6.51/3.00	WORST_CASE(Omega(n^1), O(n^1))
6.51/3.02	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.51/3.02	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.51/3.02	
6.51/3.02	
6.51/3.02	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
6.51/3.02	
6.51/3.02	(0) CpxIntTrs
6.51/3.02	(1) Koat Proof [FINISHED, 401 ms]
6.51/3.02	(2) BOUNDS(1, n^1)
6.51/3.02	(3) Loat Proof [FINISHED, 1200 ms]
6.51/3.02	(4) BOUNDS(n^1, INF)
6.51/3.02	
6.51/3.02	
6.51/3.02	----------------------------------------
6.51/3.02	
6.51/3.02	(0)
6.51/3.02	Obligation:
6.51/3.02	Complexity Int TRS consisting of the following rules:
6.51/3.02	start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 0 >= A && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
6.51/3.02	start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 0 >= G + 1 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
6.51/3.02	start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, 0, C, F, E, F, G, H)) :|: A >= 1 && F >= 0 && F <= 0 && B >= C && B <= C && D >= E && D <= E && G >= 0 && G <= 0 && H >= A && H <= A
6.51/3.02	start(A, B, C, D, E, F, G, H) -> Com_1(lM1(A, 1, C, F - 1, E, F, G, H)) :|: A >= 1 && G >= 1 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
6.51/3.02	lM1(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= B && G >= B && B >= 1 && D >= 0 && D <= 0 && H >= A && H <= A && F >= G && F <= G
6.51/3.02	lM1(A, B, C, D, E, F, G, H) -> Com_1(lZZ1(A, 0, C, D, E, F, G, H)) :|: D >= 1 && G >= D + A && A >= 1 && D >= 0 && B >= A && B <= A && H >= A && H <= A && F >= G && F <= G
6.51/3.02	lM1(A, B, C, D, E, F, G, H) -> Com_1(lM1(A, 1 + B, C, D - 1, E, F, G, H)) :|: A >= B + 1 && D >= 1 && A >= B && G >= D + B && B >= 1 && D >= 0 && H >= A && H <= A && F >= G && F <= G
6.51/3.02	lZZ1(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 0 >= D && G >= A + D && A >= 2 && D >= 1 && B >= 0 && B <= 0 && H >= A && H <= A && F >= G && F <= G
6.51/3.02	lZZ1(A, B, C, D, E, F, G, H) -> Com_1(lZZ1(A, 0, C, D, E, F, G, H)) :|: D >= 1 && 0 >= A && G >= A + D && A >= 2 && B >= 0 && B <= 0 && H >= A && H <= A && F >= G && F <= G
6.51/3.02	lZZ1(A, B, C, D, E, F, G, H) -> Com_1(lM1(A, 1 + B, C, D - 1, E, F, G, H)) :|: A >= 1 && D >= 1 && G >= A + D && A >= 2 && B >= 0 && B <= 0 && H >= A && H <= A && F >= G && F <= G
6.51/3.02	start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, E, E, G, G, A)) :|: TRUE
6.51/3.02	
6.51/3.02	The start-symbols are:[start0_8]
6.51/3.02	
6.51/3.02	
6.51/3.02	----------------------------------------
6.51/3.02	
6.51/3.02	(1) Koat Proof (FINISHED)
6.51/3.02	YES(?, 6*ar_6 + 9)
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Initial complexity problem:
6.51/3.02	
6.51/3.02	1:	T:
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_6 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, 0, ar_2, ar_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_5 = 0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_6 = 0 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_6 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\ ar_6 >= ar_1 /\ ar_1 >= 1 /\ ar_3 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\ ar_6 >= ar_3 + ar_0 /\ ar_0 >= 1 /\ ar_3 >= 0 /\ ar_1 = ar_0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\ ar_3 >= 1 /\ ar_0 >= ar_1 /\ ar_6 >= ar_3 + ar_1 /\ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_3 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_3 >= 1 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\ 0 >= ar_0 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(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))
6.51/3.02	
6.51/3.02			(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 ]
6.51/3.02	
6.51/3.02		start location:	koat_start
6.51/3.02	
6.51/3.02		leaf cost:	0
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Testing for reachability in the complexity graph removes the following transitions from problem 1:
6.51/3.02	
6.51/3.02		lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_3 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_3 >= 1 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02		lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\ 0 >= ar_0 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02	We thus obtain the following problem:
6.51/3.02	
6.51/3.02	2:	T:
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\ ar_3 >= 1 /\ ar_0 >= ar_1 /\ ar_6 >= ar_3 + ar_1 /\ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\ ar_6 >= ar_3 + ar_0 /\ ar_0 >= 1 /\ ar_3 >= 0 /\ ar_1 = ar_0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\ ar_6 >= ar_1 /\ ar_1 >= 1 /\ ar_3 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_6 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, 0, ar_2, ar_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_5 = 0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_6 = 0 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_6 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(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))
