54.93/46.25	WORST_CASE(Omega(n^1), O(n^2))
55.02/46.26	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
55.02/46.26	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
55.02/46.26	
55.02/46.26	
55.02/46.26	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2).
55.02/46.26	
55.02/46.26	(0) CpxIntTrs
55.02/46.26	(1) Koat Proof [FINISHED, 812 ms]
55.02/46.26	(2) BOUNDS(1, n^2)
55.02/46.26	(3) Loat Proof [FINISHED, 5656 ms]
55.02/46.26	(4) BOUNDS(n^1, INF)
55.02/46.26	
55.02/46.26	
55.02/46.26	----------------------------------------
55.02/46.26	
55.02/46.26	(0)
55.02/46.26	Obligation:
55.02/46.26	Complexity Int TRS consisting of the following rules:
55.02/46.26	f2(A, B, C, D, E, F, G, H) -> Com_1(f8(A, B, 0, B, E, F, G, H)) :|: A >= B + 1
55.02/46.26	f8(A, B, C, D, E, F, G, H) -> Com_1(f8(A, B, C, D, E + 1, J, I, H)) :|: A >= E && I >= J
55.02/46.26	f8(A, B, C, D, E, F, G, H) -> Com_1(f8(A, B, J, E, E + 1, I, K, H)) :|: A >= E && I >= 1 + K
55.02/46.26	f19(A, B, C, D, E, F, G, H) -> Com_1(f19(A, B, C, D, E + 1, F, G, J)) :|: A >= E
55.02/46.26	f27(A, B, C, D, E, F, G, H) -> Com_1(f27(A, B, C, D, E + 1, F, G, J)) :|: A >= E
55.02/46.26	f34(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D, E, F, G, H)) :|: 0 >= C + 1
55.02/46.26	f34(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D, E, F, G, H)) :|: C >= 1
55.02/46.26	f36(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E, F, G, J)) :|: 0 >= I + 1 && A >= D && I >= C * K && C * K + K >= I + 1 && K >= J && I >= C * L && C * L + L >= I + 1 && J >= L
55.02/46.26	f36(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E, F, G, J)) :|: I >= 1 && A >= D && I >= C * K && C * K + K >= I + 1 && K >= J && I >= C * L && C * L + L >= I + 1 && J >= L
55.02/46.26	f43(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E + 1, F, G, H)) :|: A >= E
55.02/46.26	f49(A, B, C, D, E, F, G, H) -> Com_1(f49(A, B, C, D, E + 1, F, G, H)) :|: A >= E
55.02/46.26	f36(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D + 1, E, F, G, 0)) :|: A >= D
55.02/46.26	f34(A, B, C, D, E, F, G, H) -> Com_1(f2(A, B + 1, 0, D, E, F, G, H)) :|: C >= 0 && C <= 0
55.02/46.26	f49(A, B, C, D, E, F, G, H) -> Com_1(f36(A, B, C, D + 1, E, F, G, H)) :|: E >= 1 + A
55.02/46.26	f43(A, B, C, D, E, F, G, H) -> Com_1(f49(A, B, C, D, E, F, G, H)) :|: E >= 1 + A
55.02/46.26	f36(A, B, C, D, E, F, G, H) -> Com_1(f2(A, B + 1, C, D, E, F, G, H)) :|: D >= 1 + A
55.02/46.26	f27(A, B, C, D, E, F, G, H) -> Com_1(f34(A, B, C, D, E, F, G, H)) :|: E >= 1 + A
55.02/46.26	f19(A, B, C, D, E, F, G, H) -> Com_1(f27(A, B, C, D, E, F, G, H)) :|: E >= 1 + A
55.02/46.26	f8(A, B, C, D, E, F, G, H) -> Com_1(f34(A, B, C, B, E, F, G, H)) :|: E >= 1 + A && B >= D && B <= D
55.02/46.26	f8(A, B, C, D, E, F, G, H) -> Com_1(f19(A, B, C, D, E, F, G, H)) :|: B >= D + 1 && E >= 1 + A
55.02/46.26	f8(A, B, C, D, E, F, G, H) -> Com_1(f19(A, B, C, D, E, F, G, H)) :|: D >= 1 + B && E >= 1 + A
55.02/46.26	f2(A, B, C, D, E, F, G, H) -> Com_1(f1(A, B, C, D, E, F, G, H)) :|: B >= A
55.02/46.26	start(A, B, C, D, E, F, G, H) -> Com_1(f2(A, B, C, D, E, F, G, H)) :|: TRUE
55.02/46.26	
55.02/46.26	The start-symbols are:[start_8]
55.02/46.26	
55.02/46.26	
55.02/46.26	----------------------------------------
55.02/46.26	
55.02/46.26	(1) Koat Proof (FINISHED)
55.02/46.26	YES(?, 312460831277084*ar_0 + 44637261614517*ar_1 + 267823569666587*ar_4 + 5180*ar_0^2 + 9480*ar_0*ar_4 + 5570*ar_0*ar_1 + 4860*ar_1*ar_4 + 690*ar_1^2 + 4320*ar_4^2 + 267823569662269)
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	Initial complexity problem:
55.02/46.26	
55.02/46.26	1:	T:
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, j, i, ar_7)) [ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1, i, k, ar_7)) [ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, j)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, j)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_2 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 >= 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, j)) [ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, j)) [ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f49(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, 0)) [ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 = 0 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f49(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7))
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ]
55.02/46.26	
55.02/46.26		start location:	koat_start
55.02/46.26	
55.02/46.26		leaf cost:	0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_4].
