8.47/3.72	WORST_CASE(Omega(n^1), O(n^1))
8.47/3.74	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
8.47/3.74	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.47/3.74	
8.47/3.74	
8.47/3.74	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
8.47/3.74	
8.47/3.74	(0) CpxIntTrs
8.47/3.74	(1) Koat Proof [FINISHED, 816 ms]
8.47/3.74	(2) BOUNDS(1, n^1)
8.47/3.74	(3) Loat Proof [FINISHED, 1857 ms]
8.47/3.74	(4) BOUNDS(n^1, INF)
8.47/3.74	
8.47/3.74	
8.47/3.74	----------------------------------------
8.47/3.74	
8.47/3.74	(0)
8.47/3.74	Obligation:
8.47/3.74	Complexity Int TRS consisting of the following rules:
8.47/3.74	start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, H - 10, C, 1, E, H, G, H)) :|: A >= 101 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
8.47/3.74	start(A, B, C, D, E, F, G, H) -> Com_1(lbl111(A, B, C, 2, E, 11 + H, G, H)) :|: 100 >= A && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
8.47/3.74	lbl161(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 89 >= A && D >= 1 && D <= 1 && H >= A && H <= A && F >= 101 && F <= 101 && B >= 91 && B <= 91
8.47/3.74	lbl161(A, B, C, D, E, F, G, H) -> Com_1(lbl161(A, F - 20, C, D - 1, E, F - 10, G, H)) :|: 0 >= 10 && 89 >= A && 0 >= 1 && D >= 2 && D <= 2 && H >= A && H <= A && F >= 101 && F <= 101 && B >= 91 && B <= 91
8.47/3.74	lbl161(A, B, C, D, E, F, G, H) -> Com_1(lbl221(A, B, C, D, E, 1 + F, G, H)) :|: 0 >= 2 && 89 >= A && H >= A && H <= A && F >= 101 && F <= 101 && D >= 1 && D <= 1 && B >= 91 && B <= 91
8.47/3.74	lbl161(A, B, C, D, E, F, G, H) -> Com_1(lbl221(A, B, C, D, E, 1 + F, G, H)) :|: 0 >= 1 && 89 >= A && H >= A && H <= A && F >= 101 && F <= 101 && D >= 1 && D <= 1 && B >= 91 && B <= 91
8.47/3.74	lbl161(A, B, C, D, E, F, G, H) -> Com_1(lbl221(A, B, C, D - 1, E, F - 9, G, H)) :|: 0 >= 10 && 0 >= 2 && 89 >= A && H >= A && H <= A && F >= 101 && F <= 101 && D >= 1 && D <= 1 && B >= 91 && B <= 91
8.47/3.74	lbl221(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 1 >= D && D >= 2 && F >= 102 && 111 >= F && F + 10 >= A + 11 * D && 89 >= A && H >= A && H <= A && B >= C && B <= C
8.47/3.74	lbl221(A, B, C, D, E, F, G, H) -> Com_1(lbl161(A, F - 20, C, D - 1, E, F - 10, G, H)) :|: 99 >= A && 89 >= A && F >= 111 && F <= 111 && D >= 2 && D <= 2 && H >= A && H <= A && B >= C && B <= C
8.47/3.74	lbl221(A, B, C, D, E, F, G, H) -> Com_1(lbl221(A, B, C, D, E, 1 + F, G, H)) :|: D >= 3 && 110 >= F && D >= 2 && F >= 102 && 111 >= F && F + 10 >= A + 11 * D && 89 >= A && H >= A && H <= A && B >= C && B <= C
8.47/3.74	lbl221(A, B, C, D, E, F, G, H) -> Com_1(lbl221(A, B, C, D, E, 1 + F, G, H)) :|: D >= 2 && 110 >= F && F >= 102 && 111 >= F && F + 10 >= A + 11 * D && 89 >= A && H >= A && H <= A && B >= C && B <= C
8.47/3.74	lbl221(A, B, C, D, E, F, G, H) -> Com_1(lbl221(A, B, C, D - 1, E, F - 9, G, H)) :|: D >= 3 && D >= 2 && 121 >= A + 11 * D && 89 >= A && F >= 111 && F <= 111 && H >= A && H <= A && B >= C && B <= C
8.47/3.74	lbl111(A, B, C, D, E, F, G, H) -> Com_1(lbl111(A, B, C, 1 + D, E, 11 + F, G, H)) :|: 111 >= 11 * D + A && 122 >= 11 * D + A && 11 * D >= 22 && H >= A && H <= A && B >= C && B <= C && F + 11 >= 11 * D + A && F + 11 <= 11 * D + A
8.47/3.74	lbl111(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: 11 * D + A >= 112 && 1 >= D && 122 >= 11 * D + A && 11 * D >= 22 && H >= A && H <= A && B >= C && B <= C && F + 11 >= 11 * D + A && F + 11 <= 11 * D + A
8.47/3.74	lbl111(A, B, C, D, E, F, G, H) -> Com_1(lbl161(A, F - 20, C, D - 1, E, F - 10, G, H)) :|: F >= 111 && F <= 111 && D >= 2 && D <= 2 && H >= 100 && H <= 100 && B >= C && B <= C && A >= 100 && A <= 100
8.47/3.74	lbl111(A, B, C, D, E, F, G, H) -> Com_1(lbl221(A, B, C, D, E, 1 + F, G, H)) :|: 11 * D + A >= 112 && D >= 3 && 121 >= 11 * D + A && 122 >= 11 * D + A && 11 * D >= 22 && H >= A && H <= A && B >= C && B <= C && F + 11 >= 11 * D + A && F + 11 <= 11 * D + A
8.47/3.74	lbl111(A, B, C, D, E, F, G, H) -> Com_1(lbl221(A, B, C, D, E, 1 + F, G, H)) :|: 11 * D + A >= 112 && D >= 2 && 121 >= 11 * D + A && 122 >= 11 * D + A && 11 * D >= 22 && H >= A && H <= A && B >= C && B <= C && F + 11 >= 11 * D + A && F + 11 <= 11 * D + A
8.47/3.74	lbl111(A, B, C, D, E, F, G, H) -> Com_1(lbl221(A, B, C, D - 1, E, F - 9, G, H)) :|: D >= 3 && 11 * D >= 22 && F >= 111 && F <= 111 && H + 11 * D >= 122 && H + 11 * D <= 122 && B >= C && B <= C && A + 11 * D >= 122 && A + 11 * D <= 122
8.47/3.74	start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, E, E, G, G, A)) :|: TRUE
8.47/3.74	
8.47/3.74	The start-symbols are:[start0_8]
8.47/3.74	
8.47/3.74	
8.47/3.74	----------------------------------------
8.47/3.74	
8.47/3.74	(1) Koat Proof (FINISHED)
8.47/3.74	YES(?, 44*ar_0 + 4335)
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Initial complexity problem:
8.47/3.74	
8.47/3.74	1:	T:
