5.35/2.41	WORST_CASE(Omega(n^3), O(n^3))
5.35/2.42	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.35/2.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.35/2.42	
5.35/2.42	
5.35/2.42	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^3, n^3).
5.35/2.42	
5.35/2.42	(0) CpxIntTrs
5.35/2.42	(1) Koat Proof [FINISHED, 328 ms]
5.35/2.42	(2) BOUNDS(1, n^3)
5.35/2.42	(3) Loat Proof [FINISHED, 617 ms]
5.35/2.42	(4) BOUNDS(n^3, INF)
5.35/2.42	
5.35/2.42	
5.35/2.42	----------------------------------------
5.35/2.42	
5.35/2.42	(0)
5.35/2.42	Obligation:
5.35/2.42	Complexity Int TRS consisting of the following rules:
5.35/2.42	start(A, B, C, D, E, F, G, H) -> Com_1(a(A, B, C, D, E, F, G, H)) :|: A >= 1 && B >= A && B <= A && C >= D && C <= D && E >= F && E <= F && G >= H && G <= H
5.35/2.42	a(A, B, C, D, E, F, G, H) -> Com_1(d(A, B, 1, D, E, F, G, H)) :|: A >= 1 && G >= H && G <= H && E >= F && E <= F && C >= D && C <= D && B >= A && B <= A
5.35/2.42	d(A, B, C, D, E, F, G, H) -> Com_1(b(A, B, C, D, E, F, 1 + C, H)) :|: A >= C + 1 && A >= C && A >= 1 && C >= 1 && B >= A && B <= A
5.35/2.42	d(A, B, C, D, E, F, G, H) -> Com_1(halt(A, B, C, D, E, F, G, H)) :|: A >= 1 && C >= A && C <= A && B >= A && B <= A
5.35/2.42	b(A, B, C, D, E, F, G, H) -> Com_1(d(A, B, 1 + C, D, E, F, G, H)) :|: A >= C + 1 && C >= 1 && A >= C && G >= A + 1 && G <= A + 1 && B >= A && B <= A
5.35/2.42	b(A, B, C, D, E, F, G, H) -> Com_1(c(A, B, C, D, B, F, G, H)) :|: A >= G && A + 1 >= G && A >= C + 1 && C >= 1 && G >= C + 1 && B >= A && B <= A
5.35/2.42	c(A, B, C, D, E, F, G, H) -> Com_1(c(A, B, C, D, E - 1, F, G, H)) :|: E >= C + 1 && A >= E && A >= G && C >= 1 && E >= C && G >= C + 1 && B >= A && B <= A
5.35/2.42	c(A, B, C, D, E, F, G, H) -> Com_1(b(A, B, C, D, E, F, 1 + G, H)) :|: A >= E && A >= G && E >= 1 && G >= E + 1 && C >= E && C <= E && B >= A && B <= A
5.35/2.42	start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, A, D, D, F, F, H, H)) :|: TRUE
5.35/2.42	
5.35/2.42	The start-symbols are:[start0_8]
5.35/2.42	
5.35/2.42	
5.35/2.42	----------------------------------------
5.35/2.42	
5.35/2.42	(1) Koat Proof (FINISHED)
5.35/2.42	YES(?, 20*ar_0 + 40*ar_0^2 + 16*ar_0^3 + 4)
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Initial complexity problem:
5.35/2.42	
5.35/2.42	1:	T:
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_6 = ar_7 /\ ar_4 = ar_5 /\ ar_2 = ar_3 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_2 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_2 = ar_0 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_0 >= ar_2 /\ ar_6 = ar_0 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\ ar_0 + 1 >= ar_6 /\ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_2 >= 1 /\ ar_4 >= ar_2 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_4 >= 1 /\ ar_6 >= ar_4 + 1 /\ ar_2 = ar_4 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(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_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ]
5.35/2.42	
5.35/2.42		start location:	koat_start
5.35/2.42	
5.35/2.42		leaf cost:	0
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.35/2.42	
5.35/2.42	2:	T:
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ]
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)    a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_6 = ar_7 /\ ar_4 = ar_5 /\ ar_2 = ar_3 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_2 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_2 = ar_0 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_0 >= ar_2 /\ ar_6 = ar_0 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\ ar_0 + 1 >= ar_6 /\ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_2 >= 1 /\ ar_4 >= ar_2 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_4 >= 1 /\ ar_6 >= ar_4 + 1 /\ ar_2 = ar_4 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(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_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ]
5.35/2.42	
5.35/2.42		start location:	koat_start
5.35/2.42	
5.35/2.42		leaf cost:	0
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	A polynomial rank function with
5.35/2.42	
5.35/2.42		Pol(start) = 1
5.35/2.42	
5.35/2.42		Pol(a) = 1
5.35/2.42	
5.35/2.42		Pol(d) = 1
5.35/2.42	
5.35/2.42		Pol(b) = 1
5.35/2.42	
5.35/2.42		Pol(halt) = 0
5.35/2.42	
5.35/2.42		Pol(c) = 1
5.35/2.42	
5.35/2.42		Pol(start0) = 1
5.35/2.42	
5.35/2.42		Pol(koat_start) = 1
5.35/2.42	
5.35/2.42	orients all transitions weakly and the transition
5.35/2.42	
5.35/2.42		d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_2 = ar_0 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42	strictly and produces the following problem:
5.35/2.42	
5.35/2.42	3:	T:
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ]
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)    a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_6 = ar_7 /\ ar_4 = ar_5 /\ ar_2 = ar_3 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_2 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)    d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_2 = ar_0 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_0 >= ar_2 /\ ar_6 = ar_0 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\ ar_0 + 1 >= ar_6 /\ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_2 >= 1 /\ ar_4 >= ar_2 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)    c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_4 >= 1 /\ ar_6 >= ar_4 + 1 /\ ar_2 = ar_4 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(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_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ]
5.35/2.42	
5.35/2.42		start location:	koat_start
5.35/2.42	
5.35/2.42		leaf cost:	0
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	A polynomial rank function with
5.35/2.42	
5.35/2.42		Pol(start) = 2*V_2
5.35/2.42	
5.35/2.42		Pol(a) = 2*V_2
5.35/2.42	
5.35/2.42		Pol(d) = 2*V_2 - 2*V_3
5.35/2.42	
5.35/2.42		Pol(b) = 2*V_2 - 2*V_3 - 1
5.35/2.42	
5.35/2.42		Pol(halt) = 2*V_2 - 2*V_3
5.35/2.42	
5.35/2.42		Pol(c) = 2*V_2 - 2*V_3 - 1
5.35/2.42	
5.35/2.42		Pol(start0) = 2*V_1
5.35/2.42	
5.35/2.42		Pol(koat_start) = 2*V_1
5.35/2.42	
5.35/2.42	orients all transitions weakly and the transitions
5.35/2.42	
5.35/2.42		d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_2 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42		b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_0 >= ar_2 /\ ar_6 = ar_0 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42	strictly and produces the following problem:
5.35/2.42	
5.35/2.42	4:	T:
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)         start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ]
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)         a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_6 = ar_7 /\ ar_4 = ar_5 /\ ar_2 = ar_3 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 2*ar_0, Cost: 1)    d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_2 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)         d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_2 = ar_0 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 2*ar_0, Cost: 1)    b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_0 >= ar_2 /\ ar_6 = ar_0 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)         b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\ ar_0 + 1 >= ar_6 /\ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)         c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_2 >= 1 /\ ar_4 >= ar_2 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)         c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_4 >= 1 /\ ar_6 >= ar_4 + 1 /\ ar_2 = ar_4 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(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_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ]
5.35/2.42	
5.35/2.42		start location:	koat_start
5.35/2.42	
5.35/2.42		leaf cost:	0
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	A polynomial rank function with
5.35/2.42	
5.35/2.42		Pol(c) = 2*V_1 - 2*V_7 + 1
5.35/2.42	
5.35/2.42		Pol(b) = 2*V_1 - 2*V_7 + 2
5.35/2.42	
5.35/2.42	and size complexities
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-2) = ar_3
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-4) = ar_5
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-6) = ar_7
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-2) = ar_0 + 1
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-4) = ar_0
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-6) = ?
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-2) = ar_0 + 1
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-4) = ar_0
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-6) = ?
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-2) = ar_0 + 1
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-4) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-6) = ?
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-2) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-4) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-6) = ?
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-2) = ar_0 + 1
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-4) = ar_0 + ar_5
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-6) = ?
