G'=A, [ A>=2 ], cost: 1+A 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Accelerating simple loops of location 2. 21.04/9.95 21.04/9.95 Accelerating the following rules: 21.04/9.95 21.04/9.95 23: lbl131 -> lbl131 : E'=1, G'=-1+G, [ G>=1 && A>=G && E==G && D==A && E>=2 && A>=E && G==E ], cost: 2 21.04/9.95 21.04/9.95 24: lbl131 -> lbl131 : E'=-1+G, G'=-1+G, [ A>=G && E==G && D==A && E>=2 && A>=E && G==E && -1+G>=2 ], cost: G 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Accelerated rule 23 with metering function -1-G+2*E (after strengthening guard), yielding the new rule 25. 21.04/9.95 21.04/9.95 Accelerated rule 24 with metering function -2+G, yielding the new rule 26. 21.04/9.95 21.04/9.95 Removing the simple loops: 24. 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Accelerated all simple loops using metering functions (where possible): 21.04/9.95 21.04/9.95 Start location: start0 21.04/9.95 21.04/9.95 9: lbl131 -> lbl91 : B'=free_2, [ G>=1+E && E>=1 && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 22: lbl131 -> lbl91 : B'=free_1, E'=0, G'=-1+G, [ G>=1 && A>=G && E==G && D==A && E>=2 && A>=E && G==E ], cost: 2 21.04/9.95 21.04/9.95 23: lbl131 -> lbl131 : E'=1, G'=-1+G, [ G>=1 && A>=G && E==G && D==A && E>=2 && A>=E && G==E ], cost: 2 21.04/9.95 21.04/9.95 25: lbl131 -> lbl131 : E'=1, G'=1+2*G-2*E, [ A>=G && E==G && D==A && E>=2 && A>=E && G==E && 1==-1+G && -1+G==1 && -1-G+2*E>=1 ], cost: -2-2*G+4*E 21.04/9.95 21.04/9.95 26: lbl131 -> lbl131 : E'=2, G'=2, [ A>=G && E==G && D==A && E>=2 && A>=E && G==E && -1+G>=2 ], cost: -1+1/2*G-1/2*(-2+G)^2+G*(-2+G) 21.04/9.95 21.04/9.95 11: lbl91 -> lbl131 : E'=1+E, [ E>=0 && G>=1+E && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 17: lbl91 -> lbl131 : E'=G, [ E>=0 && A>=G && D==A && G>=2+E ], cost: G-E 21.04/9.95 21.04/9.95 19: start0 -> lbl91 : B'=free, D'=A, E'=0, G'=A, [ A>=1 ], cost: 2 21.04/9.95 21.04/9.95 20: start0 -> lbl131 : B'=C, D'=A, E'=1, G'=A, [ A>=1 ], cost: 2 21.04/9.95 21.04/9.95 21: start0 -> lbl131 : B'=C, D'=A, E'=A, G'=A, [ A>=2 ], cost: 1+A 21.04/9.95 21.04/9.95 21.04/9.95 21.04/9.95 Chained accelerated rules (with incoming rules): 21.04/9.95 21.04/9.95 Start location: start0 21.04/9.95 21.04/9.95 9: lbl131 -> lbl91 : B'=free_2, [ G>=1+E && E>=1 && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 22: lbl131 -> lbl91 : B'=free_1, E'=0, G'=-1+G, [ G>=1 && A>=G && E==G && D==A && E>=2 && A>=E && G==E ], cost: 2 21.04/9.95 21.04/9.95 11: lbl91 -> lbl131 : E'=1+E, [ E>=0 && G>=1+E && A>=G && D==A ], cost: 1 21.04/9.95 21.04/9.95 17: lbl91 -> lbl131 : E'=G, [ E>=0 && A>=G && D==A && G>=2+E ], cost: G-E 21.04/9.96 21.04/9.96 27: lbl91 -> lbl131 : E'=1, G'=-1+G, [ A>=G && D==A && G>=1 && 1+E==G && 1+E>=2 && A>=1+E && G==1+E ], cost: 3 21.04/9.96 21.04/9.96 28: lbl91 -> lbl131 : E'=1, G'=-1+G, [ E>=0 && A>=G && D==A && G>=2+E && G>=2 ], cost: 2+G-E 21.04/9.96 21.04/9.96 30: lbl91 -> lbl131 : E'=1, G'=-1+2*G-2*E, [ A>=G && D==A && 1+E==G && 1+E>=2 && A>=1+E && G==1+E && 1==-1+G && -1+G==1 && 1-G+2*E>=1 ], cost: 3-2*G+4*E 21.04/9.96 21.04/9.96 31: lbl91 -> lbl131 : E'=1, G'=1, [ E>=0 && A>=G && D==A && G>=2+E && 1==-1+G && -1+G==1 ], cost: -2+3*G-E 21.04/9.96 21.04/9.96 33: lbl91 -> lbl131 : E'=2, G'=2, [ A>=G && D==A && 1+E==G && 1+E>=2 && A>=1+E && G==1+E && -1+G>=2 ], cost: 1/2*G-1/2*(-2+G)^2+G*(-2+G) 21.04/9.96 21.04/9.96 34: lbl91 -> lbl131 : E'=2, G'=2, [ E>=0 && A>=G && D==A && G>=2+E && -1+G>=2 ], cost: -1+3/2*G-1/2*(-2+G)^2+G*(-2+G)-E 21.04/9.96 21.04/9.96 19: start0 -> lbl91 : B'=free, D'=A, E'=0, G'=A, [ A>=1 ], cost: 2 21.04/9.96 21.04/9.96 20: start0 -> lbl131 : B'=C, D'=A, E'=1, G'=A, [ A>=1 ], cost: 2 21.04/9.96 21.04/9.96 21: start0 -> lbl131 : B'=C, D'=A, E'=A, G'=A, [ A>=2 ], cost: 1+A 21.04/9.96 21.04/9.96 29: start0 -> lbl131 : B'=C, D'=A, E'=1, G'=-1+A, [ A>=2 ], cost: 3+A 21.04/9.96 21.04/9.96 32: start0 -> lbl131 : B'=C, D'=A, E'=1, G'=1, [ 1==-1+A && -1+A==1 ], cost: -1+3*A 21.04/9.96 21.04/9.96 35: start0 -> lbl131 : B'=C, D'=A, E'=2, G'=2, [ -1+A>=2 ], cost: -1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Eliminated location lbl131 (as a last resort): 21.04/9.96 21.04/9.96 Start location: start0 21.04/9.96 21.04/9.96 36: lbl91 -> lbl91 : B'=free_2, E'=1+E, [ E>=0 && A>=G && D==A && G>=2+E ], cost: 2 21.04/9.96 21.04/9.96 37: lbl91 -> lbl91 : B'=free_1, E'=0, G'=-1+G, [ A>=G && D==A && G>=1 && 1+E==G && 1+E>=2 && A>=1+E && G==1+E ], cost: 3 21.04/9.96 21.04/9.96 38: lbl91 -> lbl91 : B'=free_1, E'=0, G'=-1+G, [ E>=0 && A>=G && D==A && G>=2+E && G>=2 ], cost: 2+G-E 21.04/9.96 21.04/9.96 41: lbl91 -> lbl91 : B'=free_2, E'=1, G'=-1+G, [ A>=G && D==A && 1+E==G && 1+E>=2 && A>=1+E && G==1+E && -1+G>=2 ], cost: 4 21.04/9.96 21.04/9.96 42: lbl91 -> lbl91 : B'=free_2, E'=1, G'=-1+G, [ E>=0 && A>=G && D==A && G>=2+E && -1+G>=2 ], cost: 3+G-E 21.04/9.96 21.04/9.96 44: lbl91 -> lbl91 : B'=free_1, E'=0, G'=1, [ A>=G && D==A && 1+E==G && 1+E>=2 && A>=1+E && G==1+E && -1+G>=2 && A>=2 ], cost: 2+1/2*G-1/2*(-2+G)^2+G*(-2+G) 21.04/9.96 21.04/9.96 45: lbl91 -> lbl91 : B'=free_1, E'=0, G'=1, [ E>=0 && A>=G && D==A && G>=2+E && -1+G>=2 && A>=2 ], cost: 1+3/2*G-1/2*(-2+G)^2+G*(-2+G)-E 21.04/9.96 21.04/9.96 47: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E ], cost: G-E 21.04/9.96 21.04/9.96 49: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E && G>=2 ], cost: 2+G-E 21.04/9.96 21.04/9.96 51: lbl91 -> [9] : [ A>=G && D==A && 1+E==G && 1+E>=2 && A>=1+E && G==1+E && 1==-1+G && -1+G==1 && 