6.51/3.02	
6.51/3.02			(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 ]
6.51/3.02	
6.51/3.02		start location:	koat_start
6.51/3.02	
6.51/3.02		leaf cost:	0
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Repeatedly propagating knowledge in problem 2 produces the following problem:
6.51/3.02	
6.51/3.02	3:	T:
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\ ar_3 >= 1 /\ ar_0 >= ar_1 /\ ar_6 >= ar_3 + ar_1 /\ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\ ar_6 >= ar_3 + ar_0 /\ ar_0 >= 1 /\ ar_3 >= 0 /\ ar_1 = ar_0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\ ar_6 >= ar_1 /\ ar_1 >= 1 /\ ar_3 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_6 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, 0, ar_2, ar_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_5 = 0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_6 = 0 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_6 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(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))
6.51/3.02	
6.51/3.02			(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 ]
6.51/3.02	
6.51/3.02		start location:	koat_start
6.51/3.02	
6.51/3.02		leaf cost:	0
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	A polynomial rank function with
6.51/3.02	
6.51/3.02		Pol(lZZ1) = 1
6.51/3.02	
6.51/3.02		Pol(lM1) = 1
6.51/3.02	
6.51/3.02		Pol(stop) = 0
6.51/3.02	
6.51/3.02		Pol(start) = 1
6.51/3.02	
6.51/3.02		Pol(start0) = 1
6.51/3.02	
6.51/3.02		Pol(koat_start) = 1
6.51/3.02	
6.51/3.02	orients all transitions weakly and the transition
6.51/3.02	
6.51/3.02		lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\ ar_6 >= ar_1 /\ ar_1 >= 1 /\ ar_3 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02	strictly and produces the following problem:
6.51/3.02	
6.51/3.02	4:	T:
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\ ar_3 >= 1 /\ ar_0 >= ar_1 /\ ar_6 >= ar_3 + ar_1 /\ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: ?, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\ ar_6 >= ar_3 + ar_0 /\ ar_0 >= 1 /\ ar_3 >= 0 /\ ar_1 = ar_0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\ ar_6 >= ar_1 /\ ar_1 >= 1 /\ ar_3 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_6 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, 0, ar_2, ar_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_5 = 0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_6 = 0 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_6 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(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))
6.51/3.02	
6.51/3.02			(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 ]
6.51/3.02	
6.51/3.02		start location:	koat_start
6.51/3.02	
6.51/3.02		leaf cost:	0
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	A polynomial rank function with
6.51/3.02	
6.51/3.02		Pol(lZZ1) = 2*V_4
6.51/3.02	
6.51/3.02		Pol(lM1) = 2*V_4 + 1
6.51/3.02	
6.51/3.02	and size complexities
6.51/3.02	
6.51/3.02		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
6.51/3.02	
6.51/3.02		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
6.51/3.02	
6.51/3.02		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
6.51/3.02	
6.51/3.02		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
6.51/3.02	
6.51/3.02		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
6.51/3.02	
6.51/3.02		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
6.51/3.02	
6.51/3.02		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
6.51/3.02	
6.51/3.02		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
6.51/3.02	
6.51/3.02		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))", 0-0) = ar_0
6.51/3.02	
6.51/3.02		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))", 0-1) = ar_2
6.51/3.02	
6.51/3.02		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))", 0-2) = ar_2
6.51/3.02	
6.51/3.02		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))", 0-3) = ar_4
6.51/3.02	
6.51/3.02		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))", 0-4) = ar_4
6.51/3.02	
6.51/3.02		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))", 0-5) = ar_6
6.51/3.02	
6.51/3.02		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))", 0-6) = ar_6
6.51/3.02	
6.51/3.02		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))", 0-7) = ar_0
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-0) = ar_0
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-1) = ar_2
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-2) = ar_2
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-3) = ar_4
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-4) = ar_4
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-5) = ar_6
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-6) = ar_6
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-7) = ar_0
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_6 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-0) = ar_0