55.02/46.26	
55.02/46.26	We thus obtain the following problem:
55.02/46.26	
55.02/46.26	2:	T:
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26		start location:	koat_start
55.02/46.26	
55.02/46.26		leaf cost:	0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	Testing for reachability in the complexity graph removes the following transitions from problem 2:
55.02/46.26	
55.02/46.26		f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26		f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26		f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26	We thus obtain the following problem:
55.02/46.26	
55.02/46.26	3:	T:
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
55.02/46.26	
55.02/46.26		start location:	koat_start
55.02/46.26	
55.02/46.26		leaf cost:	0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	Repeatedly propagating knowledge in problem 3 produces the following problem:
55.02/46.26	
55.02/46.26	4:	T:
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
55.02/46.26	
55.02/46.26		start location:	koat_start
55.02/46.26	
55.02/46.26		leaf cost:	0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	A polynomial rank function with
55.02/46.26	
55.02/46.26		Pol(f49) = 1
55.02/46.26	
55.02/46.26		Pol(f36) = 1
55.02/46.26	
55.02/46.26		Pol(f43) = 1
55.02/46.26	
55.02/46.26		Pol(f27) = 1
55.02/46.26	
55.02/46.26		Pol(f34) = 1
55.02/46.26	
55.02/46.26		Pol(f2) = 1
55.02/46.26	
55.02/46.26		Pol(f19) = 1
55.02/46.26	
55.02/46.26		Pol(f8) = 1
55.02/46.26	
55.02/46.26		Pol(f1) = 0
55.02/46.26	
55.02/46.26		Pol(start) = 1
55.02/46.26	
55.02/46.26		Pol(koat_start) = 1
55.02/46.26	
55.02/46.26	orients all transitions weakly and the transition
55.02/46.26	
55.02/46.26		f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26	strictly and produces the following problem:
55.02/46.26	
55.02/46.26	5:	T:
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)    f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)    f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
55.02/46.26	
55.02/46.26		start location:	koat_start
55.02/46.26	
55.02/46.26		leaf cost:	0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	A polynomial rank function with
55.02/46.26	
55.02/46.26		Pol(f49) = V_1 - V_5 + 1
55.02/46.26	
55.02/46.26		Pol(f36) = V_1 - V_5 + 1
55.02/46.26	
55.02/46.26		Pol(f43) = V_1 - V_5 + 1
55.02/46.26	
55.02/46.26		Pol(f27) = V_1 - V_5 + 1
55.02/46.26	
55.02/46.26		Pol(f34) = V_1 - V_5 + 1
55.02/46.26	
55.02/46.26		Pol(f2) = V_1 - V_5 + 1
55.02/46.26	
55.02/46.26		Pol(f19) = V_1 - V_5 + 1
55.02/46.26	
55.02/46.26		Pol(f8) = V_1 - V_5 + 1
55.02/46.26	
55.02/46.26		Pol(f1) = V_1 - V_5
55.02/46.26	
55.02/46.26		Pol(start) = V_1 - V_5 + 1
55.02/46.26	
55.02/46.26		Pol(koat_start) = V_1 - V_5 + 1
55.02/46.26	
55.02/46.26	orients all transitions weakly and the transitions
55.02/46.26	
55.02/46.26		f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26		f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26		f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26	strictly and produces the following problem:
55.02/46.26	
55.02/46.26	6:	T:
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)    f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                  f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                  f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                  start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
55.02/46.26	
55.02/46.26		start location:	koat_start
55.02/46.26	
55.02/46.26		leaf cost:	0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	Repeatedly propagating knowledge in problem 6 produces the following problem:
55.02/46.26	
55.02/46.26	7:	T:
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)        f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)    f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)    f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)        f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)        f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                      f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                      start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
55.02/46.26	
55.02/46.26		start location:	koat_start
55.02/46.26	
55.02/46.26		leaf cost:	0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	A polynomial rank function with
55.02/46.26	
55.02/46.26		Pol(f49) = V_1 - V_2 - 1
55.02/46.26	
55.02/46.26		Pol(f36) = V_1 - V_2 - 1
55.02/46.26	
55.02/46.26		Pol(f43) = V_1 - V_2 - 1
55.02/46.26	
55.02/46.26		Pol(f27) = V_1 - V_2 - 1
55.02/46.26	
55.02/46.26		Pol(f34) = V_1 - V_2 - 1
55.02/46.26	
55.02/46.26		Pol(f2) = V_1 - V_2
55.02/46.26	
55.02/46.26		Pol(f19) = V_1 - V_2 - 1
55.02/46.26	
55.02/46.26		Pol(f8) = V_1 - V_2 - 1
55.02/46.26	
55.02/46.26		Pol(f1) = V_1 - V_2
55.02/46.26	
55.02/46.26		Pol(start) = V_1 - V_2
55.02/46.26	
55.02/46.26		Pol(koat_start) = V_1 - V_2
55.02/46.26	
55.02/46.26	orients all transitions weakly and the transition
55.02/46.26	
55.02/46.26		f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26	strictly and produces the following problem:
55.02/46.26	
55.02/46.26	8:	T:
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)        f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)    f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)    f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)        f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)        f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                      f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_1, Cost: 1)            f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                      f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                      start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
55.02/46.26	
55.02/46.26		start location:	koat_start
55.02/46.26	
55.02/46.26		leaf cost:	0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	Repeatedly propagating knowledge in problem 8 produces the following problem:
55.02/46.26	
55.02/46.26	9:	T:
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                             f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)               f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                             f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)           f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                             f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                             f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                             f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                             f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)           f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)           f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)           f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)               f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)               f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1)    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_1, Cost: 1)                   f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                             f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                             start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 0)                             koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
55.02/46.26	
55.02/46.26		start location:	koat_start
55.02/46.26	
55.02/46.26		leaf cost:	0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	A polynomial rank function with
55.02/46.26	
55.02/46.26		Pol(f49) = 1
55.02/46.26	
55.02/46.26		Pol(f36) = 1
55.02/46.26	
55.02/46.26		Pol(f43) = 1
55.02/46.26	
55.02/46.26		Pol(f2) = 0
55.02/46.26	
55.02/46.26	and size complexities
55.02/46.26	
55.02/46.26		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
55.02/46.26	
55.02/46.26		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
55.02/46.26	
55.02/46.26		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
55.02/46.26	
55.02/46.26		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
55.02/46.26	
55.02/46.26		S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
55.02/46.26	
55.02/46.26		S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
55.02/46.26	
55.02/46.26		S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
55.02/46.26	
55.02/46.26		S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-4) = 4*ar_0 + 4*ar_4 + 192
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-2) = 0
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-3) = 4*ar_0 + 4*ar_4 + 192
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-2) = 0
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26		S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-1) = ?