1-G+2*E>=1 ], cost: 3-2*G+4*E 21.04/9.96 21.04/9.96 52: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E && 1==-1+G && -1+G==1 ], cost: -2+3*G-E 21.04/9.96 21.04/9.96 54: lbl91 -> [9] : [ A>=G && D==A && 1+E==G && 1+E>=2 && A>=1+E && G==1+E && -1+G>=2 ], cost: 1/2*G-1/2*(-2+G)^2+G*(-2+G) 21.04/9.96 21.04/9.96 55: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E && -1+G>=2 ], cost: -1+3/2*G-1/2*(-2+G)^2+G*(-2+G)-E 21.04/9.96 21.04/9.96 19: start0 -> lbl91 : B'=free, D'=A, E'=0, G'=A, [ A>=1 ], cost: 2 21.04/9.96 21.04/9.96 39: start0 -> lbl91 : B'=free_2, D'=A, E'=1, G'=A, [ A>=2 ], cost: 3 21.04/9.96 21.04/9.96 40: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=-1+A, [ A>=2 ], cost: 3+A 21.04/9.96 21.04/9.96 43: start0 -> lbl91 : B'=free_2, D'=A, E'=1, G'=-1+A, [ -1+A>=2 ], cost: 4+A 21.04/9.96 21.04/9.96 46: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=1, [ -1+A>=2 ], cost: 2-1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 48: start0 -> [9] : [ A>=2 ], cost: 1+A 21.04/9.96 21.04/9.96 50: start0 -> [9] : [ A>=2 ], cost: 3+A 21.04/9.96 21.04/9.96 53: start0 -> [9] : [ 1==-1+A && -1+A==1 ], cost: -1+3*A 21.04/9.96 21.04/9.96 56: start0 -> [9] : [ -1+A>=2 ], cost: -1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Applied pruning (of leafs and parallel rules): 21.04/9.96 21.04/9.96 Start location: start0 21.04/9.96 21.04/9.96 37: lbl91 -> lbl91 : B'=free_1, E'=0, G'=-1+G, [ A>=G && D==A && G>=1 && 1+E==G && 1+E>=2 && A>=1+E && G==1+E ], cost: 3 21.04/9.96 21.04/9.96 38: lbl91 -> lbl91 : B'=free_1, E'=0, G'=-1+G, [ E>=0 && A>=G && D==A && G>=2+E && G>=2 ], cost: 2+G-E 21.04/9.96 21.04/9.96 42: lbl91 -> lbl91 : B'=free_2, E'=1, G'=-1+G, [ E>=0 && A>=G && D==A && G>=2+E && -1+G>=2 ], cost: 3+G-E 21.04/9.96 21.04/9.96 44: lbl91 -> lbl91 : B'=free_1, E'=0, G'=1, [ A>=G && D==A && 1+E==G && 1+E>=2 && A>=1+E && G==1+E && -1+G>=2 && A>=2 ], cost: 2+1/2*G-1/2*(-2+G)^2+G*(-2+G) 21.04/9.96 21.04/9.96 45: lbl91 -> lbl91 : B'=free_1, E'=0, G'=1, [ E>=0 && A>=G && D==A && G>=2+E && -1+G>=2 && A>=2 ], cost: 1+3/2*G-1/2*(-2+G)^2+G*(-2+G)-E 21.04/9.96 21.04/9.96 47: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E ], cost: G-E 21.04/9.96 21.04/9.96 49: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E && G>=2 ], cost: 2+G-E 21.04/9.96 21.04/9.96 52: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E && 1==-1+G && -1+G==1 ], cost: -2+3*G-E 21.04/9.96 21.04/9.96 54: lbl91 -> [9] : [ A>=G && D==A && 1+E==G && 1+E>=2 && A>=1+E && G==1+E && -1+G>=2 ], cost: 1/2*G-1/2*(-2+G)^2+G*(-2+G) 21.04/9.96 21.04/9.96 55: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E && -1+G>=2 ], cost: -1+3/2*G-1/2*(-2+G)^2+G*(-2+G)-E 21.04/9.96 21.04/9.96 19: start0 -> lbl91 : B'=free, D'=A, E'=0, G'=A, [ A>=1 ], cost: 2 21.04/9.96 21.04/9.96 39: start0 -> lbl91 : B'=free_2, D'=A, E'=1, G'=A, [ A>=2 ], cost: 3 21.04/9.96 21.04/9.96 40: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=-1+A, [ A>=2 ], cost: 3+A 21.04/9.96 21.04/9.96 43: start0 -> lbl91 : B'=free_2, D'=A, E'=1, G'=-1+A, [ -1+A>=2 ], cost: 4+A 21.04/9.96 21.04/9.96 46: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=1, [ -1+A>=2 ], cost: 2-1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 50: start0 -> [9] : [ A>=2 ], cost: 3+A 21.04/9.96 21.04/9.96 53: start0 -> [9] : [ 1==-1+A && -1+A==1 ], cost: -1+3*A 21.04/9.96 21.04/9.96 56: start0 -> [9] : [ -1+A>=2 ], cost: -1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Accelerating simple loops of location 3. 21.04/9.96 21.04/9.96 Accelerating the following rules: 21.04/9.96 21.04/9.96 37: lbl91 -> lbl91 : B'=free_1, E'=0, G'=-1+G, [ A>=G && D==A && G>=1 && 1+E==G && 1+E>=2 && A>=1+E && G==1+E ], cost: 3 21.04/9.96 21.04/9.96 38: lbl91 -> lbl91 : B'=free_1, E'=0, G'=-1+G, [ E>=0 && A>=G && D==A && G>=2+E && G>=2 ], cost: 2+G-E 21.04/9.96 21.04/9.96 42: lbl91 -> lbl91 : B'=free_2, E'=1, G'=-1+G, [ E>=0 && A>=G && D==A && G>=2+E && -1+G>=2 ], cost: 3+G-E 21.04/9.96 21.04/9.96 44: lbl91 -> lbl91 : B'=free_1, E'=0, G'=1, [ A>=G && D==A && 1+E==G && 1+E>=2 && A>=1+E && G==1+E && -1+G>=2 && A>=2 ], cost: 2+1/2*G-1/2*(-2+G)^2+G*(-2+G) 21.04/9.96 21.04/9.96 45: lbl91 -> lbl91 : B'=free_1, E'=0, G'=1, [ E>=0 && A>=G && D==A && G>=2+E && -1+G>=2 && A>=2 ], cost: 1+3/2*G-1/2*(-2+G)^2+G*(-2+G)-E 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Accelerated rule 37 with metering function 1-G+2*E (after strengthening guard), yielding the new rule 57. 21.04/9.96 21.04/9.96 Accelerated rule 38 with metering function -1+G-E, yielding the new rule 58. 21.04/9.96 21.04/9.96 Accelerated rule 42 with metering function meter_1 (where 2*meter_1==-2+G-E), yielding the new rule 59. 21.04/9.96 21.04/9.96 Accelerated rule 44 with metering function 1-G+E, yielding the new rule 60. 21.04/9.96 21.04/9.96 Found no metering function for rule 45. 21.04/9.96 21.04/9.96 Nested simple loops 42 (outer loop) and 57 (inner loop) with metering function meter_2 (where 2*meter_2==-2+G-E), resulting in the new rules: 61. 21.04/9.96 21.04/9.96 During metering: Instantiating temporary variables by {meter_1==1} 21.04/9.96 21.04/9.96 During metering: Instantiating temporary variables by {meter_1==-3+G} 21.04/9.96 21.04/9.96 During metering: Instantiating temporary variables by {meter_1==1} 21.04/9.96 21.04/9.96 During metering: Instantiating temporary variables by {meter_1==1} 21.04/9.96 21.04/9.96 Removing the simple loops: 38 42 44. 