5.10/2.32	WORST_CASE(Omega(n^2), O(n^2))
5.22/2.89	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.22/2.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.22/2.89	
5.22/2.89	
5.22/2.89	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
5.22/2.89	
5.22/2.89	(0) CpxIntTrs
5.22/2.89	(1) Koat Proof [FINISHED, 190 ms]
5.22/2.89	(2) BOUNDS(1, n^2)
5.22/2.89	(3) Loat Proof [FINISHED, 733 ms]
5.22/2.89	(4) BOUNDS(n^2, INF)
5.22/2.89	
5.22/2.89	
5.22/2.89	----------------------------------------
5.22/2.89	
5.22/2.89	(0)
5.22/2.89	Obligation:
5.22/2.89	Complexity Int TRS consisting of the following rules:
5.22/2.89	start(A, B, C, D, E, F) -> Com_1(lbl71(A, B, 1, D, 0, F)) :|: A >= 2 && B >= A && B <= A && C >= D && C <= D && E >= F && E <= F
5.22/2.89	start(A, B, C, D, E, F) -> Com_1(stop(A, B, 0, D, 1, F)) :|: 1 >= A && B >= A && B <= A && C >= D && C <= D && E >= F && E <= F
5.22/2.89	lbl71(A, B, C, D, E, F) -> Com_1(lbl71(A, B, 1 + C, D, E, F)) :|: A >= C + 2 && A >= C + 1 && A >= E + 2 && C >= 1 && E >= 0 && B >= A && B <= A
5.22/2.89	lbl71(A, B, C, D, E, F) -> Com_1(cut(A, B, C, D, 1 + E, F)) :|: A >= E + 3 && A >= E + 2 && A >= 2 && E >= 0 && C + 1 >= A && C + 1 <= A && B >= A && B <= A
5.22/2.89	lbl71(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, 1 + E, F)) :|: A >= 2 && E + 2 >= A && E + 2 <= A && C + 1 >= A && C + 1 <= A && B >= A && B <= A
5.22/2.89	cut(A, B, C, D, E, F) -> Com_1(lbl71(A, B, 1, D, E, F)) :|: A >= 2 && A >= 2 + E && E >= 1 && C + 1 >= A && C + 1 <= A && B >= A && B <= A
5.22/2.89	cut(A, B, C, D, E, F) -> Com_1(cut(A, B, 0, D, 1 + E, F)) :|: 1 >= A && A >= E + 3 && A >= 2 + E && E >= 1 && C + 1 >= A && C + 1 <= A && B >= A && B <= A
5.22/2.89	cut(A, B, C, D, E, F) -> Com_1(stop(A, B, 0, D, 1 + E, F)) :|: 1 >= A && A >= 3 && C + 1 >= A && C + 1 <= A && E + 2 >= A && E + 2 <= A && B >= A && B <= A
5.22/2.89	start0(A, B, C, D, E, F) -> Com_1(start(A, A, D, D, F, F)) :|: TRUE
5.22/2.89	
5.22/2.89	The start-symbols are:[start0_6]
5.22/2.89	
5.22/2.89	
5.22/2.89	----------------------------------------
5.22/2.89	
5.22/2.89	(1) Koat Proof (FINISHED)
5.22/2.89	YES(?, 7*ar_0 + 2*ar_0^2 + 5)
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Initial complexity problem:
5.22/2.89	
5.22/2.89	1:	T:
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, 0, ar_5)) [ ar_0 >= 2 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, 1, ar_5)) [ 1 >= ar_0 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_2 >= 1 /\ ar_4 >= 0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_4 + 3 /\ ar_0 >= ar_4 + 2 /\ ar_0 >= 2 /\ ar_4 >= 0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= 2 /\ ar_4 + 2 = ar_0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\ ar_0 >= ar_4 + 2 /\ ar_4 >= 1 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, 0, ar_3, ar_4 + 1, ar_5)) [ 1 >= ar_0 /\ ar_0 >= ar_4 + 3 /\ ar_0 >= ar_4 + 2 /\ ar_4 >= 1 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, ar_4 + 1, ar_5)) [ 1 >= ar_0 /\ ar_0 >= 3 /\ ar_2 + 1 = ar_0 /\ ar_4 + 2 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5))
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.22/2.89	
5.22/2.89		start location:	koat_start
5.22/2.89	
5.22/2.89		leaf cost:	0
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Testing for reachability in the complexity graph removes the following transitions from problem 1:
5.22/2.89	
5.22/2.89		cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, 0, ar_3, ar_4 + 1, ar_5)) [ 1 >= ar_0 /\ ar_0 >= ar_4 + 3 /\ ar_0 >= ar_4 + 2 /\ ar_4 >= 1 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89		cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, ar_4 + 1, ar_5)) [ 1 >= ar_0 /\ ar_0 >= 3 /\ ar_2 + 1 = ar_0 /\ ar_4 + 2 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89	We thus obtain the following problem:
5.22/2.89	
5.22/2.89	2:	T:
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\ ar_0 >= ar_4 + 2 /\ ar_4 >= 1 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_4 + 3 /\ ar_0 >= ar_4 + 2 /\ ar_0 >= 2 /\ ar_4 >= 0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= 2 /\ ar_4 + 2 = ar_0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_2 >= 1 /\ ar_4 >= 0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, 1, ar_5)) [ 1 >= ar_0 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, 0, ar_5)) [ ar_0 >= 2 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5))
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.22/2.89	
5.22/2.89		start location:	koat_start
5.22/2.89	
5.22/2.89		leaf cost:	0
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Repeatedly propagating knowledge in problem 2 produces the following problem:
5.22/2.89	
5.22/2.89	3:	T:
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\ ar_0 >= ar_4 + 2 /\ ar_4 >= 1 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_4 + 3 /\ ar_0 >= ar_4 + 2 /\ ar_0 >= 2 /\ ar_4 >= 0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= 2 /\ ar_4 + 2 = ar_0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_2 >= 1 /\ ar_4 >= 0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, 1, ar_5)) [ 1 >= ar_0 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, 0, ar_5)) [ ar_0 >= 2 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5))
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.22/2.89	
5.22/2.89		start location:	koat_start
5.22/2.89	
5.22/2.89		leaf cost:	0
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	A polynomial rank function with
5.22/2.89	
5.22/2.89		Pol(cut) = 1
5.22/2.89	
5.22/2.89		Pol(lbl71) = 1
5.22/2.89	
5.22/2.89		Pol(stop) = 0
5.22/2.89	
5.22/2.89		Pol(start) = 1
5.22/2.89	
5.22/2.89		Pol(start0) = 1
5.22/2.89	
5.22/2.89		Pol(koat_start) = 1
5.22/2.89	
5.22/2.89	orients all transitions weakly and the transition
5.22/2.89	
5.22/2.89		lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= 2 /\ ar_4 + 2 = ar_0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89	strictly and produces the following problem:
5.22/2.89	
5.22/2.89	4:	T:
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\ ar_0 >= ar_4 + 2 /\ ar_4 >= 1 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_4 + 3 /\ ar_0 >= ar_4 + 2 /\ ar_0 >= 2 /\ ar_4 >= 0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= 2 /\ ar_4 + 2 = ar_0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_2 >= 1 /\ ar_4 >= 0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, 1, ar_5)) [ 1 >= ar_0 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, 0, ar_5)) [ ar_0 >= 2 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5))
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.22/2.89	
5.22/2.89		start location:	koat_start
5.22/2.89	
5.22/2.89		leaf cost:	0
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	A polynomial rank function with
5.22/2.89	
5.22/2.89		Pol(cut) = 2*V_2 - 2*V_5 + 1
5.22/2.89	
5.22/2.89		Pol(lbl71) = 2*V_2 - 2*V_5
5.22/2.89	
5.22/2.89		Pol(stop) = 2*V_1 - 2*V_5
5.22/2.89	
5.22/2.89		Pol(start) = 2*V_1
5.22/2.89	
5.22/2.89		Pol(start0) = 2*V_1
5.22/2.89	
5.22/2.89		Pol(koat_start) = 2*V_1
5.22/2.89	
5.22/2.89	orients all transitions weakly and the transitions
5.22/2.89	
5.22/2.89		lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_4 + 3 /\ ar_0 >= ar_4 + 2 /\ ar_0 >= 2 /\ ar_4 >= 0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89		cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\ ar_0 >= ar_4 + 2 /\ ar_4 >= 1 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89	strictly and produces the following problem:
5.22/2.89	
5.22/2.89	5:	T:
5.22/2.89	