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_6 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-1) = ar_2
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_6 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-2) = ar_2
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_6 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-3) = ar_4
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_6 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-4) = ar_4
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_6 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-5) = ar_6
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_6 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-6) = ar_6
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_6 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-7) = ar_0
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, 0, ar_2, ar_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_5 = 0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_6 = 0 /\\ ar_7 = ar_0 ]", 0-0) = ar_0
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, 0, ar_2, ar_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_5 = 0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_6 = 0 /\\ ar_7 = ar_0 ]", 0-1) = 0
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, 0, ar_2, ar_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_5 = 0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_6 = 0 /\\ ar_7 = ar_0 ]", 0-2) = ar_2
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, 0, ar_2, ar_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_5 = 0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_6 = 0 /\\ ar_7 = ar_0 ]", 0-3) = 0
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, 0, ar_2, ar_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_5 = 0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_6 = 0 /\\ ar_7 = ar_0 ]", 0-4) = ar_4
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, 0, ar_2, ar_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_5 = 0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_6 = 0 /\\ ar_7 = ar_0 ]", 0-5) = 0
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, 0, ar_2, ar_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_5 = 0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_6 = 0 /\\ ar_7 = ar_0 ]", 0-6) = 0
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, 0, ar_2, ar_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_5 = 0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_6 = 0 /\\ ar_7 = ar_0 ]", 0-7) = ar_0
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-0) = ar_0
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-1) = 1
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-2) = ar_2
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-3) = ar_6
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-4) = ar_4
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-5) = ar_6
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-6) = ar_6
6.51/3.02	
6.51/3.02		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_6 /\\ ar_7 = ar_0 ]", 0-7) = ar_0
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\\ ar_6 >= ar_1 /\\ ar_1 >= 1 /\\ ar_3 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-0) = ar_0
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\\ ar_6 >= ar_1 /\\ ar_1 >= 1 /\\ ar_3 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-1) = ar_6 + 2
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\\ ar_6 >= ar_1 /\\ ar_1 >= 1 /\\ ar_3 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-2) = ar_2
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\\ ar_6 >= ar_1 /\\ ar_1 >= 1 /\\ ar_3 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-3) = 0
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\\ ar_6 >= ar_1 /\\ ar_1 >= 1 /\\ ar_3 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-4) = ar_4
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\\ ar_6 >= ar_1 /\\ ar_1 >= 1 /\\ ar_3 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-5) = ar_6
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\\ ar_6 >= ar_1 /\\ ar_1 >= 1 /\\ ar_3 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-6) = ar_6
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\\ ar_6 >= ar_1 /\\ ar_1 >= 1 /\\ ar_3 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-7) = ar_0
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\\ ar_6 >= ar_3 + ar_0 /\\ ar_0 >= 1 /\\ ar_3 >= 0 /\\ ar_1 = ar_0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-0) = ar_0
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\\ ar_6 >= ar_3 + ar_0 /\\ ar_0 >= 1 /\\ ar_3 >= 0 /\\ ar_1 = ar_0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-1) = 0
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\\ ar_6 >= ar_3 + ar_0 /\\ ar_0 >= 1 /\\ ar_3 >= 0 /\\ ar_1 = ar_0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-2) = ar_2
