/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).

(0) CpxIntTrs
(1) Koat Proof [FINISHED, 222 ms]
(2) BOUNDS(1, n^1)
(3) Loat Proof [FINISHED, 1037 ms]
(4) BOUNDS(n^1, INF)


----------------------------------------

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= 5 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
start(A, B, C, D, E, F, G, H) -> Com_1(lbl92(A, B, C, H, E, 0, G, 1 + H)) :|: 2 >= A && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
start(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, 0, C, D, E, 1, G, H)) :|: A >= 3 && 4 >= A && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
lbl92(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: D >= 4 && D >= A && F + 10 >= 5 * D && F >= 0 && H >= D + 1 && H <= D + 1
lbl92(A, B, C, D, E, F, G, H) -> Com_1(lbl92(A, B, C, H, E, 0, G, 1 + H)) :|: 1 >= D && D >= A && F + 10 >= 5 * D && F >= 0 && H >= D + 1 && H <= D + 1
lbl92(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, 0, C, D, E, 1, G, H)) :|: D >= 2 && 3 >= D && D >= A && F + 10 >= 5 * D && F >= 0 && H >= D + 1 && H <= D + 1
lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl92(A, B, C, H, E, F, G, 1 + H)) :|: 2 >= H && 9 >= B && B >= 0 && H >= A && H >= 3 && 4 >= H && F >= B + 1 && F <= B + 1
lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl92(A, B, C, H, E, F, G, 1 + H)) :|: H >= A && H >= 3 && 4 >= H && F >= 10 && F <= 10 && B >= 9 && B <= 9
lbl82(A, B, C, D, E, F, G, H) -> Com_1(lbl82(A, F, C, D, E, 1 + F, G, H)) :|: H >= 3 && 8 >= B && 9 >= B && B >= 0 && H >= A && 4 >= H && F >= B + 1 && F <= B + 1
start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, E, E, G, G, A)) :|: TRUE

The start-symbols are:[start0_8]


----------------------------------------

(1) Koat Proof (FINISHED)
YES(?, 44*Ar_0 + 221)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 5 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, 0, Ar_6, Ar_7 + 1)) [ 2 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, 0, Ar_2, Ar_3, Ar_4, 1, Ar_6, Ar_7)) [ Ar_0 >= 3 /\ 4 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(Comp: ?, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 4 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: ?, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, 0, Ar_6, Ar_7 + 1)) [ 1 >= Ar_3 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: ?, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, 0, Ar_2, Ar_3, Ar_4, 1, Ar_6, Ar_7)) [ Ar_3 >= 2 /\ 3 >= Ar_3 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: ?, Cost: 1)    lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, Ar_5, Ar_6, Ar_7 + 1)) [ 2 >= Ar_7 /\ 9 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_7 >= Ar_0 /\ Ar_7 >= 3 /\ 4 >= Ar_7 /\ Ar_5 = Ar_1 + 1 ]

		(Comp: ?, Cost: 1)    lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, Ar_5, Ar_6, Ar_7 + 1)) [ Ar_7 >= Ar_0 /\ Ar_7 >= 3 /\ 4 >= Ar_7 /\ Ar_5 = 10 /\ Ar_1 = 9 ]

		(Comp: ?, Cost: 1)    lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6, Ar_7)) [ Ar_7 >= 3 /\ 8 >= Ar_1 /\ 9 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_7 >= Ar_0 /\ 4 >= Ar_7 /\ Ar_5 = Ar_1 + 1 ]

		(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))

		(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 ]

	start location:	koat_start

	leaf cost:	0



Testing for reachability in the complexity graph removes the following transition from problem 1:

	lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, Ar_5, Ar_6, Ar_7 + 1)) [ 2 >= Ar_7 /\ 9 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_7 >= Ar_0 /\ Ar_7 >= 3 /\ 4 >= Ar_7 /\ Ar_5 = Ar_1 + 1 ]

We thus obtain the following problem:

2:	T:

		(Comp: ?, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 4 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: ?, Cost: 1)    lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, Ar_5, Ar_6, Ar_7 + 1)) [ Ar_7 >= Ar_0 /\ Ar_7 >= 3 /\ 4 >= Ar_7 /\ Ar_5 = 10 /\ Ar_1 = 9 ]