5.22/2.89			(Comp: 2*ar_0, Cost: 1)    cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\ ar_0 >= ar_4 + 2 /\ ar_4 >= 1 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: 2*ar_0, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_4 + 3 /\ ar_0 >= ar_4 + 2 /\ ar_0 >= 2 /\ ar_4 >= 0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)         lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= 2 /\ ar_4 + 2 = ar_0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: ?, Cost: 1)         lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_2 >= 1 /\ ar_4 >= 0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)         start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, 1, ar_5)) [ 1 >= ar_0 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)         start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, 0, ar_5)) [ ar_0 >= 2 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)         start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5))
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.22/2.89	
5.22/2.89		start location:	koat_start
5.22/2.89	
5.22/2.89		leaf cost:	0
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	A polynomial rank function with
5.22/2.89	
5.22/2.89		Pol(lbl71) = V_1 - V_3
5.22/2.89	
5.22/2.89	and size complexities
5.22/2.89	
5.22/2.89		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-0) = ar_0
5.22/2.89	
5.22/2.89		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-1) = ar_1
5.22/2.89	
5.22/2.89		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-2) = ar_2
5.22/2.89	
5.22/2.89		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-3) = ar_3
5.22/2.89	
5.22/2.89		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-4) = ar_4
5.22/2.89	
5.22/2.89		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-5) = ar_5
5.22/2.89	
5.22/2.89		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5))", 0-0) = ar_0
5.22/2.89	
5.22/2.89		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5))", 0-1) = ar_0
5.22/2.89	
5.22/2.89		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5))", 0-2) = ar_3
5.22/2.89	
5.22/2.89		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5))", 0-3) = ar_3
5.22/2.89	
5.22/2.89		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5))", 0-4) = ar_5
5.22/2.89	
5.22/2.89		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5))", 0-5) = ar_5
5.22/2.89	
5.22/2.89		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, 0, ar_5)) [ ar_0 >= 2 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 ]", 0-0) = ar_0
5.22/2.89	
5.22/2.89		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, 0, ar_5)) [ ar_0 >= 2 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 ]", 0-1) = ar_0
5.22/2.89	
5.22/2.89		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, 0, ar_5)) [ ar_0 >= 2 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 ]", 0-2) = 1
5.22/2.89	
5.22/2.89		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, 0, ar_5)) [ ar_0 >= 2 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 ]", 0-3) = ar_3
5.22/2.89	
5.22/2.89		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, 0, ar_5)) [ ar_0 >= 2 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 ]", 0-4) = 0
5.22/2.89	
5.22/2.89		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, 0, ar_5)) [ ar_0 >= 2 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 ]", 0-5) = ar_5
5.22/2.89	
5.22/2.89		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, 1, ar_5)) [ 1 >= ar_0 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 ]", 0-0) = ar_0
5.22/2.89	
5.22/2.89		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, 1, ar_5)) [ 1 >= ar_0 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 ]", 0-1) = ar_0
5.22/2.89	
5.22/2.89		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, 1, ar_5)) [ 1 >= ar_0 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 ]", 0-2) = 0
5.22/2.89	
5.22/2.89		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, 1, ar_5)) [ 1 >= ar_0 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 ]", 0-3) = ar_3
5.22/2.89	
5.22/2.89		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, 1, ar_5)) [ 1 >= ar_0 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 ]", 0-4) = 1
5.22/2.89	
5.22/2.89		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, 1, ar_5)) [ 1 >= ar_0 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 ]", 0-5) = ar_5