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\\ ar_6 >= ar_3 + ar_0 /\\ ar_0 >= 1 /\\ ar_3 >= 0 /\\ ar_1 = ar_0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-3) = ar_6
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\\ ar_6 >= ar_3 + ar_0 /\\ ar_0 >= 1 /\\ ar_3 >= 0 /\\ ar_1 = ar_0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-4) = ar_4
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\\ ar_6 >= ar_3 + ar_0 /\\ ar_0 >= 1 /\\ ar_3 >= 0 /\\ ar_1 = ar_0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-5) = ar_6
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\\ ar_6 >= ar_3 + ar_0 /\\ ar_0 >= 1 /\\ ar_3 >= 0 /\\ ar_1 = ar_0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-6) = ar_6
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\\ ar_6 >= ar_3 + ar_0 /\\ ar_0 >= 1 /\\ ar_3 >= 0 /\\ ar_1 = ar_0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-7) = ar_0
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\\ ar_3 >= 1 /\\ ar_0 >= ar_1 /\\ ar_6 >= ar_3 + ar_1 /\\ ar_1 >= 1 /\\ ar_3 >= 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-0) = ar_0
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\\ ar_3 >= 1 /\\ ar_0 >= ar_1 /\\ ar_6 >= ar_3 + ar_1 /\\ ar_1 >= 1 /\\ ar_3 >= 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-1) = ar_6
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\\ ar_3 >= 1 /\\ ar_0 >= ar_1 /\\ ar_6 >= ar_3 + ar_1 /\\ ar_1 >= 1 /\\ ar_3 >= 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-2) = ar_2
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\\ ar_3 >= 1 /\\ ar_0 >= ar_1 /\\ ar_6 >= ar_3 + ar_1 /\\ ar_1 >= 1 /\\ ar_3 >= 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-3) = ar_6
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\\ ar_3 >= 1 /\\ ar_0 >= ar_1 /\\ ar_6 >= ar_3 + ar_1 /\\ ar_1 >= 1 /\\ ar_3 >= 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-4) = ar_4
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\\ ar_3 >= 1 /\\ ar_0 >= ar_1 /\\ ar_6 >= ar_3 + ar_1 /\\ ar_1 >= 1 /\\ ar_3 >= 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-5) = ar_6
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\\ ar_3 >= 1 /\\ ar_0 >= ar_1 /\\ ar_6 >= ar_3 + ar_1 /\\ ar_1 >= 1 /\\ ar_3 >= 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-6) = ar_6
6.51/3.02	
6.51/3.02		S("lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\\ ar_3 >= 1 /\\ ar_0 >= ar_1 /\\ ar_6 >= ar_3 + ar_1 /\\ ar_1 >= 1 /\\ ar_3 >= 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-7) = ar_0
6.51/3.02	
6.51/3.02		S("lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_6 >= ar_0 + ar_3 /\\ ar_0 >= 2 /\\ ar_1 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-0) = ar_0
6.51/3.02	
6.51/3.02		S("lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_6 >= ar_0 + ar_3 /\\ ar_0 >= 2 /\\ ar_1 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-1) = 1
6.51/3.02	
6.51/3.02		S("lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_6 >= ar_0 + ar_3 /\\ ar_0 >= 2 /\\ ar_1 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-2) = ar_2
6.51/3.02	
6.51/3.02		S("lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_6 >= ar_0 + ar_3 /\\ ar_0 >= 2 /\\ ar_1 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-3) = ar_6
6.51/3.02	
6.51/3.02		S("lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_6 >= ar_0 + ar_3 /\\ ar_0 >= 2 /\\ ar_1 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-4) = ar_4
6.51/3.02	
6.51/3.02		S("lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_6 >= ar_0 + ar_3 /\\ ar_0 >= 2 /\\ ar_1 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-5) = ar_6
6.51/3.02	
6.51/3.02		S("lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_6 >= ar_0 + ar_3 /\\ ar_0 >= 2 /\\ ar_1 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-6) = ar_6
6.51/3.02	
6.51/3.02		S("lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_6 >= ar_0 + ar_3 /\\ ar_0 >= 2 /\\ ar_1 = 0 /\\ ar_7 = ar_0 /\\ ar_5 = ar_6 ]", 0-7) = ar_0
6.51/3.02	
6.51/3.02	orients the transitions
6.51/3.02	
6.51/3.02		lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02		lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\ ar_6 >= ar_3 + ar_0 /\ ar_0 >= 1 /\ ar_3 >= 0 /\ ar_1 = ar_0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02		lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\ ar_3 >= 1 /\ ar_0 >= ar_1 /\ ar_6 >= ar_3 + ar_1 /\ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02	weakly and the transitions
6.51/3.02	
6.51/3.02		lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02		lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\ ar_6 >= ar_3 + ar_0 /\ ar_0 >= 1 /\ ar_3 >= 0 /\ ar_1 = ar_0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02		lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\ ar_3 >= 1 /\ ar_0 >= ar_1 /\ ar_6 >= ar_3 + ar_1 /\ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02	strictly and produces the following problem:
6.51/3.02	
6.51/3.02	5:	T:
6.51/3.02	