		(Comp: ?, Cost: 1)    lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6, Ar_7)) [ Ar_7 >= 3 /\ 8 >= Ar_1 /\ 9 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_7 >= Ar_0 /\ 4 >= Ar_7 /\ Ar_5 = Ar_1 + 1 ]

		(Comp: ?, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, 0, Ar_2, Ar_3, Ar_4, 1, Ar_6, Ar_7)) [ Ar_3 >= 2 /\ 3 >= Ar_3 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: ?, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, 0, Ar_6, Ar_7 + 1)) [ 1 >= Ar_3 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, 0, Ar_2, Ar_3, Ar_4, 1, Ar_6, Ar_7)) [ Ar_0 >= 3 /\ 4 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, 0, Ar_6, Ar_7 + 1)) [ 2 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(Comp: ?, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 5 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(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))

		(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 ]

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 2 produces the following problem:

3:	T:

		(Comp: ?, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 4 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: ?, Cost: 1)    lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, Ar_5, Ar_6, Ar_7 + 1)) [ Ar_7 >= Ar_0 /\ Ar_7 >= 3 /\ 4 >= Ar_7 /\ Ar_5 = 10 /\ Ar_1 = 9 ]

		(Comp: ?, Cost: 1)    lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6, Ar_7)) [ Ar_7 >= 3 /\ 8 >= Ar_1 /\ 9 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_7 >= Ar_0 /\ 4 >= Ar_7 /\ Ar_5 = Ar_1 + 1 ]

		(Comp: ?, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, 0, Ar_2, Ar_3, Ar_4, 1, Ar_6, Ar_7)) [ Ar_3 >= 2 /\ 3 >= Ar_3 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: ?, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, 0, Ar_6, Ar_7 + 1)) [ 1 >= Ar_3 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, 0, Ar_2, Ar_3, Ar_4, 1, Ar_6, Ar_7)) [ Ar_0 >= 3 /\ 4 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, 0, Ar_6, Ar_7 + 1)) [ 2 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 5 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(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))

		(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 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(lbl92) = 1

	Pol(stop) = 0

	Pol(lbl82) = 1

	Pol(start) = 1

	Pol(start0) = 1

	Pol(koat_start) = 1

orients all transitions weakly and the transition

	lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 4 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

strictly and produces the following problem:

4:	T:

		(Comp: 1, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 4 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: ?, Cost: 1)    lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, Ar_5, Ar_6, Ar_7 + 1)) [ Ar_7 >= Ar_0 /\ Ar_7 >= 3 /\ 4 >= Ar_7 /\ Ar_5 = 10 /\ Ar_1 = 9 ]

		(Comp: ?, Cost: 1)    lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6, Ar_7)) [ Ar_7 >= 3 /\ 8 >= Ar_1 /\ 9 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_7 >= Ar_0 /\ 4 >= Ar_7 /\ Ar_5 = Ar_1 + 1 ]

		(Comp: ?, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, 0, Ar_2, Ar_3, Ar_4, 1, Ar_6, Ar_7)) [ Ar_3 >= 2 /\ 3 >= Ar_3 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: ?, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, 0, Ar_6, Ar_7 + 1)) [ 1 >= Ar_3 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, 0, Ar_2, Ar_3, Ar_4, 1, Ar_6, Ar_7)) [ Ar_0 >= 3 /\ 4 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, 0, Ar_6, Ar_7 + 1)) [ 2 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(Comp: 1, Cost: 1)    start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 5 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(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))

		(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 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(lbl92) = -11*V_4 + 44

	Pol(stop) = -11*V_8

	Pol(lbl82) = -V_2 - 11*V_8 + 54

	Pol(start) = -11*V_1 + 54

	Pol(start0) = -11*V_1 + 54

	Pol(koat_start) = -11*V_1 + 54

orients all transitions weakly and the transitions

	lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, 0, Ar_6, Ar_7 + 1)) [ 1 >= Ar_3 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

	lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, 0, Ar_2, Ar_3, Ar_4, 1, Ar_6, Ar_7)) [ Ar_3 >= 2 /\ 3 >= Ar_3 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

	lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, Ar_5, Ar_6, Ar_7 + 1)) [ Ar_7 >= Ar_0 /\ Ar_7 >= 3 /\ 4 >= Ar_7 /\ Ar_5 = 10 /\ Ar_1 = 9 ]

	lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6, Ar_7)) [ Ar_7 >= 3 /\ 8 >= Ar_1 /\ 9 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_7 >= Ar_0 /\ 4 >= Ar_7 /\ Ar_5 = Ar_1 + 1 ]

strictly and produces the following problem:

5:	T:

		(Comp: 1, Cost: 1)               lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_3 >= 4 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: 11*Ar_0 + 54, Cost: 1)    lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, Ar_5, Ar_6, Ar_7 + 1)) [ Ar_7 >= Ar_0 /\ Ar_7 >= 3 /\ 4 >= Ar_7 /\ Ar_5 = 10 /\ Ar_1 = 9 ]

		(Comp: 11*Ar_0 + 54, Cost: 1)    lbl82(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, Ar_5, Ar_2, Ar_3, Ar_4, Ar_5 + 1, Ar_6, Ar_7)) [ Ar_7 >= 3 /\ 8 >= Ar_1 /\ 9 >= Ar_1 /\ Ar_1 >= 0 /\ Ar_7 >= Ar_0 /\ 4 >= Ar_7 /\ Ar_5 = Ar_1 + 1 ]

		(Comp: 11*Ar_0 + 54, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, 0, Ar_2, Ar_3, Ar_4, 1, Ar_6, Ar_7)) [ Ar_3 >= 2 /\ 3 >= Ar_3 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: 11*Ar_0 + 54, Cost: 1)    lbl92(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, 0, Ar_6, Ar_7 + 1)) [ 1 >= Ar_3 /\ Ar_3 >= Ar_0 /\ Ar_5 + 10 >= 5*Ar_3 /\ Ar_5 >= 0 /\ Ar_7 = Ar_3 + 1 ]

		(Comp: 1, Cost: 1)               start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl82(Ar_0, 0, Ar_2, Ar_3, Ar_4, 1, Ar_6, Ar_7)) [ Ar_0 >= 3 /\ 4 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(Comp: 1, Cost: 1)               start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(lbl92(Ar_0, Ar_1, Ar_2, Ar_7, Ar_4, 0, Ar_6, Ar_7 + 1)) [ 2 >= Ar_0 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(Comp: 1, Cost: 1)               start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7) -> Com_1(stop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7)) [ Ar_0 >= 5 /\ Ar_1 = Ar_2 /\ Ar_3 = Ar_4 /\ Ar_5 = Ar_6 /\ Ar_7 = Ar_0 ]

		(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))

		(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 ]

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 44*Ar_0 + 221



Time: 0.269 sec (SMT: 0.225 sec)


----------------------------------------

(2)
BOUNDS(1, n^1)

----------------------------------------

(3) Loat Proof (FINISHED)


### Pre-processing the ITS problem ###



Initial linear ITS problem

   Start location: start0

      0: start -> stop : [ A>=5 && B==C && D==E && F==G && H==A ], cost: 1

      1: start -> lbl92 : D'=H, F'=0, H'=1+H, [ 2>=A && B==C && D==E && F==G && H==A ], cost: 1

      2: start -> lbl82 : B'=0, F'=1, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A ], cost: 1

      3: lbl92 -> stop : [ D>=4 && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1

      4: lbl92 -> lbl92 : D'=H, F'=0, H'=1+H, [ 1>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1

      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1

      6: lbl82 -> lbl92 : D'=H, H'=1+H, [ 2>=H && 9>=B && B>=0 && H>=A && H>=3 && 4>=H && F==1+B ], cost: 1

      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1

      8: lbl82 -> lbl82 : B'=F, F'=1+F, [ H>=3 && 8>=B && 9>=B && B>=0 && H>=A && 4>=H && F==1+B ], cost: 1

      9: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1



Checking for constant complexity:

   The following rule is satisfiable with cost >= 1, yielding constant complexity:

      9: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1



Removed unreachable and leaf rules:

   Start location: start0

      1: start -> lbl92 : D'=H, F'=0, H'=1+H, [ 2>=A && B==C && D==E && F==G && H==A ], cost: 1