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\\ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_4 + 2 /\\ ar_2 >= 1 /\\ ar_4 >= 0 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\\ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_4 + 2 /\\ ar_2 >= 1 /\\ ar_4 >= 0 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\\ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_4 + 2 /\\ ar_2 >= 1 /\\ ar_4 >= 0 /\\ ar_1 = ar_0 ]", 0-2) = ar_0
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\\ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_4 + 2 /\\ ar_2 >= 1 /\\ ar_4 >= 0 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\\ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_4 + 2 /\\ ar_2 >= 1 /\\ ar_4 >= 0 /\\ ar_1 = ar_0 ]", 0-4) = ar_0
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\\ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_4 + 2 /\\ ar_2 >= 1 /\\ ar_4 >= 0 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= 2 /\\ ar_4 + 2 = ar_0 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= 2 /\\ ar_4 + 2 = ar_0 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= 2 /\\ ar_4 + 2 = ar_0 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-2) = ar_0 + 1
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= 2 /\\ ar_4 + 2 = ar_0 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= 2 /\\ ar_4 + 2 = ar_0 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-4) = ar_0
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= 2 /\\ ar_4 + 2 = ar_0 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_4 + 3 /\\ ar_0 >= ar_4 + 2 /\\ ar_0 >= 2 /\\ ar_4 >= 0 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_4 + 3 /\\ ar_0 >= ar_4 + 2 /\\ ar_0 >= 2 /\\ ar_4 >= 0 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_4 + 3 /\\ ar_0 >= ar_4 + 2 /\\ ar_0 >= 2 /\\ ar_4 >= 0 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-2) = ar_0
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_4 + 3 /\\ ar_0 >= ar_4 + 2 /\\ ar_0 >= 2 /\\ ar_4 >= 0 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_4 + 3 /\\ ar_0 >= ar_4 + 2 /\\ ar_0 >= 2 /\\ ar_4 >= 0 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-4) = ar_0
5.22/2.89	
5.22/2.89		S("lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_4 + 3 /\\ ar_0 >= ar_4 + 2 /\\ ar_0 >= 2 /\\ ar_4 >= 0 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.22/2.89	
5.22/2.89		S("cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\\ ar_0 >= ar_4 + 2 /\\ ar_4 >= 1 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.22/2.89	
5.22/2.89		S("cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\\ ar_0 >= ar_4 + 2 /\\ ar_4 >= 1 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.22/2.89	
5.22/2.89		S("cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\\ ar_0 >= ar_4 + 2 /\\ ar_4 >= 1 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-2) = 1
5.22/2.89	
5.22/2.89		S("cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\\ ar_0 >= ar_4 + 2 /\\ ar_4 >= 1 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.22/2.89	
5.22/2.89		S("cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\\ ar_0 >= ar_4 + 2 /\\ ar_4 >= 1 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-4) = ar_0
5.22/2.89	
5.22/2.89		S("cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\\ ar_0 >= ar_4 + 2 /\\ ar_4 >= 1 /\\ ar_2 + 1 = ar_0 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.22/2.89	
5.22/2.89	orients the transitions
5.22/2.89	
5.22/2.89		lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_2 >= 1 /\ ar_4 >= 0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89	weakly and the transition
5.22/2.89	
5.22/2.89		lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_2 >= 1 /\ ar_4 >= 0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89	strictly and produces the following problem:
5.22/2.89	
5.22/2.89	6:	T:
5.22/2.89	