55.02/46.26	
55.02/46.26		S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48
55.02/46.26	
55.02/46.26	orients the transitions
55.02/46.26	
55.02/46.26		f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26		f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26	weakly and the transition
55.02/46.26	
55.02/46.26		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26	strictly and produces the following problem:
55.02/46.26	
55.02/46.26	10:	T:
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)                    f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)                f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: 15*ar_0 + 13*ar_4 + 2*ar_1 + 13, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)                f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)                f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)                f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)         f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)         f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)         f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)                    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)                    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1)         f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_1, Cost: 1)                        f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                                  f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                                  start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 0)                                  koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
55.02/46.26	
55.02/46.26		start location:	koat_start
55.02/46.26	
55.02/46.26		leaf cost:	0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	Applied AI with 'oct' on problem 10 to obtain the following invariants:
55.02/46.26	
55.02/46.26	  For symbol f19: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0
55.02/46.26	
55.02/46.26	  For symbol f27: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0
55.02/46.26	
55.02/46.26	  For symbol f34: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0
55.02/46.26	
55.02/46.26	  For symbol f36: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0
55.02/46.26	
55.02/46.26	  For symbol f43: -X_4 + X_5 - 1 >= 0 /\ -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_4 >= 0 /\ X_1 - X_2 - 1 >= 0
55.02/46.26	
55.02/46.26	  For symbol f49: -X_4 + X_5 - 1 >= 0 /\ -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_4 >= 0 /\ X_1 - X_2 - 1 >= 0
55.02/46.26	
55.02/46.26	  For symbol f8: X_1 - X_2 - 1 >= 0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	This yielded the following problem:
55.02/46.26	
55.02/46.26	11:	T:
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 0)                                  koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                                  start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                                  f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_1, Cost: 1)                        f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1)         f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)                    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)                    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)         f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 = 0 ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)         f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 >= 1 ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)         f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= ar_2 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)                f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)                f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)                f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 15*ar_0 + 13*ar_4 + 2*ar_1 + 13, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)                f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)                    f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26		start location:	koat_start
55.02/46.26	
55.02/46.26		leaf cost:	0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	Testing for unsatisfiable constraints removes the following transition from problem 11:
55.02/46.26	
55.02/46.26		f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 ]
55.02/46.26	
55.02/46.26	We thus obtain the following problem:
55.02/46.26	
55.02/46.26	12:	T:
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 0)                                  koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                                  start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                                  f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_1, Cost: 1)                        f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1)         f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)                    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)                    f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)         f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 = 0 ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)         f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 >= 1 ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)         f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= ar_2 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)                f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)                f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)                f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 15*ar_0 + 13*ar_4 + 2*ar_1 + 13, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)                f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ?, Cost: 1)                                  f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26		start location:	koat_start
55.02/46.26	
55.02/46.26		leaf cost:	0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	A polynomial rank function with
55.02/46.26	
55.02/46.26		Pol(f49) = 2*V_1 - 3*V_4 + V_5
55.02/46.26	
55.02/46.26		Pol(f36) = 2*V_1 - 3*V_4 + V_5 + 2
55.02/46.26	
55.02/46.26		Pol(f43) = 2*V_1 - 3*V_4 + V_5 + 1
55.02/46.26	
55.02/46.26	and size complexities
55.02/46.26	
55.02/46.26		S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 64691683493
55.02/46.26	
55.02/46.26		S("f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= i + 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= i + 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= i + 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= i + 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= i + 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ i >= 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ i >= 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ i >= 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ i >= 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ i >= 1 /\\ ar_0 >= ar_3 /\\ i >= ar_2*k /\\ ar_2*k + k >= i + 1 /\\ k >= j /\\ i >= ar_2*l /\\ ar_2*l + l >= i + 1 /\\ j >= l ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 2812681891
55.02/46.26	
55.02/46.26		S("f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 122290517
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 122290517
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 1487908720339
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 1487908720339
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-2) = 0
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 1487908720339
55.02/46.26	
55.02/46.26		S("f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 5316979
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-3) = 3*ar_0 + 3*ar_4 + 54
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 231173
55.02/46.26	
55.02/46.26		S("f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-2) = 0
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 231173
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 231173
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-2) = ?
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-3) = ?
55.02/46.26	
55.02/46.26		S("f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-4) = 3*ar_0 + 3*ar_4 + 54
55.02/46.26	
55.02/46.26		S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
55.02/46.26	
55.02/46.26		S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
55.02/46.26	
55.02/46.26		S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
55.02/46.26	
55.02/46.26		S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
55.02/46.26	
55.02/46.26		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
55.02/46.26	
55.02/46.26		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
55.02/46.26	
55.02/46.26		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
55.02/46.26	
55.02/46.26		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
55.02/46.26	
55.02/46.26		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
55.02/46.26	
55.02/46.26	orients the transitions
55.02/46.26	
55.02/46.26		f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26		f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26	weakly and the transitions
55.02/46.26	
55.02/46.26		f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26		f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26	strictly and produces the following problem:
55.02/46.26	
55.02/46.26	13:	T:
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 0)                                                                                                                                                                            koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                                                                                                                                                                            start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, ar_2, ar_3, ar_4))
55.02/46.26	
55.02/46.26			(Comp: 1, Cost: 1)                                                                                                                                                                            f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_1, Cost: 1)                                                                                                                                                                  f2(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1)                                                                                                                                                   f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)                                                                                                                                                              f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= k + 1 ]
55.02/46.26	