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-2) = ar_0 + 1
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-4) = ar_0 + ar_5
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-6) = ar_0
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-2) = 1
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-4) = ar_5
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-6) = ar_7
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-2) = ar_3
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-4) = ar_5
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-6) = ar_7
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42	orients the transitions
5.35/2.42	
5.35/2.42		c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_2 >= 1 /\ ar_4 >= ar_2 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42		c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_4 >= 1 /\ ar_6 >= ar_4 + 1 /\ ar_2 = ar_4 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42		b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\ ar_0 + 1 >= ar_6 /\ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42	weakly and the transitions
5.35/2.42	
5.35/2.42		c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_4 >= 1 /\ ar_6 >= ar_4 + 1 /\ ar_2 = ar_4 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42		b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\ ar_0 + 1 >= ar_6 /\ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42	strictly and produces the following problem:
5.35/2.42	
5.35/2.42	5:	T:
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)                    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ]
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)                    a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_6 = ar_7 /\ ar_4 = ar_5 /\ ar_2 = ar_3 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 2*ar_0, Cost: 1)               d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_2 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)                    d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_2 = ar_0 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 2*ar_0, Cost: 1)               b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_0 >= ar_2 /\ ar_6 = ar_0 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 8*ar_0^2 + 4*ar_0, Cost: 1)    b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\ ar_0 + 1 >= ar_6 /\ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: ?, Cost: 1)                    c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_2 >= 1 /\ ar_4 >= ar_2 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 8*ar_0^2 + 4*ar_0, Cost: 1)    c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_4 >= 1 /\ ar_6 >= ar_4 + 1 /\ ar_2 = ar_4 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(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_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 0)                    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ]
5.35/2.42	
5.35/2.42		start location:	koat_start
5.35/2.42	
5.35/2.42		leaf cost:	0
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	A polynomial rank function with
5.35/2.42	
5.35/2.42		Pol(c) = -V_3 + V_5 + 1
5.35/2.42	
5.35/2.42	and size complexities
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		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
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-2) = ar_3
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-4) = ar_5
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-6) = ar_7
5.35/2.42	
5.35/2.42		S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-2) = ar_0 + 1
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-4) = ar_0
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-6) = 5*ar_0 + 8*ar_0^2
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_4 >= 1 /\\ ar_6 >= ar_4 + 1 /\\ ar_2 = ar_4 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-2) = ar_0 + 1
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-4) = ar_0
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-6) = 5*ar_0 + 8*ar_0^2
5.35/2.42	
5.35/2.42		S("c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\\ ar_0 >= ar_4 /\\ ar_0 >= ar_6 /\\ ar_2 >= 1 /\\ ar_4 >= ar_2 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-2) = ar_0 + 1
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-4) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-6) = 5*ar_0 + 8*ar_0^2
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\\ ar_0 + 1 >= ar_6 /\\ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_6 >= ar_2 + 1 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-2) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-4) = ar_0
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-6) = 5*ar_0 + 8*ar_0^2
5.35/2.42	
5.35/2.42		S("b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_2 >= 1 /\\ ar_0 >= ar_2 /\\ ar_6 = ar_0 + 1 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-2) = ar_0 + 1
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-4) = ar_0 + ar_5
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-6) = ar_7 + 5*ar_0 + 8*ar_0^2
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_2 = ar_0 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-2) = ar_0 + 1
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-4) = ar_0 + ar_5
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-6) = ar_0
5.35/2.42	
5.35/2.42		S("d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\\ ar_0 >= ar_2 /\\ ar_0 >= 1 /\\ ar_2 >= 1 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-2) = 1
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-4) = ar_5
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-6) = ar_7
5.35/2.42	
5.35/2.42		S("a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_6 = ar_7 /\\ ar_4 = ar_5 /\\ ar_2 = ar_3 /\\ ar_1 = ar_0 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-0) = ar_0
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-1) = ar_0
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-2) = ar_3
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-3) = ar_3
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-4) = ar_5
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-5) = ar_5
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-6) = ar_7
5.35/2.42	
5.35/2.42		S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\\ ar_1 = ar_0 /\\ ar_2 = ar_3 /\\ ar_4 = ar_5 /\\ ar_6 = ar_7 ]", 0-7) = ar_7
5.35/2.42	
5.35/2.42	orients the transitions