6.51/3.02			(Comp: 2*ar_6 + 1, Cost: 1)    lZZ1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_6 >= ar_0 + ar_3 /\ ar_0 >= 2 /\ ar_1 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: 2*ar_6 + 1, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, ar_1 + 1, ar_2, ar_3 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 /\ ar_3 >= 1 /\ ar_0 >= ar_1 /\ ar_6 >= ar_3 + ar_1 /\ ar_1 >= 1 /\ ar_3 >= 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: 2*ar_6 + 1, Cost: 1)    lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lZZ1(ar_0, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= 1 /\ ar_6 >= ar_3 + ar_0 /\ ar_0 >= 1 /\ ar_3 >= 0 /\ ar_1 = ar_0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)             lM1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 /\ ar_6 >= ar_1 /\ ar_1 >= 1 /\ ar_3 = 0 /\ ar_7 = ar_0 /\ ar_5 = ar_6 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)             start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lM1(ar_0, 1, ar_2, ar_5 - 1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_6 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)             start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, 0, ar_2, ar_5, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_5 = 0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_6 = 0 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)             start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_6 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(Comp: 1, Cost: 1)             start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
6.51/3.02	
6.51/3.02			(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))
6.51/3.02	
6.51/3.02			(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 ]
6.51/3.02	
6.51/3.02		start location:	koat_start
6.51/3.02	
6.51/3.02		leaf cost:	0
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Complexity upper bound 6*ar_6 + 9
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Time: 0.382 sec (SMT: 0.300 sec)
6.51/3.02	
6.51/3.02	
6.51/3.02	----------------------------------------
6.51/3.02	
6.51/3.02	(2)
6.51/3.02	BOUNDS(1, n^1)
6.51/3.02	
6.51/3.02	----------------------------------------
6.51/3.02	
6.51/3.02	(3) Loat Proof (FINISHED)
6.51/3.02	
6.51/3.02	
6.51/3.02	### Pre-processing the ITS problem ###
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Initial linear ITS problem
6.51/3.02	
6.51/3.02	   Start location: start0
6.51/3.02	
6.51/3.02	      0: start -> stop : [ 0>=A && B==C && D==E && F==G && H==A ], cost: 1
6.51/3.02	
6.51/3.02	      1: start -> stop : [ 0>=1+G && B==C && D==E && F==G && H==A ], cost: 1
6.51/3.02	
6.51/3.02	      2: start -> stop : B'=0, D'=F, [ A>=1 && F==0 && B==C && D==E && G==0 && H==A ], cost: 1
6.51/3.02	
6.51/3.02	      3: start -> lM1 : B'=1, D'=-1+F, [ A>=1 && G>=1 && B==C && D==E && F==G && H==A ], cost: 1
6.51/3.02	
6.51/3.02	      4: lM1 -> stop : [ A>=B && G>=B && B>=1 && D==0 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	      5: lM1 -> lZZ1 : B'=0, [ D>=1 && G>=D+A && A>=1 && D>=0 && B==A && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	      6: lM1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1+B && D>=1 && A>=B && G>=D+B && B>=1 && D>=0 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	      7: lZZ1 -> stop : [ 0>=D && G>=D+A && A>=2 && D>=1 && B==0 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	      8: lZZ1 -> lZZ1 : B'=0, [ D>=1 && 0>=A && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	      9: lZZ1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1 && D>=1 && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	     10: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Removed unreachable and leaf rules:
6.51/3.02	
6.51/3.02	   Start location: start0
6.51/3.02	
6.51/3.02	      3: start -> lM1 : B'=1, D'=-1+F, [ A>=1 && G>=1 && B==C && D==E && F==G && H==A ], cost: 1
6.51/3.02	
6.51/3.02	      5: lM1 -> lZZ1 : B'=0, [ D>=1 && G>=D+A && A>=1 && D>=0 && B==A && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	      6: lM1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1+B && D>=1 && A>=B && G>=D+B && B>=1 && D>=0 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	      8: lZZ1 -> lZZ1 : B'=0, [ D>=1 && 0>=A && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	      9: lZZ1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1 && D>=1 && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	     10: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Removed rules with unsatisfiable guard:
6.51/3.02	
6.51/3.02	   Start location: start0
6.51/3.02	
6.51/3.02	      3: start -> lM1 : B'=1, D'=-1+F, [ A>=1 && G>=1 && B==C && D==E && F==G && H==A ], cost: 1
6.51/3.02	
6.51/3.02	      5: lM1 -> lZZ1 : B'=0, [ D>=1 && G>=D+A && A>=1 && D>=0 && B==A && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	      6: lM1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1+B && D>=1 && A>=B && G>=D+B && B>=1 && D>=0 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	      9: lZZ1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1 && D>=1 && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	     10: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Simplified all rules, resulting in:
6.51/3.02	
6.51/3.02	   Start location: start0
6.51/3.02	
6.51/3.02	      3: start -> lM1 : B'=1, D'=-1+F, [ A>=1 && G>=1 && B==C && D==E && F==G && H==A ], cost: 1
6.51/3.02	
6.51/3.02	      5: lM1 -> lZZ1 : B'=0, [ D>=1 && G>=D+A && A>=1 && B==A && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	      6: lM1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1+B && D>=1 && G>=D+B && B>=1 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	      9: lZZ1 -> lM1 : B'=1+B, D'=-1+D, [ D>=1 && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	     10: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	### Simplification by acceleration and chaining ###
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Accelerating simple loops of location 1.
6.51/3.02	
6.51/3.02	   Accelerating the following rules:
6.51/3.02	
6.51/3.02	      6: lM1 -> lM1 : B'=1+B, D'=-1+D, [ A>=1+B && D>=1 && G>=D+B && B>=1 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	   Accelerated rule 6 with backward acceleration, yielding the new rule 11.
6.51/3.02	
6.51/3.02	   Accelerated rule 6 with backward acceleration, yielding the new rule 12.
6.51/3.02	
6.51/3.02	   Removing the simple loops: 6.
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Accelerated all simple loops using metering functions (where possible):
6.51/3.02	
6.51/3.02	   Start location: start0
6.51/3.02	
6.51/3.02	      3: start -> lM1 : B'=1, D'=-1+F, [ A>=1 && G>=1 && B==C && D==E && F==G && H==A ], cost: 1
6.51/3.02	
6.51/3.02	      5: lM1 -> lZZ1 : B'=0, [ D>=1 && G>=D+A && A>=1 && B==A && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	     11: lM1 -> lM1 : B'=A, D'=D-A+B, [ A>=1+B && D>=1 && G>=D+B && B>=1 && H==A && F==G && 1+D-A+B>=1 && -1+A>=1 ], cost: A-B
6.51/3.02	
6.51/3.02	     12: lM1 -> lM1 : B'=D+B, D'=0, [ A>=1+B && D>=1 && G>=D+B && B>=1 && H==A && F==G && A>=D+B && -1+D+B>=1 ], cost: D
6.51/3.02	
6.51/3.02	      9: lZZ1 -> lM1 : B'=1+B, D'=-1+D, [ D>=1 && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	     10: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Chained accelerated rules (with incoming rules):
6.51/3.02	
6.51/3.02	   Start location: start0
6.51/3.02	
6.51/3.02	      3: start -> lM1 : B'=1, D'=-1+F, [ A>=1 && G>=1 && B==C && D==E && F==G && H==A ], cost: 1
6.51/3.02	
6.51/3.02	     13: start -> lM1 : B'=A, D'=F-A, [ G>=1 && B==C && D==E && F==G && H==A && A>=2 && -1+F>=1 && 1+F-A>=1 ], cost: A
6.51/3.02	
6.51/3.02	     15: start -> lM1 : B'=F, D'=0, [ G>=1 && B==C && D==E && F==G && H==A && A>=2 && -1+F>=1 && A>=F ], cost: F
6.51/3.02	
6.51/3.02	      5: lM1 -> lZZ1 : B'=0, [ D>=1 && G>=D+A && A>=1 && B==A && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	      9: lZZ1 -> lM1 : B'=1+B, D'=-1+D, [ D>=1 && G>=D+A && A>=2 && B==0 && H==A && F==G ], cost: 1
6.51/3.02	
6.51/3.02	     14: lZZ1 -> lM1 : B'=A, D'=D-A+B, [ G>=D+A && A>=2 && B==0 && H==A && F==G && A>=2+B && -1+D>=1 && G>=D+B && 1+D-A+B>=1 ], cost: A-B
6.51/3.02	
6.51/3.02	     16: lZZ1 -> lM1 : B'=D+B, D'=0, [ G>=D+A && A>=2 && B==0 && H==A && F==G && A>=2+B && -1+D>=1 && G>=D+B && A>=D+B && -1+D+B>=1 ], cost: D
6.51/3.02	
6.51/3.02	     10: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Eliminated locations (on tree-shaped paths):
6.51/3.02	
6.51/3.02	   Start location: start0
6.51/3.02	
6.51/3.02	     20: lM1 -> lM1 : B'=1, D'=-1+D, [ D>=1 && G>=D+A && B==A && H==A && F==G && A>=2 ], cost: 2
6.51/3.02	
6.51/3.02	     21: lM1 -> lM1 : B'=A, D'=D-A, [ G>=D+A && B==A && H==A && F==G && A>=2 && -1+D>=1 && G>=D && 1+D-A>=1 ], cost: 1+A
6.51/3.02	
6.51/3.02	     22: lM1 -> lM1 : B'=D, D'=0, [ G>=D+A && B==A && H==A && F==G && A>=2 && -1+D>=1 && G>=D && A>=D ], cost: 1+D
6.51/3.02	
6.51/3.02	     17: start0 -> lM1 : B'=1, D'=-1+G, F'=G, H'=A, [ A>=1 && G>=1 ], cost: 2
6.51/3.02	
6.51/3.02	     18: start0 -> lM1 : B'=A, D'=G-A, F'=G, H'=A, [ A>=2 && -1+G>=1 && 1+G-A>=1 ], cost: 1+A
6.51/3.02	
6.51/3.02	     19: start0 -> lM1 : B'=G, D'=0, F'=G, H'=A, [ A>=2 && -1+G>=1 && A>=G ], cost: 1+G
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Accelerating simple loops of location 1.
6.51/3.02	
6.51/3.02	   Accelerating the following rules:
6.51/3.02	
6.51/3.02	     20: lM1 -> lM1 : B'=1, D'=-1+D, [ D>=1 && G>=D+A && B==A && H==A && F==G && A>=2 ], cost: 2
6.51/3.02	
6.51/3.02	     21: lM1 -> lM1 : B'=A, D'=D-A, [ G>=D+A && B==A && H==A && F==G && A>=2 && -1+D>=1 && G>=D && 1+D-A>=1 ], cost: 1+A
6.51/3.02	
6.51/3.02	     22: lM1 -> lM1 : B'=D, D'=0, [ G>=D+A && B==A && H==A && F==G && A>=2 && -1+D>=1 && G>=D && A>=D ], cost: 1+D
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	   Accelerated rule 20 with NONTERM (after strengthening guard), yielding the new rule 23.
6.51/3.02	
6.51/3.02	   Accelerated rule 21 with backward acceleration, yielding the new rule 24.