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_7 - 10, ar_2, 1, ar_4, ar_7, ar_6, ar_7)) [ ar_0 >= 101 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl111(ar_0, ar_1, ar_2, 2, ar_4, ar_7 + 11, ar_6, ar_7)) [ 100 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 89 >= ar_0 /\ ar_3 = 1 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl161(ar_0, ar_5 - 20, ar_2, ar_3 - 1, ar_4, ar_5 - 10, ar_6, ar_7)) [ 0 >= 10 /\ 89 >= ar_0 /\ 0 >= 1 /\ ar_3 = 2 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 0 >= 2 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_3 = 1 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 0 >= 1 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_3 = 1 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ 0 >= 10 /\ 0 >= 2 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_3 = 1 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 1 >= ar_3 /\ ar_3 >= 2 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl161(ar_0, ar_5 - 20, ar_2, ar_3 - 1, ar_4, ar_5 - 10, ar_6, ar_7)) [ 99 >= ar_0 /\ 89 >= ar_0 /\ ar_5 = 111 /\ ar_3 = 2 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_3 >= 3 /\ 110 >= ar_5 /\ ar_3 >= 2 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_3 >= 2 /\ 110 >= ar_5 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ ar_3 >= 3 /\ ar_3 >= 2 /\ 121 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_5 = 111 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5 + 11, ar_6, ar_7)) [ 111 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ 1 >= ar_3 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl161(ar_0, ar_5 - 20, ar_2, ar_3 - 1, ar_4, ar_5 - 10, ar_6, ar_7)) [ ar_5 = 111 /\ ar_3 = 2 /\ ar_7 = 100 /\ ar_1 = ar_2 /\ ar_0 = 100 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ ar_3 >= 3 /\ 121 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ ar_3 >= 2 /\ 121 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ ar_3 >= 3 /\ 11*ar_3 >= 22 /\ ar_5 = 111 /\ ar_7 + 11*ar_3 = 122 /\ ar_1 = ar_2 /\ ar_0 + 11*ar_3 = 122 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ]
8.47/3.74	
8.47/3.74		start location:	koat_start
8.47/3.74	
8.47/3.74		leaf cost:	0
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Testing for reachability in the complexity graph removes the following transitions from problem 1:
8.47/3.74	
8.47/3.74		lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl161(ar_0, ar_5 - 20, ar_2, ar_3 - 1, ar_4, ar_5 - 10, ar_6, ar_7)) [ 0 >= 10 /\ 89 >= ar_0 /\ 0 >= 1 /\ ar_3 = 2 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74		lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 0 >= 2 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_3 = 1 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74		lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 0 >= 1 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_3 = 1 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74		lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ 0 >= 10 /\ 0 >= 2 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_3 = 1 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74		lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 1 >= ar_3 /\ ar_3 >= 2 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74		lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ 1 >= ar_3 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74	We thus obtain the following problem:
8.47/3.74	
8.47/3.74	2:	T:
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 89 >= ar_0 /\ ar_3 = 1 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl161(ar_0, ar_5 - 20, ar_2, ar_3 - 1, ar_4, ar_5 - 10, ar_6, ar_7)) [ 99 >= ar_0 /\ 89 >= ar_0 /\ ar_5 = 111 /\ ar_3 = 2 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ ar_3 >= 3 /\ ar_3 >= 2 /\ 121 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_5 = 111 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_3 >= 2 /\ 110 >= ar_5 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_3 >= 3 /\ 110 >= ar_5 /\ ar_3 >= 2 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ ar_3 >= 3 /\ 11*ar_3 >= 22 /\ ar_5 = 111 /\ ar_7 + 11*ar_3 = 122 /\ ar_1 = ar_2 /\ ar_0 + 11*ar_3 = 122 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ ar_3 >= 3 /\ 121 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ ar_3 >= 2 /\ 121 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl161(ar_0, ar_5 - 20, ar_2, ar_3 - 1, ar_4, ar_5 - 10, ar_6, ar_7)) [ ar_5 = 111 /\ ar_3 = 2 /\ ar_7 = 100 /\ ar_1 = ar_2 /\ ar_0 = 100 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5 + 11, ar_6, ar_7)) [ 111 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl111(ar_0, ar_1, ar_2, 2, ar_4, ar_7 + 11, ar_6, ar_7)) [ 100 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_7 - 10, ar_2, 1, ar_4, ar_7, ar_6, ar_7)) [ ar_0 >= 101 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ]
8.47/3.74	
8.47/3.74		start location:	koat_start
8.47/3.74	
8.47/3.74		leaf cost:	0
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Repeatedly propagating knowledge in problem 2 produces the following problem:
8.47/3.74	
8.47/3.74	3:	T:
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 89 >= ar_0 /\ ar_3 = 1 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl161(ar_0, ar_5 - 20, ar_2, ar_3 - 1, ar_4, ar_5 - 10, ar_6, ar_7)) [ 99 >= ar_0 /\ 89 >= ar_0 /\ ar_5 = 111 /\ ar_3 = 2 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ ar_3 >= 3 /\ ar_3 >= 2 /\ 121 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_5 = 111 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_3 >= 2 /\ 110 >= ar_5 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_3 >= 3 /\ 110 >= ar_5 /\ ar_3 >= 2 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ ar_3 >= 3 /\ 11*ar_3 >= 22 /\ ar_5 = 111 /\ ar_7 + 11*ar_3 = 122 /\ ar_1 = ar_2 /\ ar_0 + 11*ar_3 = 122 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ ar_3 >= 3 /\ 121 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ ar_3 >= 2 /\ 121 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl161(ar_0, ar_5 - 20, ar_2, ar_3 - 1, ar_4, ar_5 - 10, ar_6, ar_7)) [ ar_5 = 111 /\ ar_3 = 2 /\ ar_7 = 100 /\ ar_1 = ar_2 /\ ar_0 = 100 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5 + 11, ar_6, ar_7)) [ 111 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl111(ar_0, ar_1, ar_2, 2, ar_4, ar_7 + 11, ar_6, ar_7)) [ 100 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_7 - 10, ar_2, 1, ar_4, ar_7, ar_6, ar_7)) [ ar_0 >= 101 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ]