55.02/46.26			(Comp: ar_0 + ar_4 + 1, Cost: 1)                                                                                                                                                              f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f8(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= j ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)                                                                                                                                                   f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 = 0 ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)                                                                                                                                                   f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 >= 1 ]
55.02/46.26	
55.02/46.26			(Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1)                                                                                                                                                   f34(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= ar_2 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)                                                                                                                                                          f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1)                                                                                                                                                          f8(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)                                                                                                                                                          f19(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f27(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 15*ar_0 + 13*ar_4 + 2*ar_1 + 13, Cost: 1)                                                                                                                                              f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 1036*ar_0^2 + 1896*ar_0*ar_4 + 1114*ar_0*ar_1 + 972*ar_1*ar_4 + 138*ar_1^2 + 864*ar_4^2 + 62492166255406*ar_0 + 8927452322902*ar_1 + 53564713933308*ar_4 + 53564713932444, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ]
55.02/46.26	
55.02/46.26			(Comp: 1036*ar_0^2 + 1896*ar_0*ar_4 + 1114*ar_0*ar_1 + 972*ar_1*ar_4 + 138*ar_1^2 + 864*ar_4^2 + 62492166255406*ar_0 + 8927452322902*ar_1 + 53564713933308*ar_4 + 53564713932444, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ i >= 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: 1036*ar_0^2 + 1896*ar_0*ar_4 + 1114*ar_0*ar_1 + 972*ar_1*ar_4 + 138*ar_1^2 + 864*ar_4^2 + 62492166255406*ar_0 + 8927452322902*ar_1 + 53564713933308*ar_4 + 53564713932444, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= i + 1 /\ ar_0 >= ar_3 /\ i >= ar_2*k /\ ar_2*k + k >= i + 1 /\ k >= j /\ i >= ar_2*l /\ ar_2*l + l >= i + 1 /\ j >= l ]
55.02/46.26	
55.02/46.26			(Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1)                                                                                                                                                          f27(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 1036*ar_0^2 + 1896*ar_0*ar_4 + 1114*ar_0*ar_1 + 972*ar_1*ar_4 + 138*ar_1^2 + 864*ar_4^2 + 62492166255406*ar_0 + 8927452322902*ar_1 + 53564713933308*ar_4 + 53564713932444, Cost: 1)    f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f49(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26			(Comp: 1036*ar_0^2 + 1896*ar_0*ar_4 + 1114*ar_0*ar_1 + 972*ar_1*ar_4 + 138*ar_1^2 + 864*ar_4^2 + 62492166255406*ar_0 + 8927452322902*ar_1 + 53564713933308*ar_4 + 53564713932444, Cost: 1)    f49(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ]
55.02/46.26	
55.02/46.26		start location:	koat_start
55.02/46.26	
55.02/46.26		leaf cost:	0
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	Complexity upper bound 312460831277084*ar_0 + 44637261614517*ar_1 + 267823569666587*ar_4 + 5180*ar_0^2 + 9480*ar_0*ar_4 + 5570*ar_0*ar_1 + 4860*ar_1*ar_4 + 690*ar_1^2 + 4320*ar_4^2 + 267823569662269
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	Time: 0.809 sec (SMT: 0.591 sec)
55.02/46.26	
55.02/46.26	
55.02/46.26	----------------------------------------
55.02/46.26	
55.02/46.26	(2)
55.02/46.26	BOUNDS(1, n^2)
55.02/46.26	
55.02/46.26	----------------------------------------
55.02/46.26	
55.02/46.26	(3) Loat Proof (FINISHED)
55.02/46.26	
55.02/46.26	
55.02/46.26	### Pre-processing the ITS problem ###
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	Initial linear ITS problem
55.02/46.26	
55.02/46.26	   Start location: start
55.02/46.26	
55.02/46.26	      0: f2 -> f8 : C'=0, D'=B, [ A>=1+B ], cost: 1
55.02/46.26	
55.02/46.26	     21: f2 -> f1 : [ B>=A ], cost: 1
55.02/46.26	
55.02/46.26	      1: f8 -> f8 : E'=1+E, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1
55.02/46.26	
55.02/46.26	      2: f8 -> f8 : C'=free_3, D'=E, E'=1+E, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1
55.02/46.26	
55.02/46.26	     18: f8 -> f34 : D'=B, [ E>=1+A && B==D ], cost: 1
55.02/46.26	
55.02/46.26	     19: f8 -> f19 : [ B>=1+D && E>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	     20: f8 -> f19 : [ D>=1+B && E>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	      3: f19 -> f19 : E'=1+E, H'=free_5, [ A>=E ], cost: 1
55.02/46.26	
55.02/46.26	     17: f19 -> f27 : [ E>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	      4: f27 -> f27 : E'=1+E, H'=free_6, [ A>=E ], cost: 1
55.02/46.26	
55.02/46.26	     16: f27 -> f34 : [ E>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	      5: f34 -> f36 : [ 0>=1+C ], cost: 1
55.02/46.26	
55.02/46.26	      6: f34 -> f36 : [ C>=1 ], cost: 1
55.02/46.26	
55.02/46.26	     12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1
55.02/46.26	
55.02/46.26	      7: f36 -> f43 : H'=free_9, [ 0>=1+free_8 && A>=D && free_8>=C*free_10 && C*free_10+free_10>=1+free_8 && free_10>=free_9 && free_8>=C*free_7 && free_7+C*free_7>=1+free_8 && free_9>=free_7 ], cost: 1
55.02/46.26	
55.02/46.26	      8: f36 -> f43 : H'=free_13, [ free_12>=1 && A>=D && free_12>=C*free_14 && free_14+C*free_14>=1+free_12 && free_14>=free_13 && free_12>=C*free_11 && C*free_11+free_11>=1+free_12 && free_13>=free_11 ], cost: 1
55.02/46.26	
55.02/46.26	     11: f36 -> f36 : D'=1+D, H'=0, [ A>=D ], cost: 1
55.02/46.26	
55.02/46.26	     15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	      9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1
55.02/46.26	
55.02/46.26	     14: f43 -> f49 : [ E>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	     10: f49 -> f49 : E'=1+E, [ A>=E ], cost: 1
55.02/46.26	
55.02/46.26	     13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	     22: start -> f2 : [], cost: 1
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	Removed unreachable and leaf rules:
55.02/46.26	
55.02/46.26	   Start location: start
55.02/46.26	
55.02/46.26	      0: f2 -> f8 : C'=0, D'=B, [ A>=1+B ], cost: 1
55.02/46.26	
55.02/46.26	      1: f8 -> f8 : E'=1+E, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1
55.02/46.26	
55.02/46.26	      2: f8 -> f8 : C'=free_3, D'=E, E'=1+E, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1
55.02/46.26	
55.02/46.26	     18: f8 -> f34 : D'=B, [ E>=1+A && B==D ], cost: 1
55.02/46.26	
55.02/46.26	     19: f8 -> f19 : [ B>=1+D && E>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	     20: f8 -> f19 : [ D>=1+B && E>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	      3: f19 -> f19 : E'=1+E, H'=free_5, [ A>=E ], cost: 1
55.02/46.26	
55.02/46.26	     17: f19 -> f27 : [ E>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	      4: f27 -> f27 : E'=1+E, H'=free_6, [ A>=E ], cost: 1
55.02/46.26	
55.02/46.26	     16: f27 -> f34 : [ E>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	      5: f34 -> f36 : [ 0>=1+C ], cost: 1
55.02/46.26	
55.02/46.26	      6: f34 -> f36 : [ C>=1 ], cost: 1
55.02/46.26	
55.02/46.26	     12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1
55.02/46.26	
55.02/46.26	      7: f36 -> f43 : H'=free_9, [ 0>=1+free_8 && A>=D && free_8>=C*free_10 && C*free_10+free_10>=1+free_8 && free_10>=free_9 && free_8>=C*free_7 && free_7+C*free_7>=1+free_8 && free_9>=free_7 ], cost: 1
55.02/46.26	
55.02/46.26	      8: f36 -> f43 : H'=free_13, [ free_12>=1 && A>=D && free_12>=C*free_14 && free_14+C*free_14>=1+free_12 && free_14>=free_13 && free_12>=C*free_11 && C*free_11+free_11>=1+free_12 && free_13>=free_11 ], cost: 1
55.02/46.26	
55.02/46.26	     11: f36 -> f36 : D'=1+D, H'=0, [ A>=D ], cost: 1
55.02/46.26	
55.02/46.26	     15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	      9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1
55.02/46.26	
55.02/46.26	     14: f43 -> f49 : [ E>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	     10: f49 -> f49 : E'=1+E, [ A>=E ], cost: 1
55.02/46.26	
55.02/46.26	     13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1
55.02/46.26	
55.02/46.26	     22: start -> f2 : [], cost: 1
55.02/46.26	
55.02/46.26	
55.02/46.26	
55.02/46.26	Simplified all rules, resulting in:
55.02/46.26	
55.02/46.26	   Start location: start
55.02/46.26	
55.02/46.26	      0: f2 -> f8 : C'=0, D'=B, [ A>=1+B ], cost: 1
55.02/46.26	
55.02/46.26	      1: f8 -> f8 : E'=1+E, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1
55.02/46.27	
55.02/46.27	      2: f8 -> f8 : C'=free_3, D'=E, E'=1+E, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1
55.02/46.27	
55.02/46.27	     18: f8 -> f34 : D'=B, [ E>=1+A && B==D ], cost: 1
55.02/46.27	
55.02/46.27	     19: f8 -> f19 : [ B>=1+D && E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     20: f8 -> f19 : [ D>=1+B && E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	      3: f19 -> f19 : E'=1+E, H'=free_5, [ A>=E ], cost: 1
55.02/46.27	
55.02/46.27	     17: f19 -> f27 : [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	      4: f27 -> f27 : E'=1+E, H'=free_6, [ A>=E ], cost: 1
55.02/46.27	
55.02/46.27	     16: f27 -> f34 : [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	      5: f34 -> f36 : [ 0>=1+C ], cost: 1
55.02/46.27	
55.02/46.27	      6: f34 -> f36 : [ C>=1 ], cost: 1
55.02/46.27	
55.02/46.27	     12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1
55.02/46.27	
55.02/46.27	      7: f36 -> f43 : H'=free_9, [ A>=D && free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 ], cost: 1
55.02/46.27	
55.02/46.27	      8: f36 -> f43 : H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 ], cost: 1
55.02/46.27	
55.02/46.27	     11: f36 -> f36 : D'=1+D, H'=0, [ A>=D ], cost: 1
55.02/46.27	
55.02/46.27	     15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	      9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1
55.02/46.27	
55.02/46.27	     14: f43 -> f49 : [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     10: f49 -> f49 : E'=1+E, [ A>=E ], cost: 1
55.02/46.27	
55.02/46.27	     13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     22: start -> f2 : [], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	### Simplification by acceleration and chaining ###
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Accelerating simple loops of location 1.
