5.99/2.71	WORST_CASE(Omega(n^1), O(n^1))
5.99/2.72	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.99/2.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.99/2.72	
5.99/2.72	
5.99/2.72	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
5.99/2.72	
5.99/2.72	(0) CpxIntTrs
5.99/2.72	(1) Koat Proof [FINISHED, 404 ms]
5.99/2.72	(2) BOUNDS(1, n^1)
5.99/2.72	(3) Loat Proof [FINISHED, 1008 ms]
5.99/2.72	(4) BOUNDS(n^1, INF)
5.99/2.72	
5.99/2.72	
5.99/2.72	----------------------------------------
5.99/2.72	
5.99/2.72	(0)
5.99/2.72	Obligation:
5.99/2.72	Complexity Int TRS consisting of the following rules:
5.99/2.72	start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= 5 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
5.99/2.72	start(A, B, C, D, E, F, G, H) -> Com_1(lbl92(A, B, C, H, E, 0, G, 1 + H)) :|: 2 >= A && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
5.99/2.72	start(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, 0, C, D, E, 1, G, H)) :|: A >= 3 && 4 >= A && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
5.99/2.72	lbl92(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: D >= 4 && D >= A && F + 10 >= 5 * D && F >= 0 && H >= D + 1 && H <= D + 1
5.99/2.72	lbl92(A, B, C, D, E, F, G, H) -> Com_1(lbl92(A, B, C, H, E, 0, G, 1 + H)) :|: 1 >= D && D >= A && F + 10 >= 5 * D && F >= 0 && H >= D + 1 && H <= D + 1
5.99/2.72	lbl92(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, 0, C, D, E, 1, G, H)) :|: D >= 2 && 3 >= D && D >= A && F + 10 >= 5 * D && F >= 0 && H >= D + 1 && H <= D + 1
5.99/2.72	lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl92(A, B, C, H, E, F, G, 1 + H)) :|: 2 >= H && 9 >= B && B >= 0 && H >= A && H >= 3 && 4 >= H && F >= B + 1 && F <= B + 1
5.99/2.72	lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl92(A, B, C, H, E, F, G, 1 + H)) :|: H >= A && H >= 3 && 4 >= H && F >= 10 && F <= 10 && B >= 9 && B <= 9
5.99/2.72	lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, F, C, D, E, 1 + F, G, H)) :|: H >= 3 && 8 >= B && 9 >= B && B >= 0 && H >= A && 4 >= H && F >= B + 1 && F <= B + 1
5.99/2.72	start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, E, E, G, G, A)) :|: TRUE
5.99/2.72	
5.99/2.72	The start-symbols are:[start0_8]
5.99/2.72	
5.99/2.72	
5.99/2.72	----------------------------------------
5.99/2.72	
5.99/2.72	(1) Koat Proof (FINISHED)
5.99/2.72	YES(?, 44*ar_0 + 221)
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Initial complexity problem:
5.99/2.72	
5.99/2.72	1:	T:
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 5 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, 0, ar_6, ar_7 + 1)) [ 2 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, 0, ar_2, ar_3, ar_4, 1, ar_6, ar_7)) [ ar_0 >= 3 /\ 4 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl92(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_3 >= 4 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl92(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, 0, ar_6, ar_7 + 1)) [ 1 >= ar_3 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl92(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, 0, ar_2, ar_3, ar_4, 1, ar_6, ar_7)) [ ar_3 >= 2 /\ 3 >= ar_3 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, ar_5, ar_6, ar_7 + 1)) [ 2 >= ar_7 /\ 9 >= ar_1 /\ ar_1 >= 0 /\ ar_7 >= ar_0 /\ ar_7 >= 3 /\ 4 >= ar_7 /\ ar_5 = ar_1 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, ar_5, ar_6, ar_7 + 1)) [ ar_7 >= ar_0 /\ ar_7 >= 3 /\ 4 >= ar_7 /\ ar_5 = 10 /\ ar_1 = 9 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, ar_5, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_7 >= 3 /\ 8 >= ar_1 /\ 9 >= ar_1 /\ ar_1 >= 0 /\ ar_7 >= ar_0 /\ 4 >= ar_7 /\ ar_5 = ar_1 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))