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Accelerated all simple loops using metering functions (where possible): 21.04/9.96 21.04/9.96 Start location: start0 21.04/9.96 21.04/9.96 37: lbl91 -> lbl91 : B'=free_1, E'=0, G'=-1+G, [ A>=G && D==A && G>=1 && 1+E==G && 1+E>=2 && A>=1+E && G==1+E ], cost: 3 21.04/9.96 21.04/9.96 45: lbl91 -> lbl91 : B'=free_1, E'=0, G'=1, [ E>=0 && A>=G && D==A && G>=2+E && -1+G>=2 && A>=2 ], cost: 1+3/2*G-1/2*(-2+G)^2+G*(-2+G)-E 21.04/9.96 21.04/9.96 47: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E ], cost: G-E 21.04/9.96 21.04/9.96 49: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E && G>=2 ], cost: 2+G-E 21.04/9.96 21.04/9.96 52: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E && 1==-1+G && -1+G==1 ], cost: -2+3*G-E 21.04/9.96 21.04/9.96 54: lbl91 -> [9] : [ A>=G && D==A && 1+E==G && 1+E>=2 && A>=1+E && G==1+E && -1+G>=2 ], cost: 1/2*G-1/2*(-2+G)^2+G*(-2+G) 21.04/9.96 21.04/9.96 55: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E && -1+G>=2 ], cost: -1+3/2*G-1/2*(-2+G)^2+G*(-2+G)-E 21.04/9.96 21.04/9.96 57: lbl91 -> lbl91 : B'=free_1, E'=0, G'=-1+2*G-2*E, [ A>=G && D==A && 1+E==G && 1+E>=2 && A>=1+E && G==1+E && 1==-1+G && -1+G==1 && 1-G+2*E>=1 ], cost: 3-3*G+6*E 21.04/9.96 21.04/9.96 58: lbl91 -> lbl91 : B'=free_1, E'=0, G'=1+E, [ E>=0 && A>=G && D==A && G>=2+E && G>=2 ], cost: -5/2+5/2*G-5/2*E+G*(-1+G-E)-1/2*(-1+G-E)^2 21.04/9.96 21.04/9.96 59: lbl91 -> lbl91 : B'=free_2, E'=1, G'=-meter_1+G, [ E>=0 && A>=G && D==A && G>=2+E && -1+G>=2 && 2*meter_1==-2+G-E && meter_1>=1 ], cost: meter_1*G-1/2*meter_1^2+5/2*meter_1 21.04/9.96 21.04/9.96 60: lbl91 -> lbl91 : B'=free_1, E'=0, G'=1, [ A>=G && D==A && 1+E==G && 1+E>=2 && A>=1+E && G==1+E && -1+G>=2 && A>=2 && 1-G+E>=1 ], cost: 1-G+E 21.04/9.96 21.04/9.96 61: lbl91 -> lbl91 : B'=free_1, E'=0, G'=5+2^meter_2*G-5*2^meter_2, [ E>=0 && A>=G && D==A && G>=2+E && 3-G==0 && A>=2 && -1+G==2 && 2*meter_2==-2+G-E && meter_2>=1 ], cost: -10+5*meter_2-2*2^meter_2*G+10*2^meter_2+2*G 21.04/9.96 21.04/9.96 19: start0 -> lbl91 : B'=free, D'=A, E'=0, G'=A, [ A>=1 ], cost: 2 21.04/9.96 21.04/9.96 39: start0 -> lbl91 : B'=free_2, D'=A, E'=1, G'=A, [ A>=2 ], cost: 3 21.04/9.96 21.04/9.96 40: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=-1+A, [ A>=2 ], cost: 3+A 21.04/9.96 21.04/9.96 43: start0 -> lbl91 : B'=free_2, D'=A, E'=1, G'=-1+A, [ -1+A>=2 ], cost: 4+A 21.04/9.96 21.04/9.96 46: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=1, [ -1+A>=2 ], cost: 2-1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 50: start0 -> [9] : [ A>=2 ], cost: 3+A 21.04/9.96 21.04/9.96 53: start0 -> [9] : [ 1==-1+A && -1+A==1 ], cost: -1+3*A 21.04/9.96 21.04/9.96 56: start0 -> [9] : [ -1+A>=2 ], cost: -1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Chained accelerated rules (with incoming rules): 21.04/9.96 21.04/9.96 Start location: start0 21.04/9.96 21.04/9.96 47: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E ], cost: G-E 21.04/9.96 21.04/9.96 49: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E && G>=2 ], cost: 2+G-E 21.04/9.96 21.04/9.96 52: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E && 1==-1+G && -1+G==1 ], cost: -2+3*G-E 21.04/9.96 21.04/9.96 54: lbl91 -> [9] : [ A>=G && D==A && 1+E==G && 1+E>=2 && A>=1+E && G==1+E && -1+G>=2 ], cost: 1/2*G-1/2*(-2+G)^2+G*(-2+G) 21.04/9.96 21.04/9.96 55: lbl91 -> [9] : [ E>=0 && A>=G && D==A && G>=2+E && -1+G>=2 ], cost: -1+3/2*G-1/2*(-2+G)^2+G*(-2+G)-E 21.04/9.96 21.04/9.96 19: start0 -> lbl91 : B'=free, D'=A, E'=0, G'=A, [ A>=1 ], cost: 2 21.04/9.96 21.04/9.96 39: start0 -> lbl91 : B'=free_2, D'=A, E'=1, G'=A, [ A>=2 ], cost: 3 21.04/9.96 21.04/9.96 40: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=-1+A, [ A>=2 ], cost: 3+A 21.04/9.96 21.04/9.96 43: start0 -> lbl91 : B'=free_2, D'=A, E'=1, G'=-1+A, [ -1+A>=2 ], cost: 4+A 21.04/9.96 21.04/9.96 46: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=1, [ -1+A>=2 ], cost: 2-1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 50: start0 -> [9] : [ A>=2 ], cost: 3+A 21.04/9.96 21.04/9.96 53: start0 -> [9] : [ 1==-1+A && -1+A==1 ], cost: -1+3*A 21.04/9.96 21.04/9.96 56: start0 -> [9] : [ -1+A>=2 ], cost: -1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 62: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=-1+A, [ 2==A && A==2 ], cost: 6 21.04/9.96 21.04/9.96 63: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=-2+A, [ 2==-1+A && -1+A==2 ], cost: 7+A 21.04/9.96 21.04/9.96 64: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=1, [ -1+A>=2 ], cost: 3-1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 65: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=1, [ A>=3 ], cost: 3-1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 66: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=1, [ -2+A>=2 ], cost: 5/2-1/2*(-3+A)^2+5/2*A+(-1+A)*(-3+A) 21.04/9.96 21.04/9.96 67: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=1, [ -1+A>=3 ], cost: 5/2-1/2*(-3+A)^2+5/2*A+(-1+A)*(-3+A) 21.04/9.96 21.04/9.96 68: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=-3+2*A, [ 2-A==0 && A==2 ], cost: 12-3*A 21.04/9.96 21.04/9.96 69: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=-5+2*A, [ 3-A==0 && -1+A==2 ], cost: 16-2*A 21.04/9.96 21.04/9.96 70: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=1, [ A>=2 ], cost: -1/2+(-1+A)*A+5/2*A-1/2*(-1+A)^2 21.04/9.96 21.04/9.96 71: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=2, [ A>=3 ], cost: -2-1/2*(-2+A)^2+5/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 