5.22/2.89			(Comp: 2*ar_0, Cost: 1)                   cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, ar_4, ar_5)) [ ar_0 >= 2 /\ ar_0 >= ar_4 + 2 /\ ar_4 >= 1 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: 2*ar_0, Cost: 1)                   lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= ar_4 + 3 /\ ar_0 >= ar_4 + 2 /\ ar_0 >= 2 /\ ar_4 >= 0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)                        lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5)) [ ar_0 >= 2 /\ ar_4 + 2 = ar_0 /\ ar_2 + 1 = ar_0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: 2*ar_0^2 + 3*ar_0 + 1, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5)) [ ar_0 >= ar_2 + 2 /\ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_2 >= 1 /\ ar_4 >= 0 /\ ar_1 = ar_0 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)                        start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, 0, ar_3, 1, ar_5)) [ 1 >= ar_0 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)                        start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl71(ar_0, ar_1, 1, ar_3, 0, ar_5)) [ ar_0 >= 2 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 ]
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 1)                        start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5))
5.22/2.89	
5.22/2.89			(Comp: 1, Cost: 0)                        koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]
5.22/2.89	
5.22/2.89		start location:	koat_start
5.22/2.89	
5.22/2.89		leaf cost:	0
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Complexity upper bound 7*ar_0 + 2*ar_0^2 + 5
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Time: 0.208 sec (SMT: 0.173 sec)
5.22/2.89	
5.22/2.89	
5.22/2.89	----------------------------------------
5.22/2.89	
5.22/2.89	(2)
5.22/2.89	BOUNDS(1, n^2)
5.22/2.89	
5.22/2.89	----------------------------------------
5.22/2.89	
5.22/2.89	(3) Loat Proof (FINISHED)
5.22/2.89	
5.22/2.89	
5.22/2.89	### Pre-processing the ITS problem ###
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Initial linear ITS problem
5.22/2.89	
5.22/2.89	   Start location: start0
5.22/2.89	
5.22/2.89	      0: start -> lbl71 : C'=1, E'=0, [ A>=2 && B==A && C==D && E==F ], cost: 1
5.22/2.89	
5.22/2.89	      1: start -> stop : C'=0, E'=1, [ 1>=A && B==A && C==D && E==F ], cost: 1
5.22/2.89	
5.22/2.89	      2: lbl71 -> lbl71 : C'=1+C, [ A>=2+C && A>=1+C && A>=2+E && C>=1 && E>=0 && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      3: lbl71 -> cut : E'=1+E, [ A>=3+E && A>=2+E && A>=2 && E>=0 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      4: lbl71 -> stop : E'=1+E, [ A>=2 && 2+E==A && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      5: cut -> lbl71 : C'=1, [ A>=2 && A>=2+E && E>=1 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      6: cut -> cut : C'=0, E'=1+E, [ 1>=A && A>=3+E && A>=2+E && E>=1 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      7: cut -> stop : C'=0, E'=1+E, [ 1>=A && A>=3 && 1+C==A && 2+E==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      8: start0 -> start : B'=A, C'=D, E'=F, [], cost: 1
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Removed unreachable and leaf rules:
5.22/2.89	
5.22/2.89	   Start location: start0
5.22/2.89	
5.22/2.89	      0: start -> lbl71 : C'=1, E'=0, [ A>=2 && B==A && C==D && E==F ], cost: 1
5.22/2.89	
5.22/2.89	      2: lbl71 -> lbl71 : C'=1+C, [ A>=2+C && A>=1+C && A>=2+E && C>=1 && E>=0 && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      3: lbl71 -> cut : E'=1+E, [ A>=3+E && A>=2+E && A>=2 && E>=0 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      5: cut -> lbl71 : C'=1, [ A>=2 && A>=2+E && E>=1 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      6: cut -> cut : C'=0, E'=1+E, [ 1>=A && A>=3+E && A>=2+E && E>=1 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      8: start0 -> start : B'=A, C'=D, E'=F, [], cost: 1