5.35/2.42	
5.35/2.42		c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_2 >= 1 /\ ar_4 >= ar_2 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42	weakly and the transition
5.35/2.42	
5.35/2.42		c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_2 >= 1 /\ ar_4 >= ar_2 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42	strictly and produces the following problem:
5.35/2.42	
5.35/2.42	6:	T:
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)                                 start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_1 = ar_0 /\ ar_2 = ar_3 /\ ar_4 = ar_5 /\ ar_6 = ar_7 ]
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)                                 a(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_6 = ar_7 /\ ar_4 = ar_5 /\ ar_2 = ar_3 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 2*ar_0, Cost: 1)                            d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2 + 1, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_0 >= ar_2 /\ ar_0 >= 1 /\ ar_2 >= 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 1)                                 d(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(halt(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= 1 /\ ar_2 = ar_0 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 2*ar_0, Cost: 1)                            b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(d(ar_0, ar_1, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_0 >= ar_2 /\ ar_6 = ar_0 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 8*ar_0^2 + 4*ar_0, Cost: 1)                 b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_6 /\ ar_0 + 1 >= ar_6 /\ ar_0 >= ar_2 + 1 /\ ar_2 >= 1 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 16*ar_0^3 + 24*ar_0^2 + 8*ar_0, Cost: 1)    c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(c(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5, ar_6, ar_7)) [ ar_4 >= ar_2 + 1 /\ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_2 >= 1 /\ ar_4 >= ar_2 /\ ar_6 >= ar_2 + 1 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(Comp: 8*ar_0^2 + 4*ar_0, Cost: 1)                 c(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(b(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_0 >= ar_4 /\ ar_0 >= ar_6 /\ ar_4 >= 1 /\ ar_6 >= ar_4 + 1 /\ ar_2 = ar_4 /\ ar_1 = ar_0 ]
5.35/2.42	
5.35/2.42			(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_0, ar_3, ar_3, ar_5, ar_5, ar_7, ar_7))
5.35/2.42	
5.35/2.42			(Comp: 1, Cost: 0)                                 koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ]
5.35/2.42	
5.35/2.42		start location:	koat_start
5.35/2.42	
5.35/2.42		leaf cost:	0
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Complexity upper bound 20*ar_0 + 40*ar_0^2 + 16*ar_0^3 + 4
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Time: 0.345 sec (SMT: 0.271 sec)
5.35/2.42	
5.35/2.42	
5.35/2.42	----------------------------------------
5.35/2.42	
5.35/2.42	(2)
5.35/2.42	BOUNDS(1, n^3)
5.35/2.42	
5.35/2.42	----------------------------------------
5.35/2.42	
5.35/2.42	(3) Loat Proof (FINISHED)
5.35/2.42	
5.35/2.42	
5.35/2.42	### Pre-processing the ITS problem ###
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Initial linear ITS problem
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	      0: start -> a : [ A>=1 && B==A && C==D && E==F && G==H ], cost: 1
5.35/2.42	
5.35/2.42	      1: a -> d : C'=1, [ A>=1 && G==H && E==F && C==D && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      2: d -> b : G'=1+C, [ A>=1+C && A>=C && A>=1 && C>=1 && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      3: d -> halt : [ A>=1 && C==A && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      4: b -> d : C'=1+C, [ A>=1+C && C>=1 && A>=C && G==1+A && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      5: b -> c : E'=B, [ A>=G && 1+A>=G && A>=1+C && C>=1 && G>=1+C && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      6: c -> c : E'=-1+E, [ E>=1+C && A>=E && A>=G && C>=1 && E>=C && G>=1+C && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      7: c -> b : G'=1+G, [ A>=E && A>=G && E>=1 && G>=1+E && C==E && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      8: start0 -> start : B'=A, C'=D, E'=F, G'=H, [], cost: 1
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Removed unreachable and leaf rules:
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	      0: start -> a : [ A>=1 && B==A && C==D && E==F && G==H ], cost: 1
5.35/2.42	
5.35/2.42	      1: a -> d : C'=1, [ A>=1 && G==H && E==F && C==D && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      2: d -> b : G'=1+C, [ A>=1+C && A>=C && A>=1 && C>=1 && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      4: b -> d : C'=1+C, [ A>=1+C && C>=1 && A>=C && G==1+A && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      5: b -> c : E'=B, [ A>=G && 1+A>=G && A>=1+C && C>=1 && G>=1+C && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      6: c -> c : E'=-1+E, [ E>=1+C && A>=E && A>=G && C>=1 && E>=C && G>=1+C && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      7: c -> b : G'=1+G, [ A>=E && A>=G && E>=1 && G>=1+E && C==E && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      8: start0 -> start : B'=A, C'=D, E'=F, G'=H, [], cost: 1
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Simplified all rules, resulting in:
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	      0: start -> a : [ A>=1 && B==A && C==D && E==F && G==H ], cost: 1
5.35/2.42	
5.35/2.42	      1: a -> d : C'=1, [ A>=1 && G==H && E==F && C==D && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      2: d -> b : G'=1+C, [ A>=1+C && A>=1 && C>=1 && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      4: b -> d : C'=1+C, [ A>=1+C && C>=1 && G==1+A && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      5: b -> c : E'=B, [ A>=G && A>=1+C && C>=1 && G>=1+C && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      6: c -> c : E'=-1+E, [ E>=1+C && A>=E && A>=G && C>=1 && G>=1+C && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      7: c -> b : G'=1+G, [ A>=G && E>=1 && G>=1+E && C==E && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      8: start0 -> start : B'=A, C'=D, E'=F, G'=H, [], cost: 1
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	### Simplification by acceleration and chaining ###
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Accelerating simple loops of location 4.