72: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=1, [ -1+A>=2 ], cost: -2-1/2*(-2+A)^2+7/2*A+(-1+A)*(-2+A) 21.04/9.96 21.04/9.96 73: start0 -> lbl91 : B'=free_1, D'=A, E'=0, G'=2, [ -1+A>=3 ], cost: -7/2-1/2*(-3+A)^2+7/2*A+(-1+A)*(-3+A) 21.04/9.96 21.04/9.96 74: start0 -> lbl91 : B'=free_2, D'=A, E'=1, G'=-meter_1+A, [ -1+A>=2 && 2*meter_1==-2+A && meter_1>=1 ], cost: 2-1/2*meter_1^2+meter_1*A+5/2*meter_1 21.04/9.96 21.04/9.96 75: start0 -> lbl91 : B'=free_2, D'=A, E'=1, G'=-meter_1+A, [ A>=3 && 2*meter_1==-3+A && meter_1>=1 ], cost: 3-1/2*meter_1^2+meter_1*A+5/2*meter_1 21.04/9.96 21.04/9.96 76: start0 -> lbl91 : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -2+A>=2 && 2*meter_1==-3+A && meter_1>=1 ], cost: 3-1/2*meter_1^2+5/2*meter_1+(-1+A)*meter_1+A 21.04/9.96 21.04/9.96 77: start0 -> lbl91 : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -1+A>=3 && 2*meter_1==-4+A && meter_1>=1 ], cost: 4-1/2*meter_1^2+5/2*meter_1+(-1+A)*meter_1+A 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Eliminated locations (on tree-shaped paths): 21.04/9.96 21.04/9.96 Start location: start0 21.04/9.96 21.04/9.96 50: start0 -> [9] : [ A>=2 ], cost: 3+A 21.04/9.96 21.04/9.96 53: start0 -> [9] : [ 1==-1+A && -1+A==1 ], cost: -1+3*A 21.04/9.96 21.04/9.96 56: start0 -> [9] : [ -1+A>=2 ], cost: -1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 78: start0 -> [9] : B'=free, D'=A, E'=0, G'=A, [ A>=2 ], cost: 2+A 21.04/9.96 21.04/9.96 79: start0 -> [9] : B'=free, D'=A, E'=0, G'=A, [ A>=2 ], cost: 4+A 21.04/9.96 21.04/9.96 80: start0 -> [9] : B'=free, D'=A, E'=0, G'=A, [ 1==-1+A && -1+A==1 ], cost: 3*A 21.04/9.96 21.04/9.96 81: start0 -> [9] : B'=free, D'=A, E'=0, G'=A, [ -1+A>=2 ], cost: 1-1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 82: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=A, [ A>=3 ], cost: 2+A 21.04/9.96 21.04/9.96 83: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=A, [ A>=3 ], cost: 4+A 21.04/9.96 21.04/9.96 84: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=A, [ A>=3 ], cost: 1-1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 85: start0 -> [9] : B'=free_1, D'=A, E'=0, G'=-1+A, [ -1+A>=2 ], cost: 2+2*A 21.04/9.96 21.04/9.96 86: start0 -> [9] : B'=free_1, D'=A, E'=0, G'=-1+A, [ -1+A>=2 ], cost: 4+2*A 21.04/9.96 21.04/9.96 87: start0 -> [9] : B'=free_1, D'=A, E'=0, G'=-1+A, [ 1==-2+A && -2+A==1 ], cost: -2+4*A 21.04/9.96 21.04/9.96 88: start0 -> [9] : B'=free_1, D'=A, E'=0, G'=-1+A, [ -2+A>=2 ], cost: 1/2-1/2*(-3+A)^2+5/2*A+(-1+A)*(-3+A) 21.04/9.96 21.04/9.96 89: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1+A, [ -1+A>=3 ], cost: 2+2*A 21.04/9.96 21.04/9.96 90: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1+A, [ -1+A>=3 ], cost: 4+2*A 21.04/9.96 21.04/9.96 91: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1+A, [ -1+A>=3 ], cost: 1/2-1/2*(-3+A)^2+5/2*A+(-1+A)*(-3+A) 21.04/9.96 21.04/9.96 92: start0 -> [9] : B'=free_1, D'=A, E'=0, G'=2, [ A>=3 ], cost: -1/2*(-2+A)^2+5/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 93: start0 -> [9] : B'=free_1, D'=A, E'=0, G'=2, [ A>=3 ], cost: 2-1/2*(-2+A)^2+5/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 94: start0 -> [9] : B'=free_1, D'=A, E'=0, G'=2, [ A>=3 ], cost: 2-1/2*(-2+A)^2+5/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 95: start0 -> [9] : B'=free_1, D'=A, E'=0, G'=2, [ -1+A>=3 ], cost: -3/2-1/2*(-3+A)^2+7/2*A+(-1+A)*(-3+A) 21.04/9.96 21.04/9.96 96: start0 -> [9] : B'=free_1, D'=A, E'=0, G'=2, [ -1+A>=3 ], cost: 1/2-1/2*(-3+A)^2+7/2*A+(-1+A)*(-3+A) 21.04/9.96 21.04/9.96 97: start0 -> [9] : B'=free_1, D'=A, E'=0, G'=2, [ -1+A>=3 ], cost: 1/2-1/2*(-3+A)^2+7/2*A+(-1+A)*(-3+A) 21.04/9.96 21.04/9.96 98: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-meter_1+A, [ -1+A>=2 && 2*meter_1==-2+A && meter_1>=1 && -meter_1+A>=3 ], cost: 1-1/2*meter_1^2+meter_1*A+3/2*meter_1+A 21.04/9.96 21.04/9.96 99: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-meter_1+A, [ -1+A>=2 && 2*meter_1==-2+A && meter_1>=1 && -meter_1+A>=3 ], cost: 3-1/2*meter_1^2+meter_1*A+3/2*meter_1+A 21.04/9.96 21.04/9.96 100: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-meter_1+A, [ -1+A>=2 && 2*meter_1==-2+A && meter_1>=1 && -meter_1+A>=3 ], cost: (2+meter_1-A)*(meter_1-A)-1/2*meter_1^2+meter_1*A+meter_1+3/2*A-1/2*(2+meter_1-A)^2 21.04/9.96 21.04/9.96 101: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-meter_1+A, [ A>=3 && 2*meter_1==-3+A && meter_1>=1 && -meter_1+A>=3 ], cost: 2-1/2*meter_1^2+meter_1*A+3/2*meter_1+A 21.04/9.96 21.04/9.96 102: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-meter_1+A, [ A>=3 && 2*meter_1==-3+A && meter_1>=1 && -meter_1+A>=3 ], cost: 4-1/2*meter_1^2+meter_1*A+3/2*meter_1+A 21.04/9.96 21.04/9.96 103: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-meter_1+A, [ A>=3 && 2*meter_1==-3+A && meter_1>=1 && -meter_1+A>=3 ], cost: 1+(2+meter_1-A)*(meter_1-A)-1/2*meter_1^2+meter_1*A+meter_1+3/2*A-1/2*(2+meter_1-A)^2 21.04/9.96 21.04/9.96 104: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -2+A>=2 && 2*meter_1==-3+A && meter_1>=1 && -1-meter_1+A>=3 ], cost: 1-1/2*meter_1^2+3/2*meter_1+(-1+A)*meter_1+2*A 21.04/9.96 21.04/9.96 105: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -2+A>=2 && 2*meter_1==-3+A && meter_1>=1 && -1-meter_1+A>=3 ], cost: 3-1/2*meter_1^2+3/2*meter_1+(-1+A)*meter_1+2*A 21.04/9.96 21.04/9.96 106: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -2+A>=2 && 2*meter_1==-3+A && meter_1>=1 && -1-meter_1+A>=3 ], cost: -1/2-1/2*meter_1^2+meter_1+(-1+A)*meter_1+(3+meter_1-A)*(1+meter_1-A)+5/2*A-1/2*(3+meter_1-A)^2 21.04/9.96 21.04/9.96 107: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -1+A>=3 && 2*meter_1==-4+A && meter_1>=1 && -1-meter_1+A>=3 ], cost: 2-1/2*meter_1^2+3/2*meter_1+(-1+A)*meter_1+2*A 21.04/9.96 21.04/9.96 108: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -1+A>=3 && 2*meter_1==-4+A && meter_1>=1 && -1-meter_1+A>=3 ], cost: 4-1/2*meter_1^2+3/2*meter_1+(-1+A)*meter_1+2*A 21.04/9.96 21.04/9.96 109: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -1+A>=3 && 2*meter_1==-4+A && meter_1>=1 && -1-meter_1+A>=3 ], cost: 1/2-1/2*meter_1^2+meter_1+(-1+A)*meter_1+(3+meter_1-A)*(1+meter_1-A)+5/2*A-1/2*(3+meter_1-A)^2 21.04/9.96 21.04/9.96 110: start0 -> [11] : [ A>=2 ], cost: 3+A 21.04/9.96 21.04/9.96 111: start0 -> [11] : [ -1+A>=2 ], cost: 4+A 21.04/9.96 21.04/9.96 112: start0 -> [11] : [ -1+A>=2 ], cost: 2-1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 113: start0 -> [11] : [ 2==-1+A && -1+A==2 ], cost: 7+A 21.04/9.96 21.04/9.96 114: start0 -> [11] : [ -1+A>=2 ], cost: 3-1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 115: start0 -> [11] : [ A>=3 ], cost: 3-1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 116: start0 -> [11] : [ -2+A>=2 ], cost: 5/2-1/2*(-3+A)^2+5/2*A+(-1+A)*(-3+A) 21.04/9.96 21.04/9.96 117: start0 -> [11] : [ -1+A>=3 ], cost: 5/2-1/2*(-3+A)^2+5/2*A+(-1+A)*(-3+A) 21.04/9.96 21.04/9.96 118: start0 -> [11] : [ 2-A==0 && A==2 ], cost: 12-3*A 21.04/9.96 21.04/9.96 119: start0 -> [11] : [ 3-A==0 && -1+A==2 ], cost: 16-2*A 21.04/9.96 21.04/9.96 120: start0 -> [11] : [ A>=2 ], cost: -1/2+(-1+A)*A+5/2*A-1/2*(-1+A)^2 21.04/9.96 21.04/9.96 121: start0 -> [11] : [ A>=3 ], cost: -2-1/2*(-2+A)^2+5/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 122: start0 -> [11] : [ -1+A>=2 ], cost: -2-1/2*(-2+A)^2+7/2*A+(-1+A)*(-2+A) 21.04/9.96 21.04/9.96 123: start0 -> [11] : [ -1+A>=3 ], cost: -7/2-1/2*(-3+A)^2+7/2*A+(-1+A)*(-3+A) 21.04/9.96 21.04/9.96 124: start0 -> [11] : [ -1+A>=2 && 2*meter_1==-2+A && meter_1>=1 ], cost: 2-1/2*meter_1^2+meter_1*A+5/2*meter_1 21.04/9.96 21.04/9.96 125: start0 -> [11] : [ A>=3 && 2*meter_1==-3+A && meter_1>=1 ], cost: 3-1/2*meter_1^2+meter_1*A+5/2*meter_1 21.04/9.96 21.04/9.96 126: start0 -> [11] : [ -2+A>=2 && 2*meter_1==-3+A && meter_1>=1 ], cost: 3-1/2*meter_1^2+5/2*meter_1+(-1+A)*meter_1+A 21.04/9.96 21.04/9.96 127: start0 -> [11] : [ -1+A>=3 && 2*meter_1==-4+A && meter_1>=1 ], cost: 4-1/2*meter_1^2+5/2*meter_1+(-1+A)*meter_1+A 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Applied pruning (of leafs and parallel rules): 21.04/9.96 21.04/9.96 Start location: start0 21.04/9.96 21.04/9.96 100: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-meter_1+A, [ -1+A>=2 && 2*meter_1==-2+A && meter_1>=1 && -meter_1+A>=3 ], cost: (2+meter_1-A)*(meter_1-A)-1/2*meter_1^2+meter_1*A+meter_1+3/2*A-1/2*(2+meter_1-A)^2 21.04/9.96 21.04/9.96 102: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-meter_1+A, [ A>=3 && 2*meter_1==-3+A && meter_1>=1 && -meter_1+A>=3 ], cost: 4-1/2*meter_1^2+meter_1*A+3/2*meter_1+A 21.04/9.96 21.04/9.96 106: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -2+A>=2 && 2*meter_1==-3+A && meter_1>=1 && -1-meter_1+A>=3 ], cost: -1/2-1/2*meter_1^2+meter_1+(-1+A)*meter_1+(3+meter_1-A)*(1+meter_1-A)+5/2*A-1/2*(3+meter_1-A)^2 21.04/9.96 21.04/9.96 108: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -1+A>=3 && 2*meter_1==-4+A && meter_1>=1 && -1-meter_1+A>=3 ], cost: 4-1/2*meter_1^2+3/2*meter_1+(-1+A)*meter_1+2*A 21.04/9.96 21.04/9.96 109: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -1+A>=3 && 2*meter_1==-4+A && meter_1>=1 && -1-meter_1+A>=3 ], cost: 1/2-1/2*meter_1^2+meter_1+(-1+A)*meter_1+(3+meter_1-A)*(1+meter_1-A)+5/2*A-1/2*(3+meter_1-A)^2 21.04/9.96 21.04/9.96 114: start0 -> [11] : [ -1+A>=2 ], cost: 3-1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 124: start0 -> [11] : [ -1+A>=2 && 2*meter_1==-2+A && meter_1>=1 ], cost: 2-1/2*meter_1^2+meter_1*A+5/2*meter_1 21.04/9.96 21.04/9.96 125: start0 -> [11] : [ A>=3 && 2*meter_1==-3+A && meter_1>=1 ], cost: 3-1/2*meter_1^2+meter_1*A+5/2*meter_1 21.04/9.96 21.04/9.96 126: start0 -> [11] : [ -2+A>=2 && 2*meter_1==-3+A && meter_1>=1 ], cost: 3-1/2*meter_1^2+5/2*meter_1+(-1+A)*meter_1+A 21.04/9.96 21.04/9.96 127: start0 -> [11] : [ -1+A>=3 && 2*meter_1==-4+A && meter_1>=1 ], cost: 4-1/2*meter_1^2+5/2*meter_1+(-1+A)*meter_1+A 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 ### Computing asymptotic complexity ### 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Fully simplified ITS problem 21.04/9.96 21.04/9.96 Start location: start0 21.04/9.96 21.04/9.96 100: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-meter_1+A, [ -1+A>=2 && 2*meter_1==-2+A && meter_1>=1 && -meter_1+A>=3 ], cost: (2+meter_1-A)*(meter_1-A)-1/2*meter_1^2+meter_1*A+meter_1+3/2*A-1/2*(2+meter_1-A)^2 21.04/9.96 21.04/9.96 102: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-meter_1+A, [ A>=3 && 2*meter_1==-3+A && meter_1>=1 && -meter_1+A>=3 ], cost: 4-1/2*meter_1^2+meter_1*A+3/2*meter_1+A 21.04/9.96 21.04/9.96 106: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -2+A>=2 && 2*meter_1==-3+A && meter_1>=1 && -1-meter_1+A>=3 ], cost: -1/2-1/2*meter_1^2+meter_1+(-1+A)*meter_1+(3+meter_1-A)*(1+meter_1-A)+5/2*A-1/2*(3+meter_1-A)^2 21.04/9.96 21.04/9.96 108: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -1+A>=3 && 2*meter_1==-4+A && meter_1>=1 && -1-meter_1+A>=3 ], cost: 