8.47/3.74	
8.47/3.74		start location:	koat_start
8.47/3.74	
8.47/3.74		leaf cost:	0
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	A polynomial rank function with
8.47/3.74	
8.47/3.74		Pol(lbl161) = 1
8.47/3.74	
8.47/3.74		Pol(stop) = 0
8.47/3.74	
8.47/3.74		Pol(lbl221) = 2
8.47/3.74	
8.47/3.74		Pol(lbl111) = 3
8.47/3.74	
8.47/3.74		Pol(start) = 3
8.47/3.74	
8.47/3.74		Pol(start0) = 3
8.47/3.74	
8.47/3.74		Pol(koat_start) = 3
8.47/3.74	
8.47/3.74	orients all transitions weakly and the transitions
8.47/3.74	
8.47/3.74		lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl161(ar_0, ar_5 - 20, ar_2, ar_3 - 1, ar_4, ar_5 - 10, ar_6, ar_7)) [ 99 >= ar_0 /\ 89 >= ar_0 /\ ar_5 = 111 /\ ar_3 = 2 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74		lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 89 >= ar_0 /\ ar_3 = 1 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74		lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ ar_3 >= 3 /\ 121 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74		lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ ar_3 >= 2 /\ 121 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74		lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ ar_3 >= 3 /\ 11*ar_3 >= 22 /\ ar_5 = 111 /\ ar_7 + 11*ar_3 = 122 /\ ar_1 = ar_2 /\ ar_0 + 11*ar_3 = 122 ]
8.47/3.74	
8.47/3.74	strictly and produces the following problem:
8.47/3.74	
8.47/3.74	4:	T:
8.47/3.74	
8.47/3.74			(Comp: 3, Cost: 1)    lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 89 >= ar_0 /\ ar_3 = 1 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74			(Comp: 3, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl161(ar_0, ar_5 - 20, ar_2, ar_3 - 1, ar_4, ar_5 - 10, ar_6, ar_7)) [ 99 >= ar_0 /\ 89 >= ar_0 /\ ar_5 = 111 /\ ar_3 = 2 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ ar_3 >= 3 /\ ar_3 >= 2 /\ 121 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_5 = 111 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_3 >= 2 /\ 110 >= ar_5 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_3 >= 3 /\ 110 >= ar_5 /\ ar_3 >= 2 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: 3, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ ar_3 >= 3 /\ 11*ar_3 >= 22 /\ ar_5 = 111 /\ ar_7 + 11*ar_3 = 122 /\ ar_1 = ar_2 /\ ar_0 + 11*ar_3 = 122 ]
8.47/3.74	
8.47/3.74			(Comp: 3, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ ar_3 >= 3 /\ 121 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 3, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ ar_3 >= 2 /\ 121 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl161(ar_0, ar_5 - 20, ar_2, ar_3 - 1, ar_4, ar_5 - 10, ar_6, ar_7)) [ ar_5 = 111 /\ ar_3 = 2 /\ ar_7 = 100 /\ ar_1 = ar_2 /\ ar_0 = 100 ]
8.47/3.74	
8.47/3.74			(Comp: ?, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5 + 11, ar_6, ar_7)) [ 111 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl111(ar_0, ar_1, ar_2, 2, ar_4, ar_7 + 11, ar_6, ar_7)) [ 100 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_7 - 10, ar_2, 1, ar_4, ar_7, ar_6, ar_7)) [ ar_0 >= 101 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ]
8.47/3.74	
8.47/3.74		start location:	koat_start
8.47/3.74	
8.47/3.74		leaf cost:	0
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	A polynomial rank function with
8.47/3.74	
8.47/3.74		Pol(lbl161) = -11*V_2 + 980
8.47/3.74	
8.47/3.74		Pol(stop) = -11*V_6 + 1079
8.47/3.74	
8.47/3.74		Pol(lbl221) = 110*V_4 - 11*V_6 + 991
8.47/3.74	
8.47/3.74		Pol(lbl111) = 110*V_4 - 11*V_6 + 980
8.47/3.74	
8.47/3.74		Pol(start) = -11*V_1 + 1079
8.47/3.74	
8.47/3.74		Pol(start0) = -11*V_1 + 1079
8.47/3.74	
8.47/3.74		Pol(koat_start) = -11*V_1 + 1079
8.47/3.74	
8.47/3.74	orients all transitions weakly and the transitions
8.47/3.74	
8.47/3.74		lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_3 >= 3 /\ 110 >= ar_5 /\ ar_3 >= 2 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74		lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_3 >= 2 /\ 110 >= ar_5 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74		lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ ar_3 >= 3 /\ ar_3 >= 2 /\ 121 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_5 = 111 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74		lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5 + 11, ar_6, ar_7)) [ 111 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74	strictly and produces the following problem:
8.47/3.74	
8.47/3.74	5:	T:
8.47/3.74	
8.47/3.74			(Comp: 3, Cost: 1)                 lbl161(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 89 >= ar_0 /\ ar_3 = 1 /\ ar_7 = ar_0 /\ ar_5 = 101 /\ ar_1 = 91 ]
8.47/3.74	
8.47/3.74			(Comp: 3, Cost: 1)                 lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl161(ar_0, ar_5 - 20, ar_2, ar_3 - 1, ar_4, ar_5 - 10, ar_6, ar_7)) [ 99 >= ar_0 /\ 89 >= ar_0 /\ ar_5 = 111 /\ ar_3 = 2 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: 11*ar_0 + 1079, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ ar_3 >= 3 /\ ar_3 >= 2 /\ 121 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_5 = 111 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: 11*ar_0 + 1079, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_3 >= 2 /\ 110 >= ar_5 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: 11*ar_0 + 1079, Cost: 1)    lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ ar_3 >= 3 /\ 110 >= ar_5 /\ ar_3 >= 2 /\ ar_5 >= 102 /\ 111 >= ar_5 /\ ar_5 + 10 >= ar_0 + 11*ar_3 /\ 89 >= ar_0 /\ ar_7 = ar_0 /\ ar_1 = ar_2 ]