6.51/3.02	
6.51/3.02	   Found no metering function for rule 22.
6.51/3.02	
6.51/3.02	   Removing the simple loops: 21.
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Accelerated all simple loops using metering functions (where possible):
6.51/3.02	
6.51/3.02	   Start location: start0
6.51/3.02	
6.51/3.02	     20: lM1 -> lM1 : B'=1, D'=-1+D, [ D>=1 && G>=D+A && B==A && H==A && F==G && A>=2 ], cost: 2
6.51/3.02	
6.51/3.02	     22: lM1 -> lM1 : B'=D, D'=0, [ G>=D+A && B==A && H==A && F==G && A>=2 && -1+D>=1 && G>=D && A>=D ], cost: 1+D
6.51/3.02	
6.51/3.02	     23: lM1 -> [6] : [ D>=1 && G>=D+A && B==A && H==A && F==G && A>=2 && 1==A ], cost: INF
6.51/3.02	
6.51/3.02	     24: lM1 -> lM1 : B'=A, D'=-k_1*A+D, [ G>=D+A && B==A && H==A && F==G && A>=2 && -1+D>=1 && G>=D && 1+D-A>=1 && k_1>0 && G>=D-(-1+k_1)*A+A && -1+D-(-1+k_1)*A>=1 && G>=D-(-1+k_1)*A && 1+D-(-1+k_1)*A-A>=1 ], cost: k_1*A+k_1
6.51/3.02	
6.51/3.02	     17: start0 -> lM1 : B'=1, D'=-1+G, F'=G, H'=A, [ A>=1 && G>=1 ], cost: 2
6.51/3.02	
6.51/3.02	     18: start0 -> lM1 : B'=A, D'=G-A, F'=G, H'=A, [ A>=2 && -1+G>=1 && 1+G-A>=1 ], cost: 1+A
6.51/3.02	
6.51/3.02	     19: start0 -> lM1 : B'=G, D'=0, F'=G, H'=A, [ A>=2 && -1+G>=1 && A>=G ], cost: 1+G
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Chained accelerated rules (with incoming rules):
6.51/3.02	
6.51/3.02	   Start location: start0
6.51/3.02	
6.51/3.02	     17: start0 -> lM1 : B'=1, D'=-1+G, F'=G, H'=A, [ A>=1 && G>=1 ], cost: 2
6.51/3.02	
6.51/3.02	     18: start0 -> lM1 : B'=A, D'=G-A, F'=G, H'=A, [ A>=2 && -1+G>=1 && 1+G-A>=1 ], cost: 1+A
6.51/3.02	
6.51/3.02	     19: start0 -> lM1 : B'=G, D'=0, F'=G, H'=A, [ A>=2 && -1+G>=1 && A>=G ], cost: 1+G
6.51/3.02	
6.51/3.02	     25: start0 -> lM1 : B'=1, D'=-1+G-A, F'=G, H'=A, [ A>=2 && -1+G>=1 && G-A>=1 ], cost: 3+A
6.51/3.02	
6.51/3.02	     26: start0 -> lM1 : B'=G-A, D'=0, F'=G, H'=A, [ A>=2 && -1+G>=1 && -1+G-A>=1 && A>=G-A ], cost: 2+G
6.51/3.02	
6.51/3.02	     27: start0 -> lM1 : B'=A, D'=-k_1*A+G-A, F'=G, H'=A, [ A>=2 && -1+G>=1 && -1+G-A>=1 && 1+G-2*A>=1 && k_1>0 && G>=G-(-1+k_1)*A && -1+G-(-1+k_1)*A-A>=1 && G>=G-(-1+k_1)*A-A && 1+G-(-1+k_1)*A-2*A>=1 ], cost: 1+k_1*A+k_1+A
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Removed unreachable locations (and leaf rules with constant cost):
6.51/3.02	
6.51/3.02	   Start location: start0
6.51/3.02	
6.51/3.02	     18: start0 -> lM1 : B'=A, D'=G-A, F'=G, H'=A, [ A>=2 && -1+G>=1 && 1+G-A>=1 ], cost: 1+A
6.51/3.02	
6.51/3.02	     19: start0 -> lM1 : B'=G, D'=0, F'=G, H'=A, [ A>=2 && -1+G>=1 && A>=G ], cost: 1+G
6.51/3.02	
6.51/3.02	     25: start0 -> lM1 : B'=1, D'=-1+G-A, F'=G, H'=A, [ A>=2 && -1+G>=1 && G-A>=1 ], cost: 3+A
6.51/3.02	
6.51/3.02	     26: start0 -> lM1 : B'=G-A, D'=0, F'=G, H'=A, [ A>=2 && -1+G>=1 && -1+G-A>=1 && A>=G-A ], cost: 2+G
6.51/3.02	
6.51/3.02	     27: start0 -> lM1 : B'=A, D'=-k_1*A+G-A, F'=G, H'=A, [ A>=2 && -1+G>=1 && -1+G-A>=1 && 1+G-2*A>=1 && k_1>0 && G>=G-(-1+k_1)*A && -1+G-(-1+k_1)*A-A>=1 && G>=G-(-1+k_1)*A-A && 1+G-(-1+k_1)*A-2*A>=1 ], cost: 1+k_1*A+k_1+A
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	### Computing asymptotic complexity ###
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Fully simplified ITS problem
6.51/3.02	
6.51/3.02	   Start location: start0
6.51/3.02	
6.51/3.02	     18: start0 -> lM1 : B'=A, D'=G-A, F'=G, H'=A, [ A>=2 && -1+G>=1 && 1+G-A>=1 ], cost: 1+A
6.51/3.02	
6.51/3.02	     19: start0 -> lM1 : B'=G, D'=0, F'=G, H'=A, [ A>=2 && -1+G>=1 && A>=G ], cost: 1+G
6.51/3.02	
6.51/3.02	     25: start0 -> lM1 : B'=1, D'=-1+G-A, F'=G, H'=A, [ A>=2 && -1+G>=1 && G-A>=1 ], cost: 3+A
6.51/3.02	
6.51/3.02	     26: start0 -> lM1 : B'=G-A, D'=0, F'=G, H'=A, [ A>=2 && -1+G>=1 && -1+G-A>=1 && A>=G-A ], cost: 2+G
6.51/3.02	
6.51/3.02	     27: start0 -> lM1 : B'=A, D'=-k_1*A+G-A, F'=G, H'=A, [ A>=2 && -1+G>=1 && -1+G-A>=1 && 1+G-2*A>=1 && k_1>0 && G>=G-(-1+k_1)*A && -1+G-(-1+k_1)*A-A>=1 && G>=G-(-1+k_1)*A-A && 1+G-(-1+k_1)*A-2*A>=1 ], cost: 1+k_1*A+k_1+A
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Computing asymptotic complexity for rule 18
6.51/3.02	
6.51/3.02	   Solved the limit problem by the following transformations:
6.51/3.02	
6.51/3.02	      Created initial limit problem:
6.51/3.02	
6.51/3.02	      -1+A (+/+!), -1+G (+/+!), 1+G-A (+/+!), 1+A (+) [not solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	      removing all constraints (solved by SMT)
6.51/3.02	
6.51/3.02	      resulting limit problem: [solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	      applying transformation rule (C) using substitution {G==n,A==n}
6.51/3.02	
6.51/3.02	      resulting limit problem:
6.51/3.02	
6.51/3.02	      [solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	   Solution:
6.51/3.02	
6.51/3.02	      G / n
6.51/3.02	
6.51/3.02	      A / n
6.51/3.02	
6.51/3.02	   Resulting cost 1+n has complexity: Poly(n^1)
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Found new complexity Poly(n^1).