4-1/2*meter_1^2+3/2*meter_1+(-1+A)*meter_1+2*A 21.04/9.96 21.04/9.96 109: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ -1+A>=3 && 2*meter_1==-4+A && meter_1>=1 && -1-meter_1+A>=3 ], cost: 1/2-1/2*meter_1^2+meter_1+(-1+A)*meter_1+(3+meter_1-A)*(1+meter_1-A)+5/2*A-1/2*(3+meter_1-A)^2 21.04/9.96 21.04/9.96 114: start0 -> [11] : [ -1+A>=2 ], cost: 3-1/2*(-2+A)^2+3/2*A+A*(-2+A) 21.04/9.96 21.04/9.96 124: start0 -> [11] : [ -1+A>=2 && 2*meter_1==-2+A && meter_1>=1 ], cost: 2-1/2*meter_1^2+meter_1*A+5/2*meter_1 21.04/9.96 21.04/9.96 125: start0 -> [11] : [ A>=3 && 2*meter_1==-3+A && meter_1>=1 ], cost: 3-1/2*meter_1^2+meter_1*A+5/2*meter_1 21.04/9.96 21.04/9.96 126: start0 -> [11] : [ -2+A>=2 && 2*meter_1==-3+A && meter_1>=1 ], cost: 3-1/2*meter_1^2+5/2*meter_1+(-1+A)*meter_1+A 21.04/9.96 21.04/9.96 127: start0 -> [11] : [ -1+A>=3 && 2*meter_1==-4+A && meter_1>=1 ], cost: 4-1/2*meter_1^2+5/2*meter_1+(-1+A)*meter_1+A 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Computing asymptotic complexity for rule 100 21.04/9.96 21.04/9.96 Solved the limit problem by the following transformations: 21.04/9.96 21.04/9.96 Created initial limit problem: 21.04/9.96 21.04/9.96 -1-2*meter_1+A (+/+!), -2+A (+/+!), 3+2*meter_1-A (+/+!), -2+meter_1+3/2*A+1/2*A^2 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {A==2+2*meter_1} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 1 (+/+!), 1+2*(1+meter_1)^2+4*meter_1 (+), 2*meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (B), deleting 1 (+/+!) 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 1+2*(1+meter_1)^2+4*meter_1 (+), 2*meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 removing all constraints (solved by SMT) 21.04/9.96 21.04/9.96 resulting limit problem: [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {meter_1==n} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Solved the limit problem by the following transformations: 21.04/9.96 21.04/9.96 Created initial limit problem: 21.04/9.96 21.04/9.96 -1-2*meter_1+A (+/+!), -2+A (+/+!), 3+2*meter_1-A (+/+!), -2+meter_1+3/2*A+1/2*A^2 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {A==2+2*meter_1} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 1 (+/+!), 1+2*(1+meter_1)^2+4*meter_1 (+), 2*meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (B), deleting 1 (+/+!) 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 1+2*(1+meter_1)^2+4*meter_1 (+), 2*meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 removing all constraints (solved by SMT) 21.04/9.96 21.04/9.96 resulting limit problem: [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {meter_1==n} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Solution: 21.04/9.96 21.04/9.96 meter_1 / n 21.04/9.96 21.04/9.96 A / 2+2*n 21.04/9.96 21.04/9.96 Resulting cost 3+2*n^2+8*n has complexity: Poly(n^2) 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Found new complexity Poly(n^2). 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Computing asymptotic complexity for rule 102 21.04/9.96 21.04/9.96 Simplified the guard: 21.04/9.96 21.04/9.96 102: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-meter_1+A, [ 2*meter_1==-3+A && meter_1>=1 ], cost: 4-1/2*meter_1^2+meter_1*A+3/2*meter_1+A 21.04/9.96 21.04/9.96 Solved the limit problem by the following transformations: 21.04/9.96 21.04/9.96 Created initial limit problem: 21.04/9.96 21.04/9.96 4+2*meter_1-A (+/+!), 4-1/2*meter_1^2+meter_1*A+3/2*meter_1+A (+), meter_1 (+/+!), -2-2*meter_1+A (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {A==3+2*meter_1} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 1 (+/+!), meter_1 (+/+!), 7-1/2*meter_1^2+(3+2*meter_1)*meter_1+7/2*meter_1 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (B), deleting 1 (+/+!) 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 meter_1 (+/+!), 7-1/2*meter_1^2+(3+2*meter_1)*meter_1+7/2*meter_1 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 removing all constraints (solved by SMT) 21.04/9.96 21.04/9.96 resulting limit problem: [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {meter_1==n} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Solution: 21.04/9.96 21.04/9.96 meter_1 / n 21.04/9.96 21.04/9.96 A / 3+2*n 21.04/9.96 21.04/9.96 Resulting cost 7+13/2*n+3/2*n^2 has complexity: Poly(n^2) 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Computing asymptotic complexity for rule 106 21.04/9.96 21.04/9.96 Solved the limit problem by the following transformations: 21.04/9.96 21.04/9.96 Created initial limit problem: 21.04/9.96 21.04/9.96 4+2*meter_1-A (+/+!), -3+A (+/+!), -2+meter_1+3/2*A+1/2*A^2 (+), -2-2*meter_1+A (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {A==3+2*meter_1} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 1 (+/+!), 2*meter_1 (+/+!), 5/2+1/2*(3+2*meter_1)^2+4*meter_1 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (B), deleting 1 (+/+!) 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 2*meter_1 (+/+!), 5/2+1/2*(3+2*meter_1)^2+4*meter_1 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 removing all constraints (solved by SMT) 21.04/9.96 21.04/9.96 resulting limit problem: [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {meter_1==n} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Solved the limit problem by the following transformations: 21.04/9.96 21.04/9.96 Created initial limit problem: 21.04/9.96 21.04/9.96 4+2*meter_1-A (+/+!), -3+A (+/+!), -2+meter_1+3/2*A+1/2*A^2 (+), -2-2*meter_1+A (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {A==3+2*meter_1} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 1 (+/+!), 2*meter_1 (+/+!), 5/2+1/2*(3+2*meter_1)^2+4*meter_1 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (B), deleting 1 (+/+!) 