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Removed rules with unsatisfiable guard:
5.22/2.89	
5.22/2.89	   Start location: start0
5.22/2.89	
5.22/2.89	      0: start -> lbl71 : C'=1, E'=0, [ A>=2 && B==A && C==D && E==F ], cost: 1
5.22/2.89	
5.22/2.89	      2: lbl71 -> lbl71 : C'=1+C, [ A>=2+C && A>=1+C && A>=2+E && C>=1 && E>=0 && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      3: lbl71 -> cut : E'=1+E, [ A>=3+E && A>=2+E && A>=2 && E>=0 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      5: cut -> lbl71 : C'=1, [ A>=2 && A>=2+E && E>=1 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      8: start0 -> start : B'=A, C'=D, E'=F, [], cost: 1
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Simplified all rules, resulting in:
5.22/2.89	
5.22/2.89	   Start location: start0
5.22/2.89	
5.22/2.89	      0: start -> lbl71 : C'=1, E'=0, [ A>=2 && B==A && C==D && E==F ], cost: 1
5.22/2.89	
5.22/2.89	      2: lbl71 -> lbl71 : C'=1+C, [ A>=2+C && A>=2+E && C>=1 && E>=0 && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      3: lbl71 -> cut : E'=1+E, [ A>=3+E && A>=2 && E>=0 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      5: cut -> lbl71 : C'=1, [ A>=2+E && E>=1 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      8: start0 -> start : B'=A, C'=D, E'=F, [], cost: 1
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	### Simplification by acceleration and chaining ###
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Accelerating simple loops of location 1.
5.22/2.89	
5.22/2.89	   Accelerating the following rules:
5.22/2.89	
5.22/2.89	      2: lbl71 -> lbl71 : C'=1+C, [ A>=2+C && A>=2+E && C>=1 && E>=0 && B==A ], cost: 1
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	   Accelerated rule 2 with metering function -1-C+A, yielding the new rule 9.
5.22/2.89	
5.22/2.89	   Removing the simple loops: 2.
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Accelerated all simple loops using metering functions (where possible):
5.22/2.89	
5.22/2.89	   Start location: start0
5.22/2.89	
5.22/2.89	      0: start -> lbl71 : C'=1, E'=0, [ A>=2 && B==A && C==D && E==F ], cost: 1
5.22/2.89	
5.22/2.89	      3: lbl71 -> cut : E'=1+E, [ A>=3+E && A>=2 && E>=0 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      9: lbl71 -> lbl71 : C'=-1+A, [ A>=2+C && A>=2+E && C>=1 && E>=0 && B==A ], cost: -1-C+A
5.22/2.89	
5.22/2.89	      5: cut -> lbl71 : C'=1, [ A>=2+E && E>=1 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      8: start0 -> start : B'=A, C'=D, E'=F, [], cost: 1
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Chained accelerated rules (with incoming rules):
5.22/2.89	
5.22/2.89	   Start location: start0
5.22/2.89	
5.22/2.89	      0: start -> lbl71 : C'=1, E'=0, [ A>=2 && B==A && C==D && E==F ], cost: 1
5.22/2.89	
5.22/2.89	     10: start -> lbl71 : C'=-1+A, E'=0, [ B==A && C==D && E==F && A>=3 ], cost: -1+A
5.22/2.89	
5.22/2.89	      3: lbl71 -> cut : E'=1+E, [ A>=3+E && A>=2 && E>=0 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	      5: cut -> lbl71 : C'=1, [ A>=2+E && E>=1 && 1+C==A && B==A ], cost: 1
5.22/2.89	
5.22/2.89	     11: cut -> lbl71 : C'=-1+A, [ A>=2+E && E>=1 && 1+C==A && B==A && A>=3 ], cost: -1+A
5.22/2.89	
5.22/2.89	      8: start0 -> start : B'=A, C'=D, E'=F, [], cost: 1
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Eliminated locations (on tree-shaped paths):
5.22/2.89	
5.22/2.89	   Start location: start0
5.22/2.89	
5.22/2.89	     14: lbl71 -> lbl71 : C'=1, E'=1+E, [ A>=3+E && A>=2 && E>=0 && 1+C==A && B==A ], cost: 2
5.22/2.89	
5.22/2.89	     15: lbl71 -> lbl71 : C'=-1+A, E'=1+E, [ A>=3+E && E>=0 && 1+C==A && B==A && A>=3 ], cost: A
5.22/2.89	
5.22/2.89	     12: start0 -> lbl71 : B'=A, C'=1, E'=0, [ A>=2 ], cost: 2
5.22/2.89	
5.22/2.89	     13: start0 -> lbl71 : B'=A, C'=-1+A, E'=0, [ A>=3 ], cost: A
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Accelerating simple loops of location 1.