55.02/46.27	
55.02/46.27	   Accelerating the following rules:
55.02/46.27	
55.02/46.27	      1: f8 -> f8 : E'=1+E, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1
55.02/46.27	
55.02/46.27	      2: f8 -> f8 : C'=free_3, D'=E, E'=1+E, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	   Accelerated rule 1 with metering function 1+A-E, yielding the new rule 23.
55.02/46.27	
55.02/46.27	   Accelerated rule 2 with metering function 1+A-E, yielding the new rule 24.
55.02/46.27	
55.02/46.27	   Removing the simple loops: 1 2.
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Accelerating simple loops of location 2.
55.02/46.27	
55.02/46.27	   Accelerating the following rules:
55.02/46.27	
55.02/46.27	      3: f19 -> f19 : E'=1+E, H'=free_5, [ A>=E ], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	   Accelerated rule 3 with metering function 1+A-E, yielding the new rule 25.
55.02/46.27	
55.02/46.27	   Removing the simple loops: 3.
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Accelerating simple loops of location 3.
55.02/46.27	
55.02/46.27	   Accelerating the following rules:
55.02/46.27	
55.02/46.27	      4: f27 -> f27 : E'=1+E, H'=free_6, [ A>=E ], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	   Accelerated rule 4 with metering function 1+A-E, yielding the new rule 26.
55.02/46.27	
55.02/46.27	   Removing the simple loops: 4.
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Accelerating simple loops of location 5.
55.02/46.27	
55.02/46.27	   Accelerating the following rules:
55.02/46.27	
55.02/46.27	     11: f36 -> f36 : D'=1+D, H'=0, [ A>=D ], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	   Accelerated rule 11 with metering function 1-D+A, yielding the new rule 27.
55.02/46.27	
55.02/46.27	   Removing the simple loops: 11.
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Accelerating simple loops of location 6.
55.02/46.27	
55.02/46.27	   Accelerating the following rules:
55.02/46.27	
55.02/46.27	      9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	   Accelerated rule 9 with metering function 1+A-E, yielding the new rule 28.
55.02/46.27	
55.02/46.27	   Removing the simple loops: 9.
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Accelerating simple loops of location 7.
55.02/46.27	
55.02/46.27	   Accelerating the following rules:
55.02/46.27	
55.02/46.27	     10: f49 -> f49 : E'=1+E, [ A>=E ], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	   Accelerated rule 10 with metering function 1+A-E, yielding the new rule 29.
55.02/46.27	
55.02/46.27	   Removing the simple loops: 10.
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Accelerated all simple loops using metering functions (where possible):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	      0: f2 -> f8 : C'=0, D'=B, [ A>=1+B ], cost: 1
55.02/46.27	
55.02/46.27	     18: f8 -> f34 : D'=B, [ E>=1+A && B==D ], cost: 1
55.02/46.27	
55.02/46.27	     19: f8 -> f19 : [ B>=1+D && E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     20: f8 -> f19 : [ D>=1+B && E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     23: f8 -> f8 : E'=1+A, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1+A-E
55.02/46.27	
55.02/46.27	     24: f8 -> f8 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1+A-E
55.02/46.27	
55.02/46.27	     17: f19 -> f27 : [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     25: f19 -> f19 : E'=1+A, H'=free_5, [ A>=E ], cost: 1+A-E
55.02/46.27	
55.02/46.27	     16: f27 -> f34 : [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     26: f27 -> f27 : E'=1+A, H'=free_6, [ A>=E ], cost: 1+A-E
55.02/46.27	
55.02/46.27	      5: f34 -> f36 : [ 0>=1+C ], cost: 1
55.02/46.27	
55.02/46.27	      6: f34 -> f36 : [ C>=1 ], cost: 1
55.02/46.27	
55.02/46.27	     12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1
55.02/46.27	
55.02/46.27	      7: f36 -> f43 : H'=free_9, [ A>=D && free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 ], cost: 1
55.02/46.27	
55.02/46.27	      8: f36 -> f43 : H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 ], cost: 1
55.02/46.27	
55.02/46.27	     15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     27: f36 -> f36 : D'=1+A, H'=0, [ A>=D ], cost: 1-D+A
55.02/46.27	
55.02/46.27	     14: f43 -> f49 : [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     28: f43 -> f43 : E'=1+A, [ A>=E ], cost: 1+A-E
55.02/46.27	
55.02/46.27	     13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     29: f49 -> f49 : E'=1+A, [ A>=E ], cost: 1+A-E
55.02/46.27	
55.02/46.27	     22: start -> f2 : [], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Chained accelerated rules (with incoming rules):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	      0: f2 -> f8 : C'=0, D'=B, [ A>=1+B ], cost: 1
55.02/46.27	
55.02/46.27	     30: f2 -> f8 : C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     31: f2 -> f8 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     18: f8 -> f34 : D'=B, [ E>=1+A && B==D ], cost: 1
55.02/46.27	
55.02/46.27	     19: f8 -> f19 : [ B>=1+D && E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     20: f8 -> f19 : [ D>=1+B && E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     17: f19 -> f27 : [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     16: f27 -> f34 : [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	      5: f34 -> f36 : [ 0>=1+C ], cost: 1
55.02/46.27	
55.02/46.27	      6: f34 -> f36 : [ C>=1 ], cost: 1
55.02/46.27	
55.02/46.27	     12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1
55.02/46.27	
55.02/46.27	     32: f34 -> f36 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A
55.02/46.27	
55.02/46.27	     33: f34 -> f36 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A
55.02/46.27	
55.02/46.27	      7: f36 -> f43 : H'=free_9, [ A>=D && free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 ], cost: 1
55.02/46.27	
55.02/46.27	      8: f36 -> f43 : H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 ], cost: 1
55.02/46.27	
55.02/46.27	     15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     35: f36 -> f43 : E'=1+A, H'=free_9, [ A>=D && free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && A>=E ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     36: f36 -> f43 : E'=1+A, H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && A>=E ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     14: f43 -> f49 : [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     34: f49 -> f36 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A
55.02/46.27	
55.02/46.27	     22: start -> f2 : [], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Eliminated locations (on linear paths):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	      0: f2 -> f8 : C'=0, D'=B, [ A>=1+B ], cost: 1
55.02/46.27	
55.02/46.27	     30: f2 -> f8 : C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     31: f2 -> f8 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     18: f8 -> f34 : D'=B, [ E>=1+A && B==D ], cost: 1
55.02/46.27	
55.02/46.27	     19: f8 -> f19 : [ B>=1+D && E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     20: f8 -> f19 : [ D>=1+B && E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     37: f19 -> f34 : [ E>=1+A ], cost: 2
55.02/46.27	
55.02/46.27	      5: f34 -> f36 : [ 0>=1+C ], cost: 1
55.02/46.27	
55.02/46.27	      6: f34 -> f36 : [ C>=1 ], cost: 1
55.02/46.27	
55.02/46.27	     12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1
55.02/46.27	
55.02/46.27	     32: f34 -> f36 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A
55.02/46.27	
55.02/46.27	     33: f34 -> f36 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A
55.02/46.27	
55.02/46.27	      7: f36 -> f43 : H'=free_9, [ A>=D && free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 ], cost: 1