5.99/2.72	
5.99/2.72			(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 ]
5.99/2.72	
5.99/2.72		start location:	koat_start
5.99/2.72	
5.99/2.72		leaf cost:	0
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Testing for reachability in the complexity graph removes the following transition from problem 1:
5.99/2.72	
5.99/2.72		lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, ar_5, ar_6, ar_7 + 1)) [ 2 >= ar_7 /\ 9 >= ar_1 /\ ar_1 >= 0 /\ ar_7 >= ar_0 /\ ar_7 >= 3 /\ 4 >= ar_7 /\ ar_5 = ar_1 + 1 ]
5.99/2.72	
5.99/2.72	We thus obtain the following problem:
5.99/2.72	
5.99/2.72	2:	T:
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl92(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_3 >= 4 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, ar_5, ar_6, ar_7 + 1)) [ ar_7 >= ar_0 /\ ar_7 >= 3 /\ 4 >= ar_7 /\ ar_5 = 10 /\ ar_1 = 9 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, ar_5, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_7 >= 3 /\ 8 >= ar_1 /\ 9 >= ar_1 /\ ar_1 >= 0 /\ ar_7 >= ar_0 /\ 4 >= ar_7 /\ ar_5 = ar_1 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl92(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, 0, ar_2, ar_3, ar_4, 1, ar_6, ar_7)) [ ar_3 >= 2 /\ 3 >= ar_3 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl92(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, 0, ar_6, ar_7 + 1)) [ 1 >= ar_3 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, 0, ar_2, ar_3, ar_4, 1, ar_6, ar_7)) [ ar_0 >= 3 /\ 4 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, 0, ar_6, ar_7 + 1)) [ 2 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 5 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))
5.99/2.72	
5.99/2.72			(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 ]
5.99/2.72	
5.99/2.72		start location:	koat_start
5.99/2.72	
5.99/2.72		leaf cost:	0
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Repeatedly propagating knowledge in problem 2 produces the following problem:
5.99/2.72	
5.99/2.72	3:	T:
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl92(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_3 >= 4 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, ar_5, ar_6, ar_7 + 1)) [ ar_7 >= ar_0 /\ ar_7 >= 3 /\ 4 >= ar_7 /\ ar_5 = 10 /\ ar_1 = 9 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, ar_5, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_7 >= 3 /\ 8 >= ar_1 /\ 9 >= ar_1 /\ ar_1 >= 0 /\ ar_7 >= ar_0 /\ 4 >= ar_7 /\ ar_5 = ar_1 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl92(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, 0, ar_2, ar_3, ar_4, 1, ar_6, ar_7)) [ ar_3 >= 2 /\ 3 >= ar_3 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl92(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, 0, ar_6, ar_7 + 1)) [ 1 >= ar_3 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, 0, ar_2, ar_3, ar_4, 1, ar_6, ar_7)) [ ar_0 >= 3 /\ 4 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, 0, ar_6, ar_7 + 1)) [ 2 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 5 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))
5.99/2.72	
5.99/2.72			(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 ]
5.99/2.72	
5.99/2.72		start location:	koat_start
5.99/2.72	
5.99/2.72		leaf cost:	0
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	A polynomial rank function with
5.99/2.72	
5.99/2.72		Pol(lbl92) = 1
5.99/2.72	
5.99/2.72		Pol(stop) = 0
5.99/2.72	
5.99/2.72		Pol(lbl82) = 1
5.99/2.72	
5.99/2.72		Pol(start) = 1
5.99/2.72	
5.99/2.72		Pol(start0) = 1
5.99/2.72	
5.99/2.72		Pol(koat_start) = 1
5.99/2.72	
5.99/2.72	orients all transitions weakly and the transition
5.99/2.72	