8.47/3.74	
8.47/3.74			(Comp: 3, Cost: 1)                 lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5 - 9, ar_6, ar_7)) [ ar_3 >= 3 /\ 11*ar_3 >= 22 /\ ar_5 = 111 /\ ar_7 + 11*ar_3 = 122 /\ ar_1 = ar_2 /\ ar_0 + 11*ar_3 = 122 ]
8.47/3.74	
8.47/3.74			(Comp: 3, Cost: 1)                 lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ ar_3 >= 3 /\ 121 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 3, Cost: 1)                 lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl221(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5 + 1, ar_6, ar_7)) [ 11*ar_3 + ar_0 >= 112 /\ ar_3 >= 2 /\ 121 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 1)                 lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl161(ar_0, ar_5 - 20, ar_2, ar_3 - 1, ar_4, ar_5 - 10, ar_6, ar_7)) [ ar_5 = 111 /\ ar_3 = 2 /\ ar_7 = 100 /\ ar_1 = ar_2 /\ ar_0 = 100 ]
8.47/3.74	
8.47/3.74			(Comp: 11*ar_0 + 1079, Cost: 1)    lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5 + 11, ar_6, ar_7)) [ 111 >= 11*ar_3 + ar_0 /\ 122 >= 11*ar_3 + ar_0 /\ 11*ar_3 >= 22 /\ ar_7 = ar_0 /\ ar_1 = ar_2 /\ ar_5 + 11 = 11*ar_3 + ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 1)                 start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(lbl111(ar_0, ar_1, ar_2, 2, ar_4, ar_7 + 11, ar_6, ar_7)) [ 100 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 1)                 start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(stop(ar_0, ar_7 - 10, ar_2, 1, ar_4, ar_7, ar_6, ar_7)) [ ar_0 >= 101 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_6 /\ ar_7 = ar_0 ]
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 1)                 start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_6, ar_6, ar_0))
8.47/3.74	
8.47/3.74			(Comp: 1, Cost: 0)                 koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ]
8.47/3.74	
8.47/3.74		start location:	koat_start
8.47/3.74	
8.47/3.74		leaf cost:	0
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Complexity upper bound 44*ar_0 + 4335
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Time: 0.748 sec (SMT: 0.608 sec)
8.47/3.74	
8.47/3.74	
8.47/3.74	----------------------------------------
8.47/3.74	
8.47/3.74	(2)
8.47/3.74	BOUNDS(1, n^1)
8.47/3.74	
8.47/3.74	----------------------------------------
8.47/3.74	
8.47/3.74	(3) Loat Proof (FINISHED)
8.47/3.74	
8.47/3.74	
8.47/3.74	### Pre-processing the ITS problem ###
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Initial linear ITS problem
8.47/3.74	
8.47/3.74	   Start location: start0
8.47/3.74	
8.47/3.74	      0: start -> stop : B'=-10+H, D'=1, F'=H, [ A>=101 && B==C && D==E && F==G && H==A ], cost: 1
8.47/3.74	
8.47/3.74	      1: start -> lbl111 : D'=2, F'=11+H, [ 100>=A && B==C && D==E && F==G && H==A ], cost: 1
8.47/3.74	
8.47/3.74	      2: lbl161 -> stop : [ 89>=A && D==1 && H==A && F==101 && B==91 ], cost: 1
8.47/3.74	
8.47/3.74	      3: lbl161 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ 0>=10 && 89>=A && 0>=1 && D==2 && H==A && F==101 && B==91 ], cost: 1
8.47/3.74	
8.47/3.74	      4: lbl161 -> lbl221 : F'=1+F, [ 0>=2 && 89>=A && H==A && F==101 && D==1 && B==91 ], cost: 1
8.47/3.74	
8.47/3.74	      5: lbl161 -> lbl221 : F'=1+F, [ 0>=1 && 89>=A && H==A && F==101 && D==1 && B==91 ], cost: 1
8.47/3.74	
8.47/3.74	      6: lbl161 -> lbl221 : D'=-1+D, F'=-9+F, [ 0>=10 && 0>=2 && 89>=A && H==A && F==101 && D==1 && B==91 ], cost: 1
8.47/3.74	
8.47/3.74	      7: lbl221 -> stop : [ 1>=D && D>=2 && F>=102 && 111>=F && 10+F>=11*D+A && 89>=A && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	      8: lbl221 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ 99>=A && 89>=A && F==111 && D==2 && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	      9: lbl221 -> lbl221 : F'=1+F, [ D>=3 && 110>=F && D>=2 && F>=102 && 111>=F && 10+F>=11*D+A && 89>=A && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     10: lbl221 -> lbl221 : F'=1+F, [ D>=2 && 110>=F && F>=102 && 111>=F && 10+F>=11*D+A && 89>=A && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     11: lbl221 -> lbl221 : D'=-1+D, F'=-9+F, [ D>=3 && D>=2 && 121>=11*D+A && 89>=A && F==111 && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     12: lbl111 -> lbl111 : D'=1+D, F'=11+F, [ 111>=11*D+A && 122>=11*D+A && 11*D>=22 && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     13: lbl111 -> stop : [ 11*D+A>=112 && 1>=D && 122>=11*D+A && 11*D>=22 && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     14: lbl111 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ F==111 && D==2 && H==100 && B==C && A==100 ], cost: 1
8.47/3.74	
8.47/3.74	     15: lbl111 -> lbl221 : F'=1+F, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && 122>=11*D+A && 11*D>=22 && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     16: lbl111 -> lbl221 : F'=1+F, [ 11*D+A>=112 && D>=2 && 121>=11*D+A && 122>=11*D+A && 11*D>=22 && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     17: lbl111 -> lbl221 : D'=-1+D, F'=-9+F, [ D>=3 && 11*D>=22 && F==111 && 11*D+H==122 && B==C && 11*D+A==122 ], cost: 1
8.47/3.74	