55.02/46.27	
55.02/46.27	      8: f36 -> f43 : H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 ], cost: 1
55.02/46.27	
55.02/46.27	     15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     35: f36 -> f43 : E'=1+A, H'=free_9, [ A>=D && free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && A>=E ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     36: f36 -> f43 : E'=1+A, H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && A>=E ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     14: f43 -> f49 : [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     34: f49 -> f36 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A
55.02/46.27	
55.02/46.27	     22: start -> f2 : [], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Eliminated locations (on tree-shaped paths):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	     38: f2 -> f34 : C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 2
55.02/46.27	
55.02/46.27	     39: f2 -> f34 : C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     40: f2 -> f19 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     37: f19 -> f34 : [ E>=1+A ], cost: 2
55.02/46.27	
55.02/46.27	      5: f34 -> f36 : [ 0>=1+C ], cost: 1
55.02/46.27	
55.02/46.27	      6: f34 -> f36 : [ C>=1 ], cost: 1
55.02/46.27	
55.02/46.27	     12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1
55.02/46.27	
55.02/46.27	     32: f34 -> f36 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A
55.02/46.27	
55.02/46.27	     33: f34 -> f36 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A
55.02/46.27	
55.02/46.27	     15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     43: f36 -> f49 : H'=free_9, [ A>=D && free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && E>=1+A ], cost: 2
55.02/46.27	
55.02/46.27	     44: f36 -> f49 : H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && E>=1+A ], cost: 2
55.02/46.27	
55.02/46.27	     45: f36 -> f49 : E'=1+A, H'=free_9, [ A>=D && free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && A>=E ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     46: f36 -> f49 : E'=1+A, H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && A>=E ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     34: f49 -> f36 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A
55.02/46.27	
55.02/46.27	     22: start -> f2 : [], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Eliminated locations (on linear paths):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	     38: f2 -> f34 : C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 2
55.02/46.27	
55.02/46.27	     39: f2 -> f34 : C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     47: f2 -> f34 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 5+A-E
55.02/46.27	
55.02/46.27	      5: f34 -> f36 : [ 0>=1+C ], cost: 1
55.02/46.27	
55.02/46.27	      6: f34 -> f36 : [ C>=1 ], cost: 1
55.02/46.27	
55.02/46.27	     12: f34 -> f2 : B'=1+B, C'=0, [ C==0 ], cost: 1
55.02/46.27	
55.02/46.27	     32: f34 -> f36 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A
55.02/46.27	
55.02/46.27	     33: f34 -> f36 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A
55.02/46.27	
55.02/46.27	     15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     43: f36 -> f49 : H'=free_9, [ A>=D && free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && E>=1+A ], cost: 2
55.02/46.27	
55.02/46.27	     44: f36 -> f49 : H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && E>=1+A ], cost: 2
55.02/46.27	
55.02/46.27	     45: f36 -> f49 : E'=1+A, H'=free_9, [ A>=D && free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && A>=E ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     46: f36 -> f49 : E'=1+A, H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && A>=E ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     13: f49 -> f36 : D'=1+D, [ E>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     34: f49 -> f36 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A
55.02/46.27	
55.02/46.27	     22: start -> f2 : [], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Eliminated locations (on tree-shaped paths):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	     41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     48: f2 -> f2 : B'=1+B, C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 3
55.02/46.27	
55.02/46.27	     49: f2 -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E
55.02/46.27	
55.02/46.27	     50: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	     51: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	     52: f2 -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3==0 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	     53: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     54: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     56: f36 -> f36 : D'=1+D, H'=free_9, [ A>=D && free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && E>=1+A ], cost: 3
55.02/46.27	
55.02/46.27	     57: f36 -> f36 : D'=1+A, H'=0, [ free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && E>=1+A && A>=1+D ], cost: 3-D+A
55.02/46.27	
55.02/46.27	     58: f36 -> f36 : D'=1+D, H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && E>=1+A ], cost: 3
55.02/46.27	
55.02/46.27	     59: f36 -> f36 : D'=1+A, H'=0, [ free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && E>=1+A && A>=1+D ], cost: 3-D+A
55.02/46.27	
55.02/46.27	     60: f36 -> f36 : D'=1+D, E'=1+A, H'=free_9, [ A>=D && free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && A>=E ], cost: 4+A-E
55.02/46.27	
55.02/46.27	     61: f36 -> f36 : D'=1+A, E'=1+A, H'=0, [ free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && A>=E && A>=1+D ], cost: 4-D+2*A-E
55.02/46.27	
55.02/46.27	     62: f36 -> f36 : D'=1+D, E'=1+A, H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && A>=E ], cost: 4+A-E
55.02/46.27	
55.02/46.27	     63: f36 -> f36 : D'=1+A, E'=1+A, H'=0, [ free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && A>=E && A>=1+D ], cost: 4-D+2*A-E
55.02/46.27	
55.02/46.27	     22: start -> f2 : [], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Applied pruning (of leafs and parallel rules):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	     41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     48: f2 -> f2 : B'=1+B, C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 3
55.02/46.27	
55.02/46.27	     49: f2 -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E
55.02/46.27	
55.02/46.27	     50: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	     51: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	     52: f2 -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3==0 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	     53: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     54: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     57: f36 -> f36 : D'=1+A, H'=0, [ free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && E>=1+A && A>=1+D ], cost: 3-D+A
55.02/46.27	
55.02/46.27	     59: f36 -> f36 : D'=1+A, H'=0, [ free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && E>=1+A && A>=1+D ], cost: 3-D+A
55.02/46.27	
55.02/46.27	     61: f36 -> f36 : D'=1+A, E'=1+A, H'=0, [ free_10>=free_9 && free_9>=free_7 && C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && A>=E && A>=1+D ], cost: 4-D+2*A-E
55.02/46.27	
55.02/46.27	     62: f36 -> f36 : D'=1+D, E'=1+A, H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && A>=E ], cost: 4+A-E
55.02/46.27	
55.02/46.27	     63: f36 -> f36 : D'=1+A, E'=1+A, H'=0, [ free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && A>=E && A>=1+D ], cost: 4-D+2*A-E
55.02/46.27	
55.02/46.27	     22: start -> f2 : [], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Accelerating simple loops of location 0.