      2: start -> lbl82 : B'=0, F'=1, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A ], cost: 1

      4: lbl92 -> lbl92 : D'=H, F'=0, H'=1+H, [ 1>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1

      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1

      6: lbl82 -> lbl92 : D'=H, H'=1+H, [ 2>=H && 9>=B && B>=0 && H>=A && H>=3 && 4>=H && F==1+B ], cost: 1

      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1

      8: lbl82 -> lbl82 : B'=F, F'=1+F, [ H>=3 && 8>=B && 9>=B && B>=0 && H>=A && 4>=H && F==1+B ], cost: 1

      9: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1



Removed rules with unsatisfiable guard:

   Start location: start0

      1: start -> lbl92 : D'=H, F'=0, H'=1+H, [ 2>=A && B==C && D==E && F==G && H==A ], cost: 1

      2: start -> lbl82 : B'=0, F'=1, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A ], cost: 1

      4: lbl92 -> lbl92 : D'=H, F'=0, H'=1+H, [ 1>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1

      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1

      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1

      8: lbl82 -> lbl82 : B'=F, F'=1+F, [ H>=3 && 8>=B && 9>=B && B>=0 && H>=A && 4>=H && F==1+B ], cost: 1

      9: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1



Simplified all rules, resulting in:

   Start location: start0

      1: start -> lbl92 : D'=H, F'=0, H'=1+H, [ 2>=A && B==C && D==E && F==G && H==A ], cost: 1

      2: start -> lbl82 : B'=0, F'=1, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A ], cost: 1

      4: lbl92 -> lbl92 : D'=H, F'=0, H'=1+H, [ 1>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1

      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && H==1+D ], cost: 1

      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1

      8: lbl82 -> lbl82 : B'=F, F'=1+F, [ H>=3 && 8>=B && B>=0 && H>=A && 4>=H && F==1+B ], cost: 1

      9: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 1.

   Accelerating the following rules:

      4: lbl92 -> lbl92 : D'=H, F'=0, H'=1+H, [ 1>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D ], cost: 1



   Accelerated rule 4 with metering function meter (where 2*meter==5-D-H), yielding the new rule 10.

   Removing the simple loops: 4.



Accelerating simple loops of location 2.

   Accelerating the following rules:

      8: lbl82 -> lbl82 : B'=F, F'=1+F, [ H>=3 && 8>=B && B>=0 && H>=A && 4>=H && F==1+B ], cost: 1



   Accelerated rule 8 with metering function meter_1 (where 2*meter_1==19-F-B), yielding the new rule 11.

   Removing the simple loops: 8.



Accelerated all simple loops using metering functions (where possible):

   Start location: start0

      1: start -> lbl92 : D'=H, F'=0, H'=1+H, [ 2>=A && B==C && D==E && F==G && H==A ], cost: 1

      2: start -> lbl82 : B'=0, F'=1, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A ], cost: 1

      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && H==1+D ], cost: 1

     10: lbl92 -> lbl92 : D'=-1+meter+H, F'=0, H'=meter+H, [ 1>=D && D>=A && 10+F>=5*D && F>=0 && H==1+D && 2*meter==5-D-H && meter>=1 ], cost: meter

      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1

     11: lbl82 -> lbl82 : B'=-1+F+meter_1, F'=F+meter_1, [ H>=3 && 8>=B && B>=0 && H>=A && 4>=H && F==1+B && 2*meter_1==19-F-B && meter_1>=1 ], cost: meter_1

      9: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1



Chained accelerated rules (with incoming rules):

   Start location: start0

      1: start -> lbl92 : D'=H, F'=0, H'=1+H, [ 2>=A && B==C && D==E && F==G && H==A ], cost: 1

      2: start -> lbl82 : B'=0, F'=1, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A ], cost: 1

     12: start -> lbl92 : D'=2, F'=0, H'=3, [ 2>=A && B==C && D==E && F==G && H==A && 1>=H && 10>=5*H ], cost: 3-H

     13: start -> lbl82 : B'=9, F'=10, [ A>=3 && 4>=A && B==C && D==E && F==G && H==A && H>=3 && 4>=H ], cost: 10