5.22/2.89	
5.22/2.89	   Accelerating the following rules:
5.22/2.89	
5.22/2.89	     14: lbl71 -> lbl71 : C'=1, E'=1+E, [ A>=3+E && A>=2 && E>=0 && 1+C==A && B==A ], cost: 2
5.22/2.89	
5.22/2.89	     15: lbl71 -> lbl71 : C'=-1+A, E'=1+E, [ A>=3+E && E>=0 && 1+C==A && B==A && A>=3 ], cost: A
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	   Accelerated rule 14 with NONTERM (after strengthening guard), yielding the new rule 16.
5.22/2.89	
5.22/2.89	   Accelerated rule 15 with metering function -2+A-E, yielding the new rule 17.
5.22/2.89	
5.22/2.89	   Removing the simple loops: 15.
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Accelerated all simple loops using metering functions (where possible):
5.22/2.89	
5.22/2.89	   Start location: start0
5.22/2.89	
5.22/2.89	     14: lbl71 -> lbl71 : C'=1, E'=1+E, [ A>=3+E && A>=2 && E>=0 && 1+C==A && B==A ], cost: 2
5.22/2.89	
5.22/2.89	     16: lbl71 -> [6] : [ A>=3+E && E>=0 && 1+C==A && B==A && 2==A ], cost: INF
5.22/2.89	
5.22/2.89	     17: lbl71 -> lbl71 : C'=-1+A, E'=-2+A, [ A>=3+E && E>=0 && 1+C==A && B==A && A>=3 ], cost: A*(-2+A-E)
5.22/2.89	
5.22/2.89	     12: start0 -> lbl71 : B'=A, C'=1, E'=0, [ A>=2 ], cost: 2
5.22/2.89	
5.22/2.89	     13: start0 -> lbl71 : B'=A, C'=-1+A, E'=0, [ A>=3 ], cost: A
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Chained accelerated rules (with incoming rules):
5.22/2.89	
5.22/2.89	   Start location: start0
5.22/2.89	
5.22/2.89	     12: start0 -> lbl71 : B'=A, C'=1, E'=0, [ A>=2 ], cost: 2
5.22/2.89	
5.22/2.89	     13: start0 -> lbl71 : B'=A, C'=-1+A, E'=0, [ A>=3 ], cost: A
5.22/2.89	
5.22/2.89	     18: start0 -> lbl71 : B'=A, C'=1, E'=1, [ A>=3 ], cost: 2+A
5.22/2.89	
5.22/2.89	     19: start0 -> lbl71 : B'=A, C'=-1+A, E'=-2+A, [ A>=3 ], cost: A+A*(-2+A)
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Removed unreachable locations (and leaf rules with constant cost):
5.22/2.89	
5.22/2.89	   Start location: start0
5.22/2.89	
5.22/2.89	     13: start0 -> lbl71 : B'=A, C'=-1+A, E'=0, [ A>=3 ], cost: A
5.22/2.89	
5.22/2.89	     18: start0 -> lbl71 : B'=A, C'=1, E'=1, [ A>=3 ], cost: 2+A
5.22/2.89	
5.22/2.89	     19: start0 -> lbl71 : B'=A, C'=-1+A, E'=-2+A, [ A>=3 ], cost: A+A*(-2+A)
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	### Computing asymptotic complexity ###
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Fully simplified ITS problem
5.22/2.89	
5.22/2.89	   Start location: start0
5.22/2.89	