55.02/46.27	
55.02/46.27	   Simplified some of the simple loops (and removed duplicate rules).
55.02/46.27	
55.02/46.27	   Accelerating the following rules:
55.02/46.27	
55.02/46.27	     48: f2 -> f2 : B'=1+B, C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 3
55.02/46.27	
55.02/46.27	     49: f2 -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E
55.02/46.27	
55.02/46.27	     52: f2 -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	   Accelerated rule 48 with metering function A-B, yielding the new rule 64.
55.02/46.27	
55.02/46.27	   Found no metering function for rule 49.
55.02/46.27	
55.02/46.27	   Found no metering function for rule 52.
55.02/46.27	
55.02/46.27	   Removing the simple loops: 48.
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Accelerating simple loops of location 5.
55.02/46.27	
55.02/46.27	   Simplified some of the simple loops (and removed duplicate rules).
55.02/46.27	
55.02/46.27	   Accelerating the following rules:
55.02/46.27	
55.02/46.27	     57: f36 -> f36 : D'=1+A, H'=0, [ C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && E>=1+A && A>=1+D && free_7<=free_10 ], cost: 3-D+A
55.02/46.27	
55.02/46.27	     59: f36 -> f36 : D'=1+A, H'=0, [ 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && E>=1+A && A>=1+D && free_11<=free_14 ], cost: 3-D+A
55.02/46.27	
55.02/46.27	     61: f36 -> f36 : D'=1+A, E'=1+A, H'=0, [ C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && A>=E && A>=1+D && free_7<=free_10 ], cost: 4-D+2*A-E
55.02/46.27	
55.02/46.27	     62: f36 -> f36 : D'=1+D, E'=1+A, H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && A>=E ], cost: 4+A-E
55.02/46.27	
55.02/46.27	     63: f36 -> f36 : D'=1+A, E'=1+A, H'=0, [ 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && A>=E && A>=1+D && free_11<=free_14 ], cost: 4-D+2*A-E
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	   Found no metering function for rule 57.
55.02/46.27	
55.02/46.27	   Found no metering function for rule 59.
55.02/46.27	
55.02/46.27	   Found no metering function for rule 61.
55.02/46.27	
55.02/46.27	   Found no metering function for rule 62.
55.02/46.27	
55.02/46.27	   Found no metering function for rule 63.
55.02/46.27	
55.02/46.27	   Removing the simple loops:.
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Accelerated all simple loops using metering functions (where possible):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	     41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     49: f2 -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E
55.02/46.27	
55.02/46.27	     50: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	     51: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	     52: f2 -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	     53: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     54: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     64: f2 -> f2 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 3*A-3*B
55.02/46.27	
55.02/46.27	     15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     57: f36 -> f36 : D'=1+A, H'=0, [ C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && E>=1+A && A>=1+D && free_7<=free_10 ], cost: 3-D+A
55.02/46.27	
55.02/46.27	     59: f36 -> f36 : D'=1+A, H'=0, [ 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && E>=1+A && A>=1+D && free_11<=free_14 ], cost: 3-D+A
55.02/46.27	
55.02/46.27	     61: f36 -> f36 : D'=1+A, E'=1+A, H'=0, [ C*free_10<=-1 && C*free_7<=-1 && C*free_10<=-1+C*free_10+free_10 && C*free_7<=-1+C*free_10+free_10 && C*free_10<=-1+free_7+C*free_7 && C*free_7<=-1+free_7+C*free_7 && A>=E && A>=1+D && free_7<=free_10 ], cost: 4-D+2*A-E
55.02/46.27	
55.02/46.27	     62: f36 -> f36 : D'=1+D, E'=1+A, H'=free_13, [ A>=D && free_14>=free_13 && free_13>=free_11 && 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && A>=E ], cost: 4+A-E
55.02/46.27	
55.02/46.27	     63: f36 -> f36 : D'=1+A, E'=1+A, H'=0, [ 1<=-1+free_14+C*free_14 && C*free_14<=-1+free_14+C*free_14 && C*free_11<=-1+free_14+C*free_14 && 1<=-1+C*free_11+free_11 && C*free_14<=-1+C*free_11+free_11 && C*free_11<=-1+C*free_11+free_11 && A>=E && A>=1+D && free_11<=free_14 ], cost: 4-D+2*A-E
55.02/46.27	
55.02/46.27	     22: start -> f2 : [], cost: 1
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Chained accelerated rules (with incoming rules):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	     41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     50: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	     51: f2 -> f36 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	     53: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     54: f2 -> f36 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     15: f36 -> f2 : B'=1+B, [ D>=1+A ], cost: 1
55.02/46.27	
55.02/46.27	     65: f36 -> f2 : B'=2+B, C'=0, D'=1+B, E'=1+A, F'=free_1, G'=free, [ D>=1+A && A>=2+B && A>=E && free>=free_1 ], cost: 5+A-E
55.02/46.27	
55.02/46.27	     67: f36 -> f2 : B'=2+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ D>=1+A && A>=2+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     69: f36 -> f2 : B'=A, C'=0, D'=-1+A, [ D>=1+A && A>=2+B && E>=1+A ], cost: -2+3*A-3*B
55.02/46.27	
55.02/46.27	     22: start -> f2 : [], cost: 1
55.02/46.27	
55.02/46.27	     66: start -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E
55.02/46.27	
55.02/46.27	     68: start -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     70: start -> f2 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Eliminated locations (on tree-shaped paths):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	     41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     71: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 8+A-E
55.02/46.27	
55.02/46.27	     72: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && 0>=1+free_3 && A>=2+B ], cost: 5+4*A-E-3*B
55.02/46.27	
55.02/46.27	     73: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 8+A-E
55.02/46.27	
55.02/46.27	     74: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && free_3>=1 && A>=2+B ], cost: 5+4*A-E-3*B
55.02/46.27	
55.02/46.27	     75: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	     76: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E
55.02/46.27	
55.02/46.27	     77: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     78: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     22: start -> f2 : [], cost: 1
55.02/46.27	
55.02/46.27	     66: start -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E
55.02/46.27	
55.02/46.27	     68: start -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     70: start -> f2 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Accelerating simple loops of location 0.
55.02/46.27	
55.02/46.27	   Simplified some of the simple loops (and removed duplicate rules).