      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && H==1+D ], cost: 1

     14: lbl92 -> lbl82 : B'=9, F'=10, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && H==1+D && H>=3 && H>=A && 4>=H ], cost: 10

      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1

      9: start0 -> start : B'=C, D'=E, F'=G, H'=A, [], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: start0

      5: lbl92 -> lbl82 : B'=0, F'=1, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && H==1+D ], cost: 1

     14: lbl92 -> lbl82 : B'=9, F'=10, [ D>=2 && 3>=D && D>=A && 10+F>=5*D && H==1+D && H>=3 && H>=A && 4>=H ], cost: 10

      7: lbl82 -> lbl92 : D'=H, H'=1+H, [ H>=A && H>=3 && 4>=H && F==10 && B==9 ], cost: 1

     15: start0 -> lbl92 : B'=C, D'=A, F'=0, H'=1+A, [ 2>=A ], cost: 2

     16: start0 -> lbl82 : B'=0, D'=E, F'=1, H'=A, [ A>=3 && 4>=A ], cost: 2

     17: start0 -> lbl92 : B'=C, D'=2, F'=0, H'=3, [ 1>=A && 10>=5*A ], cost: 4-A

     18: start0 -> lbl82 : B'=9, D'=E, F'=10, H'=A, [ A>=3 && 4>=A ], cost: 11



Eliminated location lbl92 (as a last resort):

   Start location: start0

     19: lbl82 -> lbl82 : B'=0, D'=H, F'=1, H'=1+H, [ H>=A && H>=3 && F==10 && B==9 && 3>=H && 10+F>=5*H ], cost: 2

     20: lbl82 -> lbl82 : B'=9, D'=H, F'=10, H'=1+H, [ H>=A && H>=3 && F==10 && B==9 && 3>=H && 10+F>=5*H ], cost: 11

     16: start0 -> lbl82 : B'=0, D'=E, F'=1, H'=A, [ A>=3 && 4>=A ], cost: 2

     18: start0 -> lbl82 : B'=9, D'=E, F'=10, H'=A, [ A>=3 && 4>=A ], cost: 11

     21: start0 -> lbl82 : B'=0, D'=A, F'=1, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 3

     22: start0 -> lbl82 : B'=9, D'=A, F'=10, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 12

     23: start0 -> lbl82 : B'=0, D'=2, F'=1, H'=3, [ 1>=A && 10>=5*A ], cost: 5-A

     24: start0 -> lbl82 : B'=9, D'=2, F'=10, H'=3, [ 1>=A && 10>=5*A ], cost: 14-A



Applied pruning (of leafs and parallel rules):

   Start location: start0

     19: lbl82 -> lbl82 : B'=0, D'=H, F'=1, H'=1+H, [ H>=A && H>=3 && F==10 && B==9 && 3>=H && 10+F>=5*H ], cost: 2

     20: lbl82 -> lbl82 : B'=9, D'=H, F'=10, H'=1+H, [ H>=A && H>=3 && F==10 && B==9 && 3>=H && 10+F>=5*H ], cost: 11

     18: start0 -> lbl82 : B'=9, D'=E, F'=10, H'=A, [ A>=3 && 4>=A ], cost: 11

     21: start0 -> lbl82 : B'=0, D'=A, F'=1, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 3

     22: start0 -> lbl82 : B'=9, D'=A, F'=10, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 12

     23: start0 -> lbl82 : B'=0, D'=2, F'=1, H'=3, [ 1>=A && 10>=5*A ], cost: 5-A

     24: start0 -> lbl82 : B'=9, D'=2, F'=10, H'=3, [ 1>=A && 10>=5*A ], cost: 14-A



Accelerating simple loops of location 2.

   Simplified some of the simple loops (and removed duplicate rules).

   Accelerating the following rules:

     19: lbl82 -> lbl82 : B'=0, D'=H, F'=1, H'=1+H, [ H>=A && 3-H==0 && F==10 && B==9 && 10+F>=5*H ], cost: 2

     20: lbl82 -> lbl82 : B'=9, D'=H, F'=10, H'=1+H, [ H>=A && 3-H==0 && F==10 && B==9 && 10+F>=5*H ], cost: 11



   Accelerated rule 19 with metering function meter_2 (where 19*meter_2==-15+F-H+B), yielding the new rule 25.