5.99/2.72		lbl92(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_3 >= 4 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72	strictly and produces the following problem:
5.99/2.72	
5.99/2.72	4:	T:
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)    lbl92(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_3 >= 4 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, ar_5, ar_6, ar_7 + 1)) [ ar_7 >= ar_0 /\ ar_7 >= 3 /\ 4 >= ar_7 /\ ar_5 = 10 /\ ar_1 = 9 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, ar_5, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_7 >= 3 /\ 8 >= ar_1 /\ 9 >= ar_1 /\ ar_1 >= 0 /\ ar_7 >= ar_0 /\ 4 >= ar_7 /\ ar_5 = ar_1 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl92(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, 0, ar_2, ar_3, ar_4, 1, ar_6, ar_7)) [ ar_3 >= 2 /\ 3 >= ar_3 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: ?, Cost: 1)    lbl92(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, 0, ar_6, ar_7 + 1)) [ 1 >= ar_3 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, 0, ar_2, ar_3, ar_4, 1, ar_6, ar_7)) [ ar_0 >= 3 /\ 4 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, 0, ar_6, ar_7 + 1)) [ 2 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 5 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))
5.99/2.72	
5.99/2.72			(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 ]
5.99/2.72	
5.99/2.72		start location:	koat_start
5.99/2.72	
5.99/2.72		leaf cost:	0
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	A polynomial rank function with
5.99/2.72	
5.99/2.72		Pol(lbl92) = -11*V_4 + 44
5.99/2.72	
5.99/2.72		Pol(stop) = -11*V_8
5.99/2.72	
5.99/2.72		Pol(lbl82) = -V_2 - 11*V_8 + 54
5.99/2.72	
5.99/2.72		Pol(start) = -11*V_1 + 54
5.99/2.72	
5.99/2.72		Pol(start0) = -11*V_1 + 54
5.99/2.72	
5.99/2.72		Pol(koat_start) = -11*V_1 + 54
5.99/2.72	
5.99/2.72	orients all transitions weakly and the transitions
5.99/2.72	
5.99/2.72		lbl92(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, 0, ar_6, ar_7 + 1)) [ 1 >= ar_3 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72		lbl92(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, 0, ar_2, ar_3, ar_4, 1, ar_6, ar_7)) [ ar_3 >= 2 /\ 3 >= ar_3 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72		lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, ar_5, ar_6, ar_7 + 1)) [ ar_7 >= ar_0 /\ ar_7 >= 3 /\ 4 >= ar_7 /\ ar_5 = 10 /\ ar_1 = 9 ]
5.99/2.72	
5.99/2.72		lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, ar_5, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_7 >= 3 /\ 8 >= ar_1 /\ 9 >= ar_1 /\ ar_1 >= 0 /\ ar_7 >= ar_0 /\ 4 >= ar_7 /\ ar_5 = ar_1 + 1 ]
5.99/2.72	
5.99/2.72	strictly and produces the following problem:
5.99/2.72	
5.99/2.72	5:	T:
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)               lbl92(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_3 >= 4 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: 11*ar_0 + 54, Cost: 1)    lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, ar_5, ar_6, ar_7 + 1)) [ ar_7 >= ar_0 /\ ar_7 >= 3 /\ 4 >= ar_7 /\ ar_5 = 10 /\ ar_1 = 9 ]
5.99/2.72	
5.99/2.72			(Comp: 11*ar_0 + 54, Cost: 1)    lbl82(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, ar_5, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_7 >= 3 /\ 8 >= ar_1 /\ 9 >= ar_1 /\ ar_1 >= 0 /\ ar_7 >= ar_0 /\ 4 >= ar_7 /\ ar_5 = ar_1 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: 11*ar_0 + 54, Cost: 1)    lbl92(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, 0, ar_2, ar_3, ar_4, 1, ar_6, ar_7)) [ ar_3 >= 2 /\ 3 >= ar_3 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: 11*ar_0 + 54, Cost: 1)    lbl92(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, 0, ar_6, ar_7 + 1)) [ 1 >= ar_3 /\ ar_3 >= ar_0 /\ ar_5 + 10 >= 5*ar_3 /\ ar_5 >= 0 /\ ar_7 = ar_3 + 1 ]