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Computing asymptotic complexity for rule 27
6.51/3.02	
6.51/3.02	   Solved the limit problem by the following transformations:
6.51/3.02	
6.51/3.02	      Created initial limit problem:
6.51/3.02	
6.51/3.02	      1+G-2*A (+/+!), -1+G-A (+/+!), -1+A (+/+!), -1+G (+/+!), k_1 (+/+!), 1+G-(-1+k_1)*A-2*A (+/+!), 1+k_1*A+k_1+A (+), -1+G-(-1+k_1)*A-A (+/+!) [not solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	      removing all constraints (solved by SMT)
6.51/3.02	
6.51/3.02	      resulting limit problem: [solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	      applying transformation rule (C) using substitution {k_1==2,G==6+3*n,A==2+n}
6.51/3.02	
6.51/3.02	      resulting limit problem:
6.51/3.02	
6.51/3.02	      [solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	   Solved the limit problem by the following transformations:
6.51/3.02	
6.51/3.02	      Created initial limit problem:
6.51/3.02	
6.51/3.02	      1+G-2*A (+/+!), -1+G-A (+/+!), -1+A (+/+!), -1+G (+/+!), k_1 (+/+!), 1+G-(-1+k_1)*A-2*A (+/+!), 1+k_1*A+k_1+A (+), -1+G-(-1+k_1)*A-A (+/+!) [not solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	      applying transformation rule (C) using substitution {k_1==1}
6.51/3.02	
6.51/3.02	      resulting limit problem:
6.51/3.02	
6.51/3.02	      1+G-2*A (+/+!), 1 (+/+!), -1+G-A (+/+!), -1+A (+/+!), -1+G (+/+!), 2+2*A (+) [not solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	      applying transformation rule (B), deleting 1 (+/+!)
6.51/3.02	
6.51/3.02	      resulting limit problem:
6.51/3.02	
6.51/3.02	      1+G-2*A (+/+!), -1+G-A (+/+!), -1+A (+/+!), -1+G (+/+!), 2+2*A (+) [not solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	      removing all constraints (solved by SMT)
6.51/3.02	
6.51/3.02	      resulting limit problem: [solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	      applying transformation rule (C) using substitution {G==3*n,A==n}
6.51/3.02	
6.51/3.02	      resulting limit problem:
6.51/3.02	
6.51/3.02	      [solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	   Solved the limit problem by the following transformations:
6.51/3.02	
6.51/3.02	      Created initial limit problem:
6.51/3.02	
6.51/3.02	      1+G-2*A (+/+!), -1+G-A (+/+!), -1+A (+/+!), -1+G (+/+!), k_1 (+/+!), 1+G-(-1+k_1)*A-2*A (+/+!), 1+k_1*A+k_1+A (+), -1+G-(-1+k_1)*A-A (+/+!) [not solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	      applying transformation rule (C) using substitution {A==2}
6.51/3.02	
6.51/3.02	      resulting limit problem:
6.51/3.02	
6.51/3.02	      1 (+/+!), -1-2*k_1+G (+/+!), 3+3*k_1 (+), -1+G (+/+!), k_1 (+/+!), -3+G (+/+!) [not solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	      applying transformation rule (B), deleting 1 (+/+!)
6.51/3.02	
6.51/3.02	      resulting limit problem:
6.51/3.02	
6.51/3.02	      -1-2*k_1+G (+/+!), 3+3*k_1 (+), -1+G (+/+!), k_1 (+/+!), -3+G (+/+!) [not solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	      removing all constraints (solved by SMT)
6.51/3.02	
6.51/3.02	      resulting limit problem: [solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	      applying transformation rule (C) using substitution {k_1==n,G==4+2*n}
6.51/3.02	
6.51/3.02	      resulting limit problem:
6.51/3.02	
6.51/3.02	      [solved]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	   Solution:
6.51/3.02	
6.51/3.02	      k_1 / 2
6.51/3.02	
6.51/3.02	      G / 6+3*n
6.51/3.02	
6.51/3.02	      A / 2+n
6.51/3.02	
6.51/3.02	   Resulting cost 9+3*n has complexity: Poly(n^1)
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	Obtained the following overall complexity (w.r.t. the length of the input n):
6.51/3.02	
6.51/3.02	   Complexity:  Poly(n^1)
6.51/3.02	
6.51/3.02	   Cpx degree:  1
6.51/3.02	
6.51/3.02	   Solved cost: 1+n
6.51/3.02	
6.51/3.02	   Rule cost:   1+A
6.51/3.02	
6.51/3.02	   Rule guard:  [ A>=2 && -1+G>=1 && 1+G-A>=1 ]
6.51/3.02	
6.51/3.02	
6.51/3.02	
6.51/3.02	WORST_CASE(Omega(n^1),?)
6.51/3.02	
6.51/3.02	
6.51/3.02	----------------------------------------
6.51/3.02	
6.51/3.02	(4)
6.51/3.02	BOUNDS(n^1, INF)
6.68/3.04	EOF