55.02/46.27	
55.02/46.27	   Accelerating the following rules:
55.02/46.27	
55.02/46.27	     71: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 8+A-E
55.02/46.27	
55.02/46.27	     73: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 8+A-E
55.02/46.27	
55.02/46.27	     74: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 5+4*A-E-3*B
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	   Found no metering function for rule 71.
55.02/46.27	
55.02/46.27	   Found no metering function for rule 73.
55.02/46.27	
55.02/46.27	   Found no metering function for rule 74.
55.02/46.27	
55.02/46.27	   Removing the simple loops:.
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Accelerated all simple loops using metering functions (where possible):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	     41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     71: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 8+A-E
55.02/46.27	
55.02/46.27	     73: f2 -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 8+A-E
55.02/46.27	
55.02/46.27	     74: f2 -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 5+4*A-E-3*B
55.02/46.27	
55.02/46.27	     77: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     78: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     22: start -> f2 : [], cost: 1
55.02/46.27	
55.02/46.27	     66: start -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E
55.02/46.27	
55.02/46.27	     68: start -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     70: start -> f2 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Chained accelerated rules (with incoming rules):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	     41: f2 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     42: f2 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E
55.02/46.27	
55.02/46.27	     55: f2 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     77: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     78: f2 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     22: start -> f2 : [], cost: 1
55.02/46.27	
55.02/46.27	     66: start -> f2 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E
55.02/46.27	
55.02/46.27	     68: start -> f2 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     70: start -> f2 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B
55.02/46.27	
55.02/46.27	     79: start -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E
55.02/46.27	
55.02/46.27	     80: start -> f2 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 9+A-E
55.02/46.27	
55.02/46.27	     81: start -> f2 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 6+4*A-E-3*B
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Eliminated locations (on tree-shaped paths):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	     82: start -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     83: start -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     84: start -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E
55.02/46.27	
55.02/46.27	     85: start -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 8+A-E
55.02/46.27	
55.02/46.27	     86: start -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 8+A-E
55.02/46.27	
55.02/46.27	     87: start -> [22] : [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E
55.02/46.27	
55.02/46.27	     88: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     89: start -> [22] : [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B
55.02/46.27	
55.02/46.27	     90: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E
55.02/46.27	
55.02/46.27	     91: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 9+A-E
55.02/46.27	
55.02/46.27	     92: start -> [22] : [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 6+4*A-E-3*B
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Applied pruning (of leafs and parallel rules):
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	     82: start -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     83: start -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 3+A-E
55.02/46.27	
55.02/46.27	     84: start -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E
55.02/46.27	
55.02/46.27	     85: start -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 8+A-E
55.02/46.27	
55.02/46.27	     86: start -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 8+A-E
55.02/46.27	
55.02/46.27	     87: start -> [22] : [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E
55.02/46.27	
55.02/46.27	     88: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     89: start -> [22] : [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B
55.02/46.27	
55.02/46.27	     90: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E
55.02/46.27	
55.02/46.27	     92: start -> [22] : [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 6+4*A-E-3*B
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	### Computing asymptotic complexity ###
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Fully simplified ITS problem
55.02/46.27	
55.02/46.27	   Start location: start
55.02/46.27	
55.02/46.27	     86: start -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 8+A-E
55.02/46.27	
55.02/46.27	     87: start -> [22] : [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E
55.02/46.27	
55.02/46.27	     88: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E
55.02/46.27	
55.02/46.27	     89: start -> [22] : [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B
55.02/46.27	
55.02/46.27	     90: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E
55.02/46.27	
55.02/46.27	     92: start -> [22] : [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 6+4*A-E-3*B
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Computing asymptotic complexity for rule 86
55.02/46.27	
55.02/46.27	   Solved the limit problem by the following transformations:
55.02/46.27	
55.02/46.27	      Created initial limit problem:
55.02/46.27	
55.02/46.27	      free_3 (+/+!), -free_4+free_2 (+/+!), 1+A-E (+/+!), 8+A-E (+), A-B (+/+!) [not solved]
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	      applying transformation rule (C) using substitution {A==1+B}
55.02/46.27	
55.02/46.27	      resulting limit problem:
55.02/46.27	
55.02/46.27	      1 (+/+!), free_3 (+/+!), -free_4+free_2 (+/+!), 9-E+B (+), 2-E+B (+/+!) [not solved]
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	      applying transformation rule (C) using substitution {A==E}
55.02/46.27	
55.02/46.27	      resulting limit problem:
55.02/46.27	
55.02/46.27	      1 (+/+!), free_3 (+/+!), -free_4+free_2 (+/+!), 9-E+B (+), 2-E+B (+/+!) [not solved]
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	      applying transformation rule (C) using substitution {free_2==1+free_4}
55.02/46.27	
55.02/46.27	      resulting limit problem:
55.02/46.27	
55.02/46.27	      1 (+/+!), free_3 (+/+!), 9-E+B (+), 2-E+B (+/+!) [not solved]
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	      applying transformation rule (C) using substitution {free_3==1}
55.02/46.27	
55.02/46.27	      resulting limit problem:
55.02/46.27	
55.02/46.27	      1 (+/+!), 9-E+B (+), 2-E+B (+/+!) [not solved]
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	      applying transformation rule (B), deleting 1 (+/+!)
55.02/46.27	
55.02/46.27	      resulting limit problem:
55.02/46.27	
55.02/46.27	      9-E+B (+), 2-E+B (+/+!) [not solved]
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	      removing all constraints (solved by SMT)
55.02/46.27	
55.02/46.27	      resulting limit problem: [solved]
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	      applying transformation rule (C) using substitution {E==-n,B==0}
55.02/46.27	
55.02/46.27	      resulting limit problem:
55.02/46.27	
55.02/46.27	      [solved]
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	   Solution:
55.02/46.27	
55.02/46.27	      free_3 / 1
55.02/46.27	
55.02/46.27	      free_4 / 0
55.02/46.27	
55.02/46.27	      A / 1
55.02/46.27	
55.02/46.27	      E / -n
55.02/46.27	
55.02/46.27	      B / 0
55.02/46.27	
55.02/46.27	      free_2 / 1
55.02/46.27	
55.02/46.27	   Resulting cost 9+n has complexity: Poly(n^1)
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Found new complexity Poly(n^1).
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	Obtained the following overall complexity (w.r.t. the length of the input n):
55.02/46.27	
55.02/46.27	   Complexity:  Poly(n^1)
55.02/46.27	
55.02/46.27	   Cpx degree:  1
55.02/46.27	
55.02/46.27	   Solved cost: 9+n
55.02/46.27	
55.02/46.27	   Rule cost:   8+A-E
55.02/46.27	
55.02/46.27	   Rule guard:  [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ]
55.02/46.27	
55.02/46.27	
55.02/46.27	
55.02/46.27	WORST_CASE(Omega(n^1),?)
55.02/46.27	
55.02/46.27	
55.02/46.27	----------------------------------------
55.02/46.27	
55.02/46.27	(4)
55.02/46.27	BOUNDS(n^1, INF)
55.02/46.27	EOF