   Accelerated rule 20 with metering function 4-H, yielding the new rule 26.

   Removing the simple loops: 19 20.



Accelerated all simple loops using metering functions (where possible):

   Start location: start0

     25: lbl82 -> lbl82 : B'=0, D'=-1+meter_2+H, F'=1, H'=meter_2+H, [ H>=A && 3-H==0 && F==10 && B==9 && 10+F>=5*H && 19*meter_2==-15+F-H+B && meter_2>=1 ], cost: 2*meter_2

     26: lbl82 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ H>=A && 3-H==0 && F==10 && B==9 && 10+F>=5*H ], cost: 44-11*H

     18: start0 -> lbl82 : B'=9, D'=E, F'=10, H'=A, [ A>=3 && 4>=A ], cost: 11

     21: start0 -> lbl82 : B'=0, D'=A, F'=1, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 3

     22: start0 -> lbl82 : B'=9, D'=A, F'=10, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 12

     23: start0 -> lbl82 : B'=0, D'=2, F'=1, H'=3, [ 1>=A && 10>=5*A ], cost: 5-A

     24: start0 -> lbl82 : B'=9, D'=2, F'=10, H'=3, [ 1>=A && 10>=5*A ], cost: 14-A



Chained accelerated rules (with incoming rules):

   Start location: start0

     18: start0 -> lbl82 : B'=9, D'=E, F'=10, H'=A, [ A>=3 && 4>=A ], cost: 11

     21: start0 -> lbl82 : B'=0, D'=A, F'=1, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 3

     22: start0 -> lbl82 : B'=9, D'=A, F'=10, H'=1+A, [ 2>=A && A>=2 && 10>=5*A ], cost: 12

     23: start0 -> lbl82 : B'=0, D'=2, F'=1, H'=3, [ 1>=A && 10>=5*A ], cost: 5-A

     24: start0 -> lbl82 : B'=9, D'=2, F'=10, H'=3, [ 1>=A && 10>=5*A ], cost: 14-A

     27: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ 3-A==0 && 20>=5*A ], cost: 55-11*A

     28: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ -2+A==0 && 10>=5*A && 2-A==0 ], cost: 45-11*A

     29: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ 1>=A && 10>=5*A ], cost: 25-A



Removed unreachable locations (and leaf rules with constant cost):

   Start location: start0

     23: start0 -> lbl82 : B'=0, D'=2, F'=1, H'=3, [ 1>=A && 10>=5*A ], cost: 5-A

     24: start0 -> lbl82 : B'=9, D'=2, F'=10, H'=3, [ 1>=A && 10>=5*A ], cost: 14-A

     27: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ 3-A==0 && 20>=5*A ], cost: 55-11*A

     28: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ -2+A==0 && 10>=5*A && 2-A==0 ], cost: 45-11*A

     29: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ 1>=A && 10>=5*A ], cost: 25-A



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: start0

     27: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ 3-A==0 && 20>=5*A ], cost: 55-11*A

     28: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ -2+A==0 && 10>=5*A && 2-A==0 ], cost: 45-11*A

     29: start0 -> lbl82 : B'=9, D'=3, F'=10, H'=4, [ 1>=A && 10>=5*A ], cost: 25-A



Computing asymptotic complexity for rule 27

   Could not solve the limit problem.

   Resulting cost 0 has complexity: Unknown



Computing asymptotic complexity for rule 28

   Could not solve the limit problem.

   Resulting cost 0 has complexity: Unknown



Computing asymptotic complexity for rule 29

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      2-A (+/+!), 25-A (+) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {A==-n}

      resulting limit problem:

      [solved]



   Solution:

      A / -n

   Resulting cost 25+n has complexity: Poly(n^1)



Found new complexity Poly(n^1).



Obtained the following overall complexity (w.r.t. the length of the input n):

   Complexity:  Poly(n^1)

   Cpx degree:  1

   Solved cost: 25+n

   Rule cost:   25-A

   Rule guard:  [ 1>=A ]



WORST_CASE(Omega(n^1),?)


----------------------------------------

(4)
BOUNDS(n^1, INF)