5.35/2.42	
5.35/2.42	   Accelerating the following rules:
5.35/2.42	
5.35/2.42	      6: c -> c : E'=-1+E, [ E>=1+C && A>=E && A>=G && C>=1 && G>=1+C && B==A ], cost: 1
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	   Accelerated rule 6 with metering function -C+E, yielding the new rule 9.
5.35/2.42	
5.35/2.42	   Removing the simple loops: 6.
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Accelerated all simple loops using metering functions (where possible):
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	      0: start -> a : [ A>=1 && B==A && C==D && E==F && G==H ], cost: 1
5.35/2.42	
5.35/2.42	      1: a -> d : C'=1, [ A>=1 && G==H && E==F && C==D && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      2: d -> b : G'=1+C, [ A>=1+C && A>=1 && C>=1 && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      4: b -> d : C'=1+C, [ A>=1+C && C>=1 && G==1+A && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      5: b -> c : E'=B, [ A>=G && A>=1+C && C>=1 && G>=1+C && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      7: c -> b : G'=1+G, [ A>=G && E>=1 && G>=1+E && C==E && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      9: c -> c : E'=C, [ E>=1+C && A>=E && A>=G && C>=1 && G>=1+C && B==A ], cost: -C+E
5.35/2.42	
5.35/2.42	      8: start0 -> start : B'=A, C'=D, E'=F, G'=H, [], cost: 1
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Chained accelerated rules (with incoming rules):
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	      0: start -> a : [ A>=1 && B==A && C==D && E==F && G==H ], cost: 1
5.35/2.42	
5.35/2.42	      1: a -> d : C'=1, [ A>=1 && G==H && E==F && C==D && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      2: d -> b : G'=1+C, [ A>=1+C && A>=1 && C>=1 && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      4: b -> d : C'=1+C, [ A>=1+C && C>=1 && G==1+A && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      5: b -> c : E'=B, [ A>=G && A>=1+C && C>=1 && G>=1+C && B==A ], cost: 1
5.35/2.42	
5.35/2.42	     10: b -> c : E'=C, [ A>=G && A>=1+C && C>=1 && G>=1+C && B==A && B>=1+C ], cost: 1-C+B
5.35/2.42	
5.35/2.42	      7: c -> b : G'=1+G, [ A>=G && E>=1 && G>=1+E && C==E && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      8: start0 -> start : B'=A, C'=D, E'=F, G'=H, [], cost: 1
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Eliminated locations (on linear paths):
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	      2: d -> b : G'=1+C, [ A>=1+C && A>=1 && C>=1 && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      4: b -> d : C'=1+C, [ A>=1+C && C>=1 && G==1+A && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      5: b -> c : E'=B, [ A>=G && A>=1+C && C>=1 && G>=1+C && B==A ], cost: 1
5.35/2.42	
5.35/2.42	     10: b -> c : E'=C, [ A>=G && A>=1+C && C>=1 && G>=1+C && B==A && B>=1+C ], cost: 1-C+B
5.35/2.42	
5.35/2.42	      7: c -> b : G'=1+G, [ A>=G && E>=1 && G>=1+E && C==E && B==A ], cost: 1
5.35/2.42	
5.35/2.42	     12: start0 -> d : B'=A, C'=1, E'=F, G'=H, [ A>=1 ], cost: 3
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Eliminated locations (on tree-shaped paths):
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	      2: d -> b : G'=1+C, [ A>=1+C && A>=1 && C>=1 && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      4: b -> d : C'=1+C, [ A>=1+C && C>=1 && G==1+A && B==A ], cost: 1
5.35/2.42	
5.35/2.42	     13: b -> b : E'=C, G'=1+G, [ A>=G && A>=1+C && C>=1 && G>=1+C && B==A && B>=1+C ], cost: 2-C+B
5.35/2.42	
5.35/2.42	     12: start0 -> d : B'=A, C'=1, E'=F, G'=H, [ A>=1 ], cost: 3
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Accelerating simple loops of location 3.