8.47/3.74	     18: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Removed unreachable and leaf rules:
8.47/3.74	
8.47/3.74	   Start location: start0
8.47/3.74	
8.47/3.74	      1: start -> lbl111 : D'=2, F'=11+H, [ 100>=A && B==C && D==E && F==G && H==A ], cost: 1
8.47/3.74	
8.47/3.74	      3: lbl161 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ 0>=10 && 89>=A && 0>=1 && D==2 && H==A && F==101 && B==91 ], cost: 1
8.47/3.74	
8.47/3.74	      4: lbl161 -> lbl221 : F'=1+F, [ 0>=2 && 89>=A && H==A && F==101 && D==1 && B==91 ], cost: 1
8.47/3.74	
8.47/3.74	      5: lbl161 -> lbl221 : F'=1+F, [ 0>=1 && 89>=A && H==A && F==101 && D==1 && B==91 ], cost: 1
8.47/3.74	
8.47/3.74	      6: lbl161 -> lbl221 : D'=-1+D, F'=-9+F, [ 0>=10 && 0>=2 && 89>=A && H==A && F==101 && D==1 && B==91 ], cost: 1
8.47/3.74	
8.47/3.74	      8: lbl221 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ 99>=A && 89>=A && F==111 && D==2 && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	      9: lbl221 -> lbl221 : F'=1+F, [ D>=3 && 110>=F && D>=2 && F>=102 && 111>=F && 10+F>=11*D+A && 89>=A && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     10: lbl221 -> lbl221 : F'=1+F, [ D>=2 && 110>=F && F>=102 && 111>=F && 10+F>=11*D+A && 89>=A && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     11: lbl221 -> lbl221 : D'=-1+D, F'=-9+F, [ D>=3 && D>=2 && 121>=11*D+A && 89>=A && F==111 && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     12: lbl111 -> lbl111 : D'=1+D, F'=11+F, [ 111>=11*D+A && 122>=11*D+A && 11*D>=22 && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     14: lbl111 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ F==111 && D==2 && H==100 && B==C && A==100 ], cost: 1
8.47/3.74	
8.47/3.74	     15: lbl111 -> lbl221 : F'=1+F, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && 122>=11*D+A && 11*D>=22 && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     16: lbl111 -> lbl221 : F'=1+F, [ 11*D+A>=112 && D>=2 && 121>=11*D+A && 122>=11*D+A && 11*D>=22 && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     17: lbl111 -> lbl221 : D'=-1+D, F'=-9+F, [ D>=3 && 11*D>=22 && F==111 && 11*D+H==122 && B==C && 11*D+A==122 ], cost: 1
8.47/3.74	
8.47/3.74	     18: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Removed rules with unsatisfiable guard:
8.47/3.74	
8.47/3.74	   Start location: start0
8.47/3.74	
8.47/3.74	      1: start -> lbl111 : D'=2, F'=11+H, [ 100>=A && B==C && D==E && F==G && H==A ], cost: 1
8.47/3.74	
8.47/3.74	      8: lbl221 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ 99>=A && 89>=A && F==111 && D==2 && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	      9: lbl221 -> lbl221 : F'=1+F, [ D>=3 && 110>=F && D>=2 && F>=102 && 111>=F && 10+F>=11*D+A && 89>=A && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     10: lbl221 -> lbl221 : F'=1+F, [ D>=2 && 110>=F && F>=102 && 111>=F && 10+F>=11*D+A && 89>=A && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     11: lbl221 -> lbl221 : D'=-1+D, F'=-9+F, [ D>=3 && D>=2 && 121>=11*D+A && 89>=A && F==111 && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     12: lbl111 -> lbl111 : D'=1+D, F'=11+F, [ 111>=11*D+A && 122>=11*D+A && 11*D>=22 && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     14: lbl111 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ F==111 && D==2 && H==100 && B==C && A==100 ], cost: 1
8.47/3.74	
8.47/3.74	     15: lbl111 -> lbl221 : F'=1+F, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && 122>=11*D+A && 11*D>=22 && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     16: lbl111 -> lbl221 : F'=1+F, [ 11*D+A>=112 && D>=2 && 121>=11*D+A && 122>=11*D+A && 11*D>=22 && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     17: lbl111 -> lbl221 : D'=-1+D, F'=-9+F, [ D>=3 && 11*D>=22 && F==111 && 11*D+H==122 && B==C && 11*D+A==122 ], cost: 1
8.47/3.74	
8.47/3.74	     18: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Simplified all rules, resulting in:
8.47/3.74	
8.47/3.74	   Start location: start0
8.47/3.74	
8.47/3.74	      1: start -> lbl111 : D'=2, F'=11+H, [ 100>=A && B==C && D==E && F==G && H==A ], cost: 1
8.47/3.74	
8.47/3.74	      8: lbl221 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ 89>=A && F==111 && D==2 && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	      9: lbl221 -> lbl221 : F'=1+F, [ D>=3 && 110>=F && F>=102 && 10+F>=11*D+A && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     10: lbl221 -> lbl221 : F'=1+F, [ D>=2 && 110>=F && F>=102 && 10+F>=11*D+A && 89>=A && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     11: lbl221 -> lbl221 : D'=-1+D, F'=-9+F, [ D>=3 && 121>=11*D+A && F==111 && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     12: lbl111 -> lbl111 : D'=1+D, F'=11+F, [ 111>=11*D+A && 11*D>=22 && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     14: lbl111 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ F==111 && D==2 && H==100 && B==C && A==100 ], cost: 1
8.47/3.74	
8.47/3.74	     15: lbl111 -> lbl221 : F'=1+F, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     16: lbl111 -> lbl221 : F'=1+F, [ 11*D+A>=112 && D>=2 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     17: lbl111 -> lbl221 : D'=-1+D, F'=-9+F, [ D>=3 && F==111 && 11*D+H==122 && B==C && 11*D+A==122 ], cost: 1
8.47/3.74	
8.47/3.74	     18: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	### Simplification by acceleration and chaining ###
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Accelerating simple loops of location 2.