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)               start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl82(ar_0, 0, ar_2, ar_3, ar_4, 1, ar_6, ar_7)) [ ar_0 >= 3 /\ 4 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)               start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl92(ar_0, ar_1, ar_2, ar_7, ar_4, 0, ar_6, ar_7 + 1)) [ 2 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)               start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 5 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
5.99/2.72	
5.99/2.72			(Comp: 1, Cost: 1)               start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))
5.99/2.72	
5.99/2.72			(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 ]
5.99/2.72	
5.99/2.72		start location:	koat_start
5.99/2.72	
5.99/2.72		leaf cost:	0
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Complexity upper bound 44*ar_0 + 221
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Time: 0.367 sec (SMT: 0.314 sec)
5.99/2.72	
5.99/2.72	
5.99/2.72	----------------------------------------
5.99/2.72	
5.99/2.72	(2)
5.99/2.72	BOUNDS(1, n^1)
5.99/2.72	
5.99/2.72	----------------------------------------
5.99/2.72	
5.99/2.72	(3) Loat Proof (FINISHED)
5.99/2.72	
5.99/2.72	
5.99/2.72	### Pre-processing the ITS problem ###
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Initial linear ITS problem
5.99/2.72	
5.99/2.72	   Start location: start0
5.99/2.72	
5.99/2.72	      0: start -> stop : [ A>=5 && B==C && D==E && F==G && H==A ], cost: 1
5.99/2.72	
5.99/2.72	      1: start -> lbl92 : D'=H, F'=0, H'=1+H, [ 2>=A && B==C && D==E && F==G && H==A ], cost: 1
5.99/2.72	
5.99/2.72	      2: start -> lbl82 : B'=0, F'=1, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A ], cost: 1
5.99/2.72	
5.99/2.72	      3: lbl92 -> stop : [ D>=4 && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1
5.99/2.72	
5.99/2.72	      4: lbl92 -> lbl92 : D'=H, F'=0, H'=1+H, [ 1>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1
5.99/2.72	
5.99/2.72	      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1
5.99/2.72	
5.99/2.72	      6: lbl82 -> lbl92 : D'=H, H'=1+H, [ 2>=H && 9>=B && B>=0 && H>=A && H>=3 && 4>=H && F==1+B ], cost: 1
5.99/2.72	
5.99/2.72	      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1
5.99/2.72	
5.99/2.72	      8: lbl82 -> lbl82 : B'=F, F'=1+F, [ H>=3 && 8>=B && 9>=B && B>=0 && H>=A && 4>=H && F==1+B ], cost: 1
5.99/2.72	
5.99/2.72	      9: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Removed unreachable and leaf rules:
5.99/2.72	
5.99/2.72	   Start location: start0
5.99/2.72	
5.99/2.72	      1: start -> lbl92 : D'=H, F'=0, H'=1+H, [ 2>=A && B==C && D==E && F==G && H==A ], cost: 1
5.99/2.72	
5.99/2.72	      2: start -> lbl82 : B'=0, F'=1, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A ], cost: 1
5.99/2.72	
5.99/2.72	      4: lbl92 -> lbl92 : D'=H, F'=0, H'=1+H, [ 1>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1
5.99/2.72	
5.99/2.72	      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1
5.99/2.72	
5.99/2.72	      6: lbl82 -> lbl92 : D'=H, H'=1+H, [ 2>=H && 9>=B && B>=0 && H>=A && H>=3 && 4>=H && F==1+B ], cost: 1
5.99/2.72	
5.99/2.72	      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1
5.99/2.72	
5.99/2.72	      8: lbl82 -> lbl82 : B'=F, F'=1+F, [ H>=3 && 8>=B && 9>=B && B>=0 && H>=A && 4>=H && F==1+B ], cost: 1
5.99/2.72	
5.99/2.72	      9: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Removed rules with unsatisfiable guard:
5.99/2.72	
5.99/2.72	   Start location: start0
5.99/2.72	
5.99/2.72	      1: start -> lbl92 : D'=H, F'=0, H'=1+H, [ 2>=A && B==C && D==E && F==G && H==A ], cost: 1
5.99/2.72	