5.22/2.89	     18: start0 -> lbl71 : B'=A, C'=1, E'=1, [ A>=3 ], cost: 2+A
5.22/2.89	
5.22/2.89	     19: start0 -> lbl71 : B'=A, C'=-1+A, E'=-2+A, [ A>=3 ], cost: A+A*(-2+A)
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	Computing asymptotic complexity for rule 18
5.22/2.89	
5.22/2.89	   Solved the limit problem by the following transformations:
5.22/2.89	
5.22/2.89	      Created initial limit problem:
5.22/2.89	
5.22/2.89	      2+A (+), -2+A (+/+!) [not solved]
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	      removing all constraints (solved by SMT)
5.22/2.89	
5.22/2.89	      resulting limit problem: [solved]
5.22/2.89	
5.22/2.89	
5.22/2.89	
5.22/2.89	      applying transformation rule (C) using substitution {A==n}
5.22/2.90	
5.22/2.90	      resulting limit problem:
5.22/2.90	
5.22/2.90	      [solved]
5.22/2.90	
5.22/2.90	
5.22/2.90	
5.22/2.90	   Solution:
5.22/2.90	
5.22/2.90	      A / n
5.22/2.90	
5.22/2.90	   Resulting cost 2+n has complexity: Poly(n^1)
5.22/2.90	
5.22/2.90	
5.22/2.90	
5.22/2.90	Found new complexity Poly(n^1).
5.22/2.90	
5.22/2.90	
5.22/2.90	
5.22/2.90	Computing asymptotic complexity for rule 19
5.22/2.90	
5.22/2.90	   Solved the limit problem by the following transformations:
5.22/2.90	
5.22/2.90	      Created initial limit problem:
5.22/2.90	
5.22/2.90	      -2+A (+/+!), -A+A^2 (+) [not solved]
5.22/2.90	
5.22/2.90	
5.22/2.90	
5.22/2.90	      removing all constraints (solved by SMT)
5.22/2.90	
5.22/2.90	      resulting limit problem: [solved]
5.22/2.90	
5.22/2.90	
5.22/2.90	
5.22/2.90	      applying transformation rule (C) using substitution {A==n}
5.22/2.90	
5.22/2.90	      resulting limit problem:
5.22/2.90	
5.22/2.90	      [solved]
5.22/2.90	
5.22/2.90	
5.22/2.90	
5.22/2.90	   Solution:
5.22/2.90	
5.22/2.90	      A / n
5.22/2.90	
5.22/2.90	   Resulting cost -n+n^2 has complexity: Poly(n^2)
5.22/2.90	
5.22/2.90	
5.22/2.90	
5.22/2.90	Found new complexity Poly(n^2).
5.22/2.90	
5.22/2.90	
5.22/2.90	
5.22/2.90	Obtained the following overall complexity (w.r.t. the length of the input n):
5.22/2.90	
5.22/2.90	   Complexity:  Poly(n^2)
5.22/2.90	
5.22/2.90	   Cpx degree:  2
5.22/2.90	
5.22/2.90	   Solved cost: -n+n^2
5.22/2.90	
5.22/2.90	   Rule cost:   A+A*(-2+A)
5.22/2.90	
5.22/2.90	   Rule guard:  [ A>=3 ]
5.22/2.90	
5.22/2.90	
5.22/2.90	
5.22/2.90	WORST_CASE(Omega(n^2),?)
5.22/2.90	
5.22/2.90	
5.22/2.90	----------------------------------------
5.22/2.90	
5.22/2.90	(4)
5.22/2.90	BOUNDS(n^2, INF)
5.22/2.90	EOF