8.47/3.74	
8.47/3.74	   Accelerating the following rules:
8.47/3.74	
8.47/3.74	      9: lbl221 -> lbl221 : F'=1+F, [ D>=3 && 110>=F && F>=102 && 10+F>=11*D+A && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     10: lbl221 -> lbl221 : F'=1+F, [ D>=2 && 110>=F && F>=102 && 10+F>=11*D+A && 89>=A && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     11: lbl221 -> lbl221 : D'=-1+D, F'=-9+F, [ D>=3 && 121>=11*D+A && F==111 && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	   Accelerated rule 9 with metering function 111-F, yielding the new rule 19.
8.47/3.74	
8.47/3.74	   Accelerated rule 10 with metering function 111-F, yielding the new rule 20.
8.47/3.74	
8.47/3.74	   Accelerated rule 11 with metering function meter (where 9*meter==-111+F), yielding the new rule 21.
8.47/3.74	
8.47/3.74	   Removing the simple loops: 9 10 11.
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Accelerating simple loops of location 3.
8.47/3.74	
8.47/3.74	   Accelerating the following rules:
8.47/3.74	
8.47/3.74	     12: lbl111 -> lbl111 : D'=1+D, F'=11+F, [ 111>=11*D+A && 11*D>=22 && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	   Accelerated rule 12 with metering function meter_3 (where 11*meter_3==112-11*D-A), yielding the new rule 22.
8.47/3.74	
8.47/3.74	   Removing the simple loops: 12.
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Accelerated all simple loops using metering functions (where possible):
8.47/3.74	
8.47/3.74	   Start location: start0
8.47/3.74	
8.47/3.74	      1: start -> lbl111 : D'=2, F'=11+H, [ 100>=A && B==C && D==E && F==G && H==A ], cost: 1
8.47/3.74	
8.47/3.74	      8: lbl221 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ 89>=A && F==111 && D==2 && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     19: lbl221 -> lbl221 : F'=111, [ D>=3 && 110>=F && F>=102 && 10+F>=11*D+A && H==A && B==C ], cost: 111-F
8.47/3.74	
8.47/3.74	     20: lbl221 -> lbl221 : F'=111, [ D>=2 && 110>=F && F>=102 && 10+F>=11*D+A && 89>=A && H==A && B==C ], cost: 111-F
8.47/3.74	
8.47/3.74	     21: lbl221 -> lbl221 : D'=-meter+D, F'=-9*meter+F, [ D>=3 && 121>=11*D+A && F==111 && H==A && B==C && 9*meter==-111+F && meter>=1 ], cost: meter
8.47/3.74	
8.47/3.74	     14: lbl111 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ F==111 && D==2 && H==100 && B==C && A==100 ], cost: 1
8.47/3.74	
8.47/3.74	     15: lbl111 -> lbl221 : F'=1+F, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     16: lbl111 -> lbl221 : F'=1+F, [ 11*D+A>=112 && D>=2 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     17: lbl111 -> lbl221 : D'=-1+D, F'=-9+F, [ D>=3 && F==111 && 11*D+H==122 && B==C && 11*D+A==122 ], cost: 1
8.47/3.74	
8.47/3.74	     22: lbl111 -> lbl111 : D'=meter_3+D, F'=F+11*meter_3, [ 111>=11*D+A && 11*D>=22 && H==A && B==C && 11+F==11*D+A && 11*meter_3==112-11*D-A && meter_3>=1 ], cost: meter_3
8.47/3.74	
8.47/3.74	     18: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Chained accelerated rules (with incoming rules):
8.47/3.74	
8.47/3.74	   Start location: start0
8.47/3.74	
8.47/3.74	      1: start -> lbl111 : D'=2, F'=11+H, [ 100>=A && B==C && D==E && F==G && H==A ], cost: 1
8.47/3.74	
8.47/3.74	     29: start -> lbl111 : D'=2+meter_3, F'=11+11*meter_3+H, [ B==C && D==E && F==G && H==A && 111>=22+A && 11*meter_3==90-A && meter_3>=1 ], cost: 1+meter_3
8.47/3.74	
8.47/3.74	      8: lbl221 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ 89>=A && F==111 && D==2 && H==A && B==C ], cost: 1
8.47/3.74	
8.47/3.74	     14: lbl111 -> lbl161 : B'=-20+F, D'=-1+D, F'=-10+F, [ F==111 && D==2 && H==100 && B==C && A==100 ], cost: 1
8.47/3.74	
8.47/3.74	     15: lbl111 -> lbl221 : F'=1+F, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     16: lbl111 -> lbl221 : F'=1+F, [ 11*D+A>=112 && D>=2 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A ], cost: 1
8.47/3.74	
8.47/3.74	     17: lbl111 -> lbl221 : D'=-1+D, F'=-9+F, [ D>=3 && F==111 && 11*D+H==122 && B==C && 11*D+A==122 ], cost: 1
8.47/3.74	
8.47/3.74	     23: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && 110>=1+F && 1+F>=102 ], cost: 111-F
8.47/3.74	
8.47/3.74	     24: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && D>=3 && 110>=1+F && 1+F>=102 ], cost: 111-F
8.47/3.74	
8.47/3.74	     25: lbl111 -> lbl221 : D'=-1+D, F'=111, [ F==111 && 11*D+H==122 && B==C && 11*D+A==122 && -1+D>=3 && 1+F>=-11+11*D+A && H==A ], cost: 121-F
8.47/3.74	
8.47/3.74	     26: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && 110>=1+F && 1+F>=102 && 89>=A ], cost: 111-F
8.47/3.74	
8.47/3.74	     27: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && D>=2 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && 110>=1+F && 1+F>=102 && 89>=A ], cost: 111-F
8.47/3.74	
8.47/3.74	     28: lbl111 -> lbl221 : D'=-1+D, F'=111, [ D>=3 && F==111 && 11*D+H==122 && B==C && 11*D+A==122 && 1+F>=-11+11*D+A && 89>=A && H==A ], cost: 121-F
8.47/3.74	
8.47/3.74	     18: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Removed unreachable locations (and leaf rules with constant cost):
8.47/3.74	
8.47/3.74	   Start location: start0
8.47/3.74	
8.47/3.74	      1: start -> lbl111 : D'=2, F'=11+H, [ 100>=A && B==C && D==E && F==G && H==A ], cost: 1
8.47/3.74	
8.47/3.74	     29: start -> lbl111 : D'=2+meter_3, F'=11+11*meter_3+H, [ B==C && D==E && F==G && H==A && 111>=22+A && 11*meter_3==90-A && meter_3>=1 ], cost: 1+meter_3