5.99/2.72	      2: start -> lbl82 : B'=0, F'=1, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A ], cost: 1
5.99/2.72	
5.99/2.72	      4: lbl92 -> lbl92 : D'=H, F'=0, H'=1+H, [ 1>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1
5.99/2.72	
5.99/2.72	      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1
5.99/2.72	
5.99/2.72	      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1
5.99/2.72	
5.99/2.72	      8: lbl82 -> lbl82 : B'=F, F'=1+F, [ H>=3 && 8>=B && 9>=B && B>=0 && H>=A && 4>=H && F==1+B ], cost: 1
5.99/2.72	
5.99/2.72	      9: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Simplified all rules, resulting in:
5.99/2.72	
5.99/2.72	   Start location: start0
5.99/2.72	
5.99/2.72	      1: start -> lbl92 : D'=H, F'=0, H'=1+H, [ 2>=A && B==C && D==E && F==G && H==A ], cost: 1
5.99/2.72	
5.99/2.72	      2: start -> lbl82 : B'=0, F'=1, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A ], cost: 1
5.99/2.72	
5.99/2.72	      4: lbl92 -> lbl92 : D'=H, F'=0, H'=1+H, [ 1>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1
5.99/2.72	
5.99/2.72	      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && H==1+D ], cost: 1
5.99/2.72	
5.99/2.72	      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1
5.99/2.72	
5.99/2.72	      8: lbl82 -> lbl82 : B'=F, F'=1+F, [ H>=3 && 8>=B && B>=0 && H>=A && 4>=H && F==1+B ], cost: 1
5.99/2.72	
5.99/2.72	      9: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	### Simplification by acceleration and chaining ###
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Accelerating simple loops of location 1.
5.99/2.72	
5.99/2.72	   Accelerating the following rules:
5.99/2.72	
5.99/2.72	      4: lbl92 -> lbl92 : D'=H, F'=0, H'=1+H, [ 1>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	   Accelerated rule 4 with metering function meter (where 2*meter==5-D-H), yielding the new rule 10.
5.99/2.72	
5.99/2.72	   Removing the simple loops: 4.
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Accelerating simple loops of location 2.
5.99/2.72	
5.99/2.72	   Accelerating the following rules:
5.99/2.72	
5.99/2.72	      8: lbl82 -> lbl82 : B'=F, F'=1+F, [ H>=3 && 8>=B && B>=0 && H>=A && 4>=H && F==1+B ], cost: 1
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	   Accelerated rule 8 with metering function meter_1 (where 2*meter_1==19-F-B), yielding the new rule 11.
5.99/2.72	
5.99/2.72	   Removing the simple loops: 8.
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Accelerated all simple loops using metering functions (where possible):
5.99/2.72	
5.99/2.72	   Start location: start0
5.99/2.72	
5.99/2.72	      1: start -> lbl92 : D'=H, F'=0, H'=1+H, [ 2>=A && B==C && D==E && F==G && H==A ], cost: 1
5.99/2.72	
5.99/2.72	      2: start -> lbl82 : B'=0, F'=1, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A ], cost: 1
5.99/2.72	
5.99/2.72	      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && H==1+D ], cost: 1
5.99/2.72	
5.99/2.72	     10: lbl92 -> lbl92 : D'=-1+meter+H, F'=0, H'=meter+H, [ 1>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D && 2*meter==5-D-H && meter>=1 ], cost: meter
5.99/2.72	
5.99/2.72	      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1
5.99/2.72	
5.99/2.72	     11: lbl82 -> lbl82 : B'=-1+meter_1+F, F'=meter_1+F, [ H>=3 && 8>=B && B>=0 && H>=A && 4>=H && F==1+B && 2*meter_1==19-F-B && meter_1>=1 ], cost: meter_1
5.99/2.72	
5.99/2.72	      9: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Chained accelerated rules (with incoming rules):
5.99/2.72	
5.99/2.72	   Start location: start0
5.99/2.72	
5.99/2.72	      1: start -> lbl92 : D'=H, F'=0, H'=1+H, [ 2>=A && B==C && D==E && F==G && H==A ], cost: 1
5.99/2.72	