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 2*meter_1 (+/+!), 5/2+1/2*(3+2*meter_1)^2+4*meter_1 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 removing all constraints (solved by SMT) 21.04/9.96 21.04/9.96 resulting limit problem: [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {meter_1==n} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Solution: 21.04/9.96 21.04/9.96 meter_1 / n 21.04/9.96 21.04/9.96 A / 3+2*n 21.04/9.96 21.04/9.96 Resulting cost 7+2*n^2+10*n has complexity: Poly(n^2) 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Computing asymptotic complexity for rule 108 21.04/9.96 21.04/9.96 Simplified the guard: 21.04/9.96 21.04/9.96 108: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ 2*meter_1==-4+A && meter_1>=1 ], cost: 4-1/2*meter_1^2+3/2*meter_1+(-1+A)*meter_1+2*A 21.04/9.96 21.04/9.96 Solved the limit problem by the following transformations: 21.04/9.96 21.04/9.96 Created initial limit problem: 21.04/9.96 21.04/9.96 5+2*meter_1-A (+/+!), 4-1/2*meter_1^2+meter_1*A+1/2*meter_1+2*A (+), meter_1 (+/+!), -3-2*meter_1+A (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {A==4+2*meter_1} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 1 (+/+!), meter_1 (+/+!), 12+2*(2+meter_1)*meter_1-1/2*meter_1^2+9/2*meter_1 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (B), deleting 1 (+/+!) 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 meter_1 (+/+!), 12+2*(2+meter_1)*meter_1-1/2*meter_1^2+9/2*meter_1 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 removing all constraints (solved by SMT) 21.04/9.96 21.04/9.96 resulting limit problem: [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {meter_1==n} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Solution: 21.04/9.96 21.04/9.96 meter_1 / n 21.04/9.96 21.04/9.96 A / 4+2*n 21.04/9.96 21.04/9.96 Resulting cost 12+3/2*n^2+17/2*n has complexity: Poly(n^2) 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Computing asymptotic complexity for rule 109 21.04/9.96 21.04/9.96 Simplified the guard: 21.04/9.96 21.04/9.96 109: start0 -> [9] : B'=free_2, D'=A, E'=1, G'=-1-meter_1+A, [ 2*meter_1==-4+A && meter_1>=1 ], cost: 1/2-1/2*meter_1^2+meter_1+(-1+A)*meter_1+(3+meter_1-A)*(1+meter_1-A)+5/2*A-1/2*(3+meter_1-A)^2 21.04/9.96 21.04/9.96 Solved the limit problem by the following transformations: 21.04/9.96 21.04/9.96 Created initial limit problem: 21.04/9.96 21.04/9.96 -1+meter_1+3/2*A+1/2*A^2 (+), 5+2*meter_1-A (+/+!), meter_1 (+/+!), -3-2*meter_1+A (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {A==4+2*meter_1} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 5+4*meter_1+2*(2+meter_1)^2 (+), 1 (+/+!), meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (B), deleting 1 (+/+!) 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 5+4*meter_1+2*(2+meter_1)^2 (+), meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 removing all constraints (solved by SMT) 21.04/9.96 21.04/9.96 resulting limit problem: [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {meter_1==n} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Solution: 21.04/9.96 21.04/9.96 meter_1 / n 21.04/9.96 21.04/9.96 A / 4+2*n 21.04/9.96 21.04/9.96 Resulting cost 13+12*n+2*n^2 has complexity: Poly(n^2) 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Computing asymptotic complexity for rule 124 21.04/9.96 21.04/9.96 Solved the limit problem by the following transformations: 21.04/9.96 21.04/9.96 Created initial limit problem: 21.04/9.96 21.04/9.96 -1-2*meter_1+A (+/+!), 2-1/2*meter_1^2+meter_1*A+5/2*meter_1 (+), -2+A (+/+!), 3+2*meter_1-A (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {A==2+2*meter_1} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 1 (+/+!), 2-1/2*meter_1^2+5/2*meter_1+2*meter_1*(1+meter_1) (+), 2*meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (B), deleting 1 (+/+!) 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 2-1/2*meter_1^2+5/2*meter_1+2*meter_1*(1+meter_1) (+), 2*meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 removing all constraints (solved by SMT) 21.04/9.96 21.04/9.96 resulting limit problem: [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {meter_1==n} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Solved the limit problem by the following transformations: 21.04/9.96 21.04/9.96 Created initial limit problem: 21.04/9.96 21.04/9.96 -1-2*meter_1+A (+/+!), 2-1/2*meter_1^2+meter_1*A+5/2*meter_1 (+), -2+A (+/+!), 3+2*meter_1-A (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {A==2+2*meter_1} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 1 (+/+!), 2-1/2*meter_1^2+5/2*meter_1+2*meter_1*(1+meter_1) (+), 2*meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (B), deleting 1 (+/+!) 