8.47/3.74	
8.47/3.74	     23: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && 110>=1+F && 1+F>=102 ], cost: 111-F
8.47/3.74	
8.47/3.74	     24: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && D>=3 && 110>=1+F && 1+F>=102 ], cost: 111-F
8.47/3.74	
8.47/3.74	     25: lbl111 -> lbl221 : D'=-1+D, F'=111, [ F==111 && 11*D+H==122 && B==C && 11*D+A==122 && -1+D>=3 && 1+F>=-11+11*D+A && H==A ], cost: 121-F
8.47/3.74	
8.47/3.74	     26: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && 110>=1+F && 1+F>=102 && 89>=A ], cost: 111-F
8.47/3.74	
8.47/3.74	     27: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && D>=2 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && 110>=1+F && 1+F>=102 && 89>=A ], cost: 111-F
8.47/3.74	
8.47/3.74	     28: lbl111 -> lbl221 : D'=-1+D, F'=111, [ D>=3 && F==111 && 11*D+H==122 && B==C && 11*D+A==122 && 1+F>=-11+11*D+A && 89>=A && H==A ], cost: 121-F
8.47/3.74	
8.47/3.74	     18: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Eliminated locations (on tree-shaped paths):
8.47/3.74	
8.47/3.74	   Start location: start0
8.47/3.74	
8.47/3.74	     23: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && 110>=1+F && 1+F>=102 ], cost: 111-F
8.47/3.74	
8.47/3.74	     24: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && D>=3 && 110>=1+F && 1+F>=102 ], cost: 111-F
8.47/3.74	
8.47/3.74	     25: lbl111 -> lbl221 : D'=-1+D, F'=111, [ F==111 && 11*D+H==122 && B==C && 11*D+A==122 && -1+D>=3 && 1+F>=-11+11*D+A && H==A ], cost: 121-F
8.47/3.74	
8.47/3.74	     26: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && 110>=1+F && 1+F>=102 && 89>=A ], cost: 111-F
8.47/3.74	
8.47/3.74	     27: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && D>=2 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && 110>=1+F && 1+F>=102 && 89>=A ], cost: 111-F
8.47/3.74	
8.47/3.74	     28: lbl111 -> lbl221 : D'=-1+D, F'=111, [ D>=3 && F==111 && 11*D+H==122 && B==C && 11*D+A==122 && 1+F>=-11+11*D+A && 89>=A && H==A ], cost: 121-F
8.47/3.74	
8.47/3.74	     30: start0 -> lbl111 : B'=C, D'=2, F'=11+A, H'=A, [ 100>=A ], cost: 2
8.47/3.74	
8.47/3.74	     31: start0 -> lbl111 : B'=C, D'=2+meter_3, F'=11+11*meter_3+A, H'=A, [ 111>=22+A && 11*meter_3==90-A && meter_3>=1 ], cost: 2+meter_3
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Applied pruning (of leafs and parallel rules):
8.47/3.74	
8.47/3.74	   Start location: start0
8.47/3.74	
8.47/3.74	     23: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && 110>=1+F && 1+F>=102 ], cost: 111-F
8.47/3.74	
8.47/3.74	     24: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && D>=3 && 110>=1+F && 1+F>=102 ], cost: 111-F
8.47/3.74	
8.47/3.74	     25: lbl111 -> lbl221 : D'=-1+D, F'=111, [ F==111 && 11*D+H==122 && B==C && 11*D+A==122 && -1+D>=3 && 1+F>=-11+11*D+A && H==A ], cost: 121-F
8.47/3.74	
8.47/3.74	     26: lbl111 -> lbl221 : F'=111, [ 11*D+A>=112 && D>=3 && 121>=11*D+A && H==A && B==C && 11+F==11*D+A && 110>=1+F && 1+F>=102 && 89>=A ], cost: 111-F
8.47/3.74	
8.47/3.74	     28: lbl111 -> lbl221 : D'=-1+D, F'=111, [ D>=3 && F==111 && 11*D+H==122 && B==C && 11*D+A==122 && 1+F>=-11+11*D+A && 89>=A && H==A ], cost: 121-F
8.47/3.74	
8.47/3.74	     30: start0 -> lbl111 : B'=C, D'=2, F'=11+A, H'=A, [ 100>=A ], cost: 2
8.47/3.74	
8.47/3.74	     31: start0 -> lbl111 : B'=C, D'=2+meter_3, F'=11+11*meter_3+A, H'=A, [ 111>=22+A && 11*meter_3==90-A && meter_3>=1 ], cost: 2+meter_3
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Eliminated locations (on tree-shaped paths):
8.47/3.74	
8.47/3.74	   Start location: start0
8.47/3.74	
8.47/3.74	     32: start0 -> lbl221 : B'=C, D'=2+meter_3, F'=111, H'=A, [ 111>=22+A && 11*meter_3==90-A && meter_3>=1 ], cost: 102-10*meter_3-A
8.47/3.74	
8.47/3.74	     33: start0 -> lbl221 : B'=C, D'=2+meter_3, F'=111, H'=A, [ 111>=22+A && 11*meter_3==90-A && meter_3>=1 ], cost: 102-10*meter_3-A
8.47/3.74	
8.47/3.74	     34: start0 -> lbl221 : B'=C, D'=2+meter_3, F'=111, H'=A, [ 111>=22+A && 11*meter_3==90-A && meter_3>=1 ], cost: 102-10*meter_3-A
8.47/3.74	
8.47/3.74	     35: start0 -> [8] : [ 111>=22+A && 11*meter_3==90-A && meter_3>=1 ], cost: 2+meter_3
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	### Computing asymptotic complexity ###
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Fully simplified ITS problem
8.47/3.74	
8.47/3.74	   Start location: start0
8.47/3.74	
8.47/3.74	     34: start0 -> lbl221 : B'=C, D'=2+meter_3, F'=111, H'=A, [ 111>=22+A && 11*meter_3==90-A && meter_3>=1 ], cost: 102-10*meter_3-A
8.47/3.74	
8.47/3.74	     35: start0 -> [8] : [ 111>=22+A && 11*meter_3==90-A && meter_3>=1 ], cost: 2+meter_3
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Computing asymptotic complexity for rule 34
8.47/3.74	
8.47/3.74	   Solved the limit problem by the following transformations:
8.47/3.74	
8.47/3.74	      Created initial limit problem:
8.47/3.74	
8.47/3.74	      102-10*meter_3-A (+), 91-11*meter_3-A (+/+!), -89+11*meter_3+A (+/+!), 90-A (+/+!) [not solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      applying transformation rule (C) using substitution {A==90-11*meter_3}
8.47/3.74	
8.47/3.74	      resulting limit problem:
8.47/3.74	
8.47/3.74	      1 (+/+!), 11*meter_3 (+/+!), 12+meter_3 (+) [not solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      applying transformation rule (B), deleting 1 (+/+!)