5.99/2.72	      2: start -> lbl82 : B'=0, F'=1, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A ], cost: 1
5.99/2.72	
5.99/2.72	     12: start -> lbl92 : D'=2, F'=0, H'=3, [ 2>=A && B==C && D==E && F==G && H==A && 1>=H && 10>=5*H ], cost: 3-H
5.99/2.72	
5.99/2.72	     13: start -> lbl82 : B'=9, F'=10, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A && H>=3 && 4>=H ], cost: 10
5.99/2.72	
5.99/2.72	      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && H==1+D ], cost: 1
5.99/2.72	
5.99/2.72	     14: lbl92 -> lbl82 : B'=9, F'=10, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && H==1+D && H>=3 && H>=A && 4>=H ], cost: 10
5.99/2.72	
5.99/2.72	      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1
5.99/2.72	
5.99/2.72	      9: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Eliminated locations (on tree-shaped paths):
5.99/2.72	
5.99/2.72	   Start location: start0
5.99/2.72	
5.99/2.72	      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && H==1+D ], cost: 1
5.99/2.72	
5.99/2.72	     14: lbl92 -> lbl82 : B'=9, F'=10, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && H==1+D && H>=3 && H>=A && 4>=H ], cost: 10
5.99/2.72	
5.99/2.72	      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1
5.99/2.72	
5.99/2.72	     15: start0 -> lbl92 : B'=C, D'=A, F'=0, H'=1+A, [ 2>=A ], cost: 2
5.99/2.72	
5.99/2.72	     16: start0 -> lbl82 : B'=0, D'=E, F'=1, H'=A, [ A>=3 && 4>=A ], cost: 2
5.99/2.72	
5.99/2.72	     17: start0 -> lbl92 : B'=C, D'=2, F'=0, H'=3, [ 1>=A && 10>=5*A ], cost: 4-A
5.99/2.72	
5.99/2.72	     18: start0 -> lbl82 : B'=9, D'=E, F'=10, H'=A, [ A>=3 && 4>=A ], cost: 11
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Eliminated location lbl92 (as a last resort):
5.99/2.72	
5.99/2.72	   Start location: start0
5.99/2.72	
5.99/2.72	     19: lbl82 -> lbl82 : B'=0, D'=H, F'=1, H'=1+H, [ H>=A && H>=3 && F==10 && B==9 && 3>=H && 10+F>=5*H ], cost: 2
5.99/2.72	
5.99/2.72	     20: lbl82 -> lbl82 : B'=9, D'=H, F'=10, H'=1+H, [ H>=A && H>=3 && F==10 && B==9 && 3>=H && 10+F>=5*H ], cost: 11
5.99/2.72	
5.99/2.72	     16: start0 -> lbl82 : B'=0, D'=E, F'=1, H'=A, [ A>=3 && 4>=A ], cost: 2
5.99/2.72	
5.99/2.72	     18: start0 -> lbl82 : B'=9, D'=E, F'=10, H'=A, [ A>=3 && 4>=A ], cost: 11
5.99/2.72	
5.99/2.72	     21: start0 -> lbl82 : B'=0, D'=A, F'=1, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 3
5.99/2.72	
5.99/2.72	     22: start0 -> lbl82 : B'=9, D'=A, F'=10, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 12
5.99/2.72	
5.99/2.72	     23: start0 -> lbl82 : B'=0, D'=2, F'=1, H'=3, [ 1>=A && 10>=5*A ], cost: 5-A
5.99/2.72	
5.99/2.72	     24: start0 -> lbl82 : B'=9, D'=2, F'=10, H'=3, [ 1>=A && 10>=5*A ], cost: 14-A
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Applied pruning (of leafs and parallel rules):
5.99/2.72	
5.99/2.72	   Start location: start0
5.99/2.72	
5.99/2.72	     19: lbl82 -> lbl82 : B'=0, D'=H, F'=1, H'=1+H, [ H>=A && H>=3 && F==10 && B==9 && 3>=H && 10+F>=5*H ], cost: 2
5.99/2.72	
5.99/2.72	     20: lbl82 -> lbl82 : B'=9, D'=H, F'=10, H'=1+H, [ H>=A && H>=3 && F==10 && B==9 && 3>=H && 10+F>=5*H ], cost: 11
5.99/2.72	
5.99/2.72	     18: start0 -> lbl82 : B'=9, D'=E, F'=10, H'=A, [ A>=3 && 4>=A ], cost: 11
5.99/2.72	
5.99/2.72	     21: start0 -> lbl82 : B'=0, D'=A, F'=1, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 3
5.99/2.72	
5.99/2.72	     22: start0 -> lbl82 : B'=9, D'=A, F'=10, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 12
5.99/2.72	
5.99/2.72	     23: start0 -> lbl82 : B'=0, D'=2, F'=1, H'=3, [ 1>=A && 10>=5*A ], cost: 5-A
5.99/2.72	
5.99/2.72	     24: start0 -> lbl82 : B'=9, D'=2, F'=10, H'=3, [ 1>=A && 10>=5*A ], cost: 14-A
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Accelerating simple loops of location 2.