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 2-1/2*meter_1^2+5/2*meter_1+2*meter_1*(1+meter_1) (+), 2*meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 removing all constraints (solved by SMT) 21.04/9.96 21.04/9.96 resulting limit problem: [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {meter_1==n} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Solution: 21.04/9.96 21.04/9.96 meter_1 / n 21.04/9.96 21.04/9.96 A / 2+2*n 21.04/9.96 21.04/9.96 Resulting cost 2+3/2*n^2+9/2*n has complexity: Poly(n^2) 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Computing asymptotic complexity for rule 125 21.04/9.96 21.04/9.96 Simplified the guard: 21.04/9.96 21.04/9.96 125: start0 -> [11] : [ 2*meter_1==-3+A && meter_1>=1 ], cost: 3-1/2*meter_1^2+meter_1*A+5/2*meter_1 21.04/9.96 21.04/9.96 Solved the limit problem by the following transformations: 21.04/9.96 21.04/9.96 Created initial limit problem: 21.04/9.96 21.04/9.96 4+2*meter_1-A (+/+!), 3-1/2*meter_1^2+meter_1*A+5/2*meter_1 (+), meter_1 (+/+!), -2-2*meter_1+A (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {A==3+2*meter_1} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 1 (+/+!), 3-1/2*meter_1^2+(3+2*meter_1)*meter_1+5/2*meter_1 (+), meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (B), deleting 1 (+/+!) 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 3-1/2*meter_1^2+(3+2*meter_1)*meter_1+5/2*meter_1 (+), meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 removing all constraints (solved by SMT) 21.04/9.96 21.04/9.96 resulting limit problem: [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {meter_1==n} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Solution: 21.04/9.96 21.04/9.96 meter_1 / n 21.04/9.96 21.04/9.96 A / 3+2*n 21.04/9.96 21.04/9.96 Resulting cost 3+3/2*n^2+11/2*n has complexity: Poly(n^2) 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Computing asymptotic complexity for rule 126 21.04/9.96 21.04/9.96 Solved the limit problem by the following transformations: 21.04/9.96 21.04/9.96 Created initial limit problem: 21.04/9.96 21.04/9.96 4+2*meter_1-A (+/+!), 3-1/2*meter_1^2+meter_1*A+3/2*meter_1+A (+), -3+A (+/+!), -2-2*meter_1+A (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {A==3+2*meter_1} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 1 (+/+!), 2*meter_1 (+/+!), 6-1/2*meter_1^2+(3+2*meter_1)*meter_1+7/2*meter_1 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (B), deleting 1 (+/+!) 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 2*meter_1 (+/+!), 6-1/2*meter_1^2+(3+2*meter_1)*meter_1+7/2*meter_1 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 removing all constraints (solved by SMT) 21.04/9.96 21.04/9.96 resulting limit problem: [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {meter_1==n} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Solved the limit problem by the following transformations: 21.04/9.96 21.04/9.96 Created initial limit problem: 21.04/9.96 21.04/9.96 4+2*meter_1-A (+/+!), 3-1/2*meter_1^2+meter_1*A+3/2*meter_1+A (+), -3+A (+/+!), -2-2*meter_1+A (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {A==3+2*meter_1} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 1 (+/+!), 2*meter_1 (+/+!), 6-1/2*meter_1^2+(3+2*meter_1)*meter_1+7/2*meter_1 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (B), deleting 1 (+/+!) 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 2*meter_1 (+/+!), 6-1/2*meter_1^2+(3+2*meter_1)*meter_1+7/2*meter_1 (+) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 removing all constraints (solved by SMT) 21.04/9.96 21.04/9.96 resulting limit problem: [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {meter_1==n} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Solution: 21.04/9.96 21.04/9.96 meter_1 / n 21.04/9.96 21.04/9.96 A / 3+2*n 21.04/9.96 21.04/9.96 Resulting cost 6+13/2*n+3/2*n^2 has complexity: Poly(n^2) 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Computing asymptotic complexity for rule 127 21.04/9.96 21.04/9.96 Simplified the guard: 21.04/9.96 21.04/9.96 127: start0 -> [11] : [ 2*meter_1==-4+A && meter_1>=1 ], cost: 4-1/2*meter_1^2+5/2*meter_1+(-1+A)*meter_1+A 21.04/9.96 21.04/9.96 Solved the limit problem by the following transformations: 21.04/9.96 21.04/9.96 Created initial limit problem: 21.04/9.96 21.04/9.96 5+2*meter_1-A (+/+!), 4-1/2*meter_1^2+meter_1*A+3/2*meter_1+A (+), meter_1 (+/+!), -3-2*meter_1+A (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {A==4+2*meter_1} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 8+2*(2+meter_1)*meter_1-1/2*meter_1^2+7/2*meter_1 (+), 1 (+/+!), meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (B), deleting 1 (+/+!) 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 8+2*(2+meter_1)*meter_1-1/2*meter_1^2+7/2*meter_1 (+), meter_1 (+/+!) [not solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 removing all constraints (solved by SMT) 21.04/9.96 21.04/9.96 resulting limit problem: [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 applying transformation rule (C) using substitution {meter_1==n} 21.04/9.96 21.04/9.96 resulting limit problem: 21.04/9.96 21.04/9.96 [solved] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Solution: 21.04/9.96 21.04/9.96 meter_1 / n 21.04/9.96 21.04/9.96 A / 4+2*n 21.04/9.96 21.04/9.96 Resulting cost 8+3/2*n^2+15/2*n has complexity: Poly(n^2) 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 Obtained the following overall complexity (w.r.t. the length of the input n): 21.04/9.96 21.04/9.96 Complexity: Poly(n^2) 21.04/9.96 21.04/9.96 Cpx degree: 2 21.04/9.96 21.04/9.96 Solved cost: 3+2*n^2+8*n 21.04/9.96 21.04/9.96 Rule cost: (2+meter_1-A)*(meter_1-A)-1/2*meter_1^2+meter_1*A+meter_1+3/2*A-1/2*(2+meter_1-A)^2 21.04/9.96 21.04/9.96 Rule guard: [ -1+A>=2 && 2*meter_1==-2+A ] 21.04/9.96 21.04/9.96 21.04/9.96 21.04/9.96 WORST_CASE(Omega(n^2),?) 21.04/9.96 21.04/9.96 21.04/9.96 ---------------------------------------- 21.04/9.96 21.04/9.96 (4) 21.04/9.96 BOUNDS(n^2, INF) 21.18/10.32 EOF