8.47/3.74	
8.47/3.74	      resulting limit problem:
8.47/3.74	
8.47/3.74	      11*meter_3 (+/+!), 12+meter_3 (+) [not solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      removing all constraints (solved by SMT)
8.47/3.74	
8.47/3.74	      resulting limit problem: [solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      applying transformation rule (C) using substitution {meter_3==n}
8.47/3.74	
8.47/3.74	      resulting limit problem:
8.47/3.74	
8.47/3.74	      [solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	   Solved the limit problem by the following transformations:
8.47/3.74	
8.47/3.74	      Created initial limit problem:
8.47/3.74	
8.47/3.74	      102-10*meter_3-A (+), 91-11*meter_3-A (+/+!), -89+11*meter_3+A (+/+!), 90-A (+/+!) [not solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      applying transformation rule (C) using substitution {A==90-11*meter_3}
8.47/3.74	
8.47/3.74	      resulting limit problem:
8.47/3.74	
8.47/3.74	      1 (+/+!), 11*meter_3 (+/+!), 12+meter_3 (+) [not solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      applying transformation rule (B), deleting 1 (+/+!)
8.47/3.74	
8.47/3.74	      resulting limit problem:
8.47/3.74	
8.47/3.74	      11*meter_3 (+/+!), 12+meter_3 (+) [not solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      removing all constraints (solved by SMT)
8.47/3.74	
8.47/3.74	      resulting limit problem: [solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      applying transformation rule (C) using substitution {meter_3==n}
8.47/3.74	
8.47/3.74	      resulting limit problem:
8.47/3.74	
8.47/3.74	      [solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	   Solution:
8.47/3.74	
8.47/3.74	      meter_3 / n
8.47/3.74	
8.47/3.74	      A / 90-11*n
8.47/3.74	
8.47/3.74	   Resulting cost 12+n has complexity: Poly(n^1)
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Found new complexity Poly(n^1).
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Computing asymptotic complexity for rule 35
8.47/3.74	
8.47/3.74	   Solved the limit problem by the following transformations:
8.47/3.74	
8.47/3.74	      Created initial limit problem:
8.47/3.74	
8.47/3.74	      2+meter_3 (+), 91-11*meter_3-A (+/+!), -89+11*meter_3+A (+/+!), 90-A (+/+!) [not solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      applying transformation rule (C) using substitution {A==90-11*meter_3}
8.47/3.74	
8.47/3.74	      resulting limit problem:
8.47/3.74	
8.47/3.74	      1 (+/+!), 2+meter_3 (+), 11*meter_3 (+/+!) [not solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      applying transformation rule (B), deleting 1 (+/+!)
8.47/3.74	
8.47/3.74	      resulting limit problem:
8.47/3.74	
8.47/3.74	      2+meter_3 (+), 11*meter_3 (+/+!) [not solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      removing all constraints (solved by SMT)
8.47/3.74	
8.47/3.74	      resulting limit problem: [solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      applying transformation rule (C) using substitution {meter_3==n}
8.47/3.74	
8.47/3.74	      resulting limit problem:
8.47/3.74	
8.47/3.74	      [solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	   Solved the limit problem by the following transformations:
8.47/3.74	
8.47/3.74	      Created initial limit problem:
8.47/3.74	
8.47/3.74	      2+meter_3 (+), 91-11*meter_3-A (+/+!), -89+11*meter_3+A (+/+!), 90-A (+/+!) [not solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      applying transformation rule (C) using substitution {A==90-11*meter_3}
8.47/3.74	
8.47/3.74	      resulting limit problem:
8.47/3.74	
8.47/3.74	      1 (+/+!), 2+meter_3 (+), 11*meter_3 (+/+!) [not solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      applying transformation rule (B), deleting 1 (+/+!)
8.47/3.74	
8.47/3.74	      resulting limit problem:
8.47/3.74	
8.47/3.74	      2+meter_3 (+), 11*meter_3 (+/+!) [not solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      removing all constraints (solved by SMT)
8.47/3.74	
8.47/3.74	      resulting limit problem: [solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	      applying transformation rule (C) using substitution {meter_3==n}
8.47/3.74	
8.47/3.74	      resulting limit problem:
8.47/3.74	
8.47/3.74	      [solved]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	   Solution:
8.47/3.74	
8.47/3.74	      meter_3 / n
8.47/3.74	
8.47/3.74	      A / 90-11*n
8.47/3.74	
8.47/3.74	   Resulting cost 2+n has complexity: Poly(n^1)
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	Obtained the following overall complexity (w.r.t. the length of the input n):
8.47/3.74	
8.47/3.74	   Complexity:  Poly(n^1)
8.47/3.74	
8.47/3.74	   Cpx degree:  1
8.47/3.74	
8.47/3.74	   Solved cost: 12+n
8.47/3.74	
8.47/3.74	   Rule cost:   102-10*meter_3-A
8.47/3.74	
8.47/3.74	   Rule guard:  [ 111>=22+A && 11*meter_3==90-A ]
8.47/3.74	
8.47/3.74	
8.47/3.74	
8.47/3.74	WORST_CASE(Omega(n^1),?)
8.47/3.74	
8.47/3.74	
8.47/3.74	----------------------------------------
8.47/3.74	
8.47/3.74	(4)
8.47/3.74	BOUNDS(n^1, INF)
8.62/3.77	EOF