5.99/2.72	
5.99/2.72	   Simplified some of the simple loops (and removed duplicate rules).
5.99/2.72	
5.99/2.72	   Accelerating the following rules:
5.99/2.72	
5.99/2.72	     19: lbl82 -> lbl82 : B'=0, D'=H, F'=1, H'=1+H, [ H>=A && 3-H==0 && F==10 && B==9 && 10+F>=5*H ], cost: 2
5.99/2.72	
5.99/2.72	     20: lbl82 -> lbl82 : B'=9, D'=H, F'=10, H'=1+H, [ H>=A && 3-H==0 && F==10 && B==9 && 10+F>=5*H ], cost: 11
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	   Accelerated rule 19 with metering function meter_2 (where 19*meter_2==-15+F-H+B), yielding the new rule 25.
5.99/2.72	
5.99/2.72	   Accelerated rule 20 with metering function 4-H, yielding the new rule 26.
5.99/2.72	
5.99/2.72	   Removing the simple loops: 19 20.
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Accelerated all simple loops using metering functions (where possible):
5.99/2.72	
5.99/2.72	   Start location: start0
5.99/2.72	
5.99/2.72	     25: lbl82 -> lbl82 : B'=0, D'=-1+meter_2+H, F'=1, H'=meter_2+H, [ H>=A && 3-H==0 && F==10 && B==9 && 10+F>=5*H && 19*meter_2==-15+F-H+B && meter_2>=1 ], cost: 2*meter_2
5.99/2.72	
5.99/2.72	     26: lbl82 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ H>=A && 3-H==0 && F==10 && B==9 && 10+F>=5*H ], cost: 44-11*H
5.99/2.72	
5.99/2.72	     18: start0 -> lbl82 : B'=9, D'=E, F'=10, H'=A, [ A>=3 && 4>=A ], cost: 11
5.99/2.72	
5.99/2.72	     21: start0 -> lbl82 : B'=0, D'=A, F'=1, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 3
5.99/2.72	
5.99/2.72	     22: start0 -> lbl82 : B'=9, D'=A, F'=10, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 12
5.99/2.72	
5.99/2.72	     23: start0 -> lbl82 : B'=0, D'=2, F'=1, H'=3, [ 1>=A && 10>=5*A ], cost: 5-A
5.99/2.72	
5.99/2.72	     24: start0 -> lbl82 : B'=9, D'=2, F'=10, H'=3, [ 1>=A && 10>=5*A ], cost: 14-A
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Chained accelerated rules (with incoming rules):
5.99/2.72	
5.99/2.72	   Start location: start0
5.99/2.72	
5.99/2.72	     18: start0 -> lbl82 : B'=9, D'=E, F'=10, H'=A, [ A>=3 && 4>=A ], cost: 11
5.99/2.72	
5.99/2.72	     21: start0 -> lbl82 : B'=0, D'=A, F'=1, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 3
5.99/2.72	
5.99/2.72	     22: start0 -> lbl82 : B'=9, D'=A, F'=10, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 12
5.99/2.72	
5.99/2.72	     23: start0 -> lbl82 : B'=0, D'=2, F'=1, H'=3, [ 1>=A && 10>=5*A ], cost: 5-A
5.99/2.72	
5.99/2.72	     24: start0 -> lbl82 : B'=9, D'=2, F'=10, H'=3, [ 1>=A && 10>=5*A ], cost: 14-A
5.99/2.72	
5.99/2.72	     27: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ 3-A==0 && 20>=5*A ], cost: 55-11*A
5.99/2.72	
5.99/2.72	     28: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ -2+A==0 && 10>=5*A && 2-A==0 ], cost: 45-11*A
5.99/2.72	
5.99/2.72	     29: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ 1>=A && 10>=5*A ], cost: 25-A
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Removed unreachable locations (and leaf rules with constant cost):
5.99/2.72	
5.99/2.72	   Start location: start0
5.99/2.72	