5.35/2.42	
5.35/2.42	   Accelerating the following rules:
5.35/2.42	
5.35/2.42	     13: b -> b : E'=C, G'=1+G, [ A>=G && A>=1+C && C>=1 && G>=1+C && B==A && B>=1+C ], cost: 2-C+B
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	   Accelerated rule 13 with metering function 1-G+A, yielding the new rule 14.
5.35/2.42	
5.35/2.42	   Removing the simple loops: 13.
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Accelerated all simple loops using metering functions (where possible):
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	      2: d -> b : G'=1+C, [ A>=1+C && A>=1 && C>=1 && B==A ], cost: 1
5.35/2.42	
5.35/2.42	      4: b -> d : C'=1+C, [ A>=1+C && C>=1 && G==1+A && B==A ], cost: 1
5.35/2.42	
5.35/2.42	     14: b -> b : E'=C, G'=1+A, [ A>=G && A>=1+C && C>=1 && G>=1+C && B==A && B>=1+C ], cost: 2-2*G-(-1+G-A)*B+2*A+(-1+G-A)*C
5.35/2.42	
5.35/2.42	     12: start0 -> d : B'=A, C'=1, E'=F, G'=H, [ A>=1 ], cost: 3
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Chained accelerated rules (with incoming rules):
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	      2: d -> b : G'=1+C, [ A>=1+C && A>=1 && C>=1 && B==A ], cost: 1
5.35/2.42	
5.35/2.42	     15: d -> b : E'=C, G'=1+A, [ A>=1+C && A>=1 && C>=1 && B==A && B>=1+C ], cost: 1-(C-A)*B+C*(C-A)-2*C+2*A
5.35/2.42	
5.35/2.42	      4: b -> d : C'=1+C, [ A>=1+C && C>=1 && G==1+A && B==A ], cost: 1
5.35/2.42	
5.35/2.42	     12: start0 -> d : B'=A, C'=1, E'=F, G'=H, [ A>=1 ], cost: 3
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Eliminated locations (on tree-shaped paths):
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	     16: d -> d : C'=1+C, E'=C, G'=1+A, [ A>=1+C && A>=1 && C>=1 && B==A && B>=1+C ], cost: 2-(C-A)*B+C*(C-A)-2*C+2*A
5.35/2.42	
5.35/2.42	     12: start0 -> d : B'=A, C'=1, E'=F, G'=H, [ A>=1 ], cost: 3
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Accelerating simple loops of location 2.
5.35/2.42	
5.35/2.42	   Accelerating the following rules:
5.35/2.42	
5.35/2.42	     16: d -> d : C'=1+C, E'=C, G'=1+A, [ A>=1+C && A>=1 && C>=1 && B==A && B>=1+C ], cost: 2-(C-A)*B+C*(C-A)-2*C+2*A
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	   Accelerated rule 16 with metering function -C+2*A-B, yielding the new rule 17.
5.35/2.42	
5.35/2.42	   Removing the simple loops: 16.