5.99/2.72	     23: start0 -> lbl82 : B'=0, D'=2, F'=1, H'=3, [ 1>=A && 10>=5*A ], cost: 5-A
5.99/2.72	
5.99/2.72	     24: start0 -> lbl82 : B'=9, D'=2, F'=10, H'=3, [ 1>=A && 10>=5*A ], cost: 14-A
5.99/2.72	
5.99/2.72	     27: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ 3-A==0 && 20>=5*A ], cost: 55-11*A
5.99/2.72	
5.99/2.72	     28: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ -2+A==0 && 10>=5*A && 2-A==0 ], cost: 45-11*A
5.99/2.72	
5.99/2.72	     29: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ 1>=A && 10>=5*A ], cost: 25-A
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	### Computing asymptotic complexity ###
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Fully simplified ITS problem
5.99/2.72	
5.99/2.72	   Start location: start0
5.99/2.72	
5.99/2.72	     27: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ 3-A==0 && 20>=5*A ], cost: 55-11*A
5.99/2.72	
5.99/2.72	     28: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ -2+A==0 && 10>=5*A && 2-A==0 ], cost: 45-11*A
5.99/2.72	
5.99/2.72	     29: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ 1>=A && 10>=5*A ], cost: 25-A
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Computing asymptotic complexity for rule 27
5.99/2.72	
5.99/2.72	   Could not solve the limit problem.
5.99/2.72	
5.99/2.72	   Resulting cost 0 has complexity: Unknown
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Computing asymptotic complexity for rule 28
5.99/2.72	
5.99/2.72	   Could not solve the limit problem.
5.99/2.72	
5.99/2.72	   Resulting cost 0 has complexity: Unknown
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Computing asymptotic complexity for rule 29
5.99/2.72	
5.99/2.72	   Solved the limit problem by the following transformations:
5.99/2.72	
5.99/2.72	      Created initial limit problem:
5.99/2.72	
5.99/2.72	      2-A (+/+!), 25-A (+) [not solved]
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	      removing all constraints (solved by SMT)
5.99/2.72	
5.99/2.72	      resulting limit problem: [solved]
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	      applying transformation rule (C) using substitution {A==-n}
5.99/2.72	
5.99/2.72	      resulting limit problem:
5.99/2.72	
5.99/2.72	      [solved]
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	   Solution:
5.99/2.72	
5.99/2.72	      A / -n
5.99/2.72	
5.99/2.72	   Resulting cost 25+n has complexity: Poly(n^1)
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Found new complexity Poly(n^1).
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	Obtained the following overall complexity (w.r.t. the length of the input n):
5.99/2.72	
5.99/2.72	   Complexity:  Poly(n^1)
5.99/2.72	
5.99/2.72	   Cpx degree:  1
5.99/2.72	
5.99/2.72	   Solved cost: 25+n
5.99/2.72	
5.99/2.72	   Rule cost:   25-A
5.99/2.72	
5.99/2.72	   Rule guard:  [ 1>=A ]
5.99/2.72	
5.99/2.72	
5.99/2.72	
5.99/2.72	WORST_CASE(Omega(n^1),?)
5.99/2.72	
5.99/2.72	
5.99/2.72	----------------------------------------
5.99/2.72	
5.99/2.72	(4)
5.99/2.72	BOUNDS(n^1, INF)
5.99/2.74	EOF