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Accelerated all simple loops using metering functions (where possible):
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	     17: d -> d : C'=2*A-B, E'=-1+2*A-B, G'=1+A, [ A>=1+C && A>=1 && C>=1 && B==A && B>=1+C && -C+2*A-B>=1 ], cost: -1/2*A*(C-2*A+B)^2-C^2*(C-2*A+B)-19/6*C-5/2*A*(C-2*A+B)+C*(C-2*A+B)*B-1/2*(C-2*A+B)^2*B-A*(C-2*A+B)*B-1/2*(C-2*A+B)*B+19/3*A+C*(C-2*A+B)^2+C*A*(C-2*A+B)-1/3*(C-2*A+B)^3+3*C*(C-2*A+B)-19/6*B-3/2*(C-2*A+B)^2
5.35/2.42	
5.35/2.42	     12: start0 -> d : B'=A, C'=1, E'=F, G'=H, [ A>=1 ], cost: 3
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Chained accelerated rules (with incoming rules):
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	     12: start0 -> d : B'=A, C'=1, E'=F, G'=H, [ A>=1 ], cost: 3
5.35/2.42	
5.35/2.42	     18: start0 -> d : B'=A, C'=A, E'=-1+A, G'=1+A, [ A>=2 ], cost: 11/6+(-1+A)*A+(-1+A)*A^2+7/6*A-(-1+A)^2*A+1/3*(-1+A)^3-1/2*(-1+A)^2
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Removed unreachable locations (and leaf rules with constant cost):
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	     18: start0 -> d : B'=A, C'=A, E'=-1+A, G'=1+A, [ A>=2 ], cost: 11/6+(-1+A)*A+(-1+A)*A^2+7/6*A-(-1+A)^2*A+1/3*(-1+A)^3-1/2*(-1+A)^2
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	### Computing asymptotic complexity ###
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Fully simplified ITS problem
5.35/2.42	
5.35/2.42	   Start location: start0
5.35/2.42	
5.35/2.42	     18: start0 -> d : B'=A, C'=A, E'=-1+A, G'=1+A, [ A>=2 ], cost: 11/6+(-1+A)*A+(-1+A)*A^2+7/6*A-(-1+A)^2*A+1/3*(-1+A)^3-1/2*(-1+A)^2
5.35/2.42	
5.35/2.42	
5.35/2.42	
5.35/2.42	Computing asymptotic complexity for rule 18
5.35/2.42	
5.35/2.42	   Solved the limit problem by the following transformations:
5.35/2.42	
5.35/2.43	      Created initial limit problem:
5.35/2.43	
5.35/2.43	      1+7/6*A+1/2*A^2+1/3*A^3 (+), -1+A (+/+!) [not solved]
5.35/2.43	
5.35/2.43	
5.35/2.43	
5.35/2.43	      removing all constraints (solved by SMT)
5.35/2.43	
5.35/2.43	      resulting limit problem: [solved]
5.35/2.43	
5.35/2.43	
5.35/2.43	
5.35/2.43	      applying transformation rule (C) using substitution {A==n}
5.35/2.43	
5.35/2.43	      resulting limit problem:
5.35/2.43	
5.35/2.43	      [solved]
5.35/2.43	
5.35/2.43	
5.35/2.43	
5.35/2.43	   Solution:
5.35/2.43	
5.35/2.43	      A / n
5.35/2.43	
5.35/2.43	   Resulting cost 1+1/2*n^2+7/6*n+1/3*n^3 has complexity: Poly(n^3)
5.35/2.43	
5.35/2.43	
5.35/2.43	
5.35/2.43	Found new complexity Poly(n^3).
5.35/2.43	
5.35/2.43	
5.35/2.43	
5.35/2.43	Obtained the following overall complexity (w.r.t. the length of the input n):
5.35/2.43	
5.35/2.43	   Complexity:  Poly(n^3)
5.35/2.43	
5.35/2.43	   Cpx degree:  3
5.35/2.43	
5.35/2.43	   Solved cost: 1+1/2*n^2+7/6*n+1/3*n^3
5.35/2.43	
5.35/2.43	   Rule cost:   11/6+(-1+A)*A+(-1+A)*A^2+7/6*A-(-1+A)^2*A+1/3*(-1+A)^3-1/2*(-1+A)^2
5.35/2.43	
5.35/2.43	   Rule guard:  [ A>=2 ]
5.35/2.43	
5.35/2.43	
5.35/2.43	
5.35/2.43	WORST_CASE(Omega(n^3),?)
5.35/2.43	
5.35/2.43	
5.35/2.43	----------------------------------------
5.35/2.43	
5.35/2.43	(4)
5.35/2.43	BOUNDS(n^3, INF)
5.35/2.44	EOF