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


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WORST_CASE(Omega(n^2), O(n^2))
proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).

(0) CpxIntTrs
(1) Koat Proof [FINISHED, 227 ms]
(2) BOUNDS(1, n^2)
(3) Loat Proof [FINISHED, 725 ms]
(4) BOUNDS(n^2, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
start(A, B, C, D, E, F) -> Com_1(stop(A, B, C, F, E, F)) :|: 0 >= A && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A
start(A, B, C, D, E, F) -> Com_1(lbl62(A, F - 1, C, F, E, F)) :|: A >= 1 && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A
lbl72(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: A >= 1 && D >= 0 && D <= 0 && B >= 0 && B <= 0 && F >= A && F <= A
lbl72(A, B, C, D, E, F) -> Com_1(lbl72(A, F, C, D - 1, E, F)) :|: D >= 1 && 0 >= A && D >= 0 && A >= D + 1 && B >= 0 && B <= 0 && F >= A && F <= A
lbl72(A, B, C, D, E, F) -> Com_1(lbl62(A, F - 1, C, D, E, F)) :|: A >= 1 && D >= 1 && D >= 0 && A >= D + 1 && B >= 0 && B <= 0 && F >= A && F <= A
lbl62(A, B, C, D, E, F) -> Com_1(lbl72(A, B, C, D - 1, E, F)) :|: A >= D && A >= 1 && D >= 1 && B >= 0 && B <= 0 && F >= A && F <= A
lbl62(A, B, C, D, E, F) -> Com_1(lbl62(A, B - 1, C, D, E, F)) :|: B >= 1 && A >= D && A >= B + 1 && B >= 0 && D >= 1 && F >= A && F <= A
start0(A, B, C, D, E, F) -> Com_1(start(A, C, C, E, E, A)) :|: TRUE

The start-symbols are:[start0_6]


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(1) Koat Proof (FINISHED)
YES(?, 7*ar_0 + 2*ar_0^2 + 5)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_5, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_5, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 = 0 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_5, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_3 >= 1 /\ 0 >= ar_0 /\ ar_3 >= 0 /\ ar_0 >= ar_3 + 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_3 >= 0 /\ ar_0 >= ar_3 + 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_0 >= ar_3 /\ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\ ar_0 >= ar_3 /\ ar_0 >= ar_1 + 1 /\ ar_1 >= 0 /\ ar_3 >= 1 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_0))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



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

	lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_5, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_3 >= 1 /\ 0 >= ar_0 /\ ar_3 >= 0 /\ ar_0 >= ar_3 + 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

We thus obtain the following problem:

2:	T:

		(Comp: ?, Cost: 1)    lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_3 >= 0 /\ ar_0 >= ar_3 + 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 = 0 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\ ar_0 >= ar_3 /\ ar_0 >= ar_1 + 1 /\ ar_1 >= 0 /\ ar_3 >= 1 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_0 >= ar_3 /\ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_5, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_5, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_0))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 2 produces the following problem:

3:	T:

		(Comp: ?, Cost: 1)    lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_3 >= 0 /\ ar_0 >= ar_3 + 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 = 0 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\ ar_0 >= ar_3 /\ ar_0 >= ar_1 + 1 /\ ar_1 >= 0 /\ ar_3 >= 1 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_0 >= ar_3 /\ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_5, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_5, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_0))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(lbl72) = 1

	Pol(lbl62) = 1

	Pol(stop) = 0

	Pol(start) = 1

	Pol(start0) = 1

	Pol(koat_start) = 1

orients all transitions weakly and the transition

	lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 = 0 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

strictly and produces the following problem:

4:	T:

		(Comp: ?, Cost: 1)    lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_3 >= 0 /\ ar_0 >= ar_3 + 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)    lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 = 0 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\ ar_0 >= ar_3 /\ ar_0 >= ar_1 + 1 /\ ar_1 >= 0 /\ ar_3 >= 1 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)    lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_0 >= ar_3 /\ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_5, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_5, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_0))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(lbl72) = 2*V_4 + 1

	Pol(lbl62) = 2*V_4

	Pol(stop) = 2*V_1 + 2*V_4 - 2*V_6

	Pol(start) = 2*V_1

	Pol(start0) = 2*V_1

	Pol(koat_start) = 2*V_1

orients all transitions weakly and the transitions

	lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_3 >= 0 /\ ar_0 >= ar_3 + 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

	lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_0 >= ar_3 /\ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

strictly and produces the following problem:

5:	T:

		(Comp: 2*ar_0, Cost: 1)    lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_3 >= 0 /\ ar_0 >= ar_3 + 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)         lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 = 0 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: ?, Cost: 1)         lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\ ar_0 >= ar_3 /\ ar_0 >= ar_1 + 1 /\ ar_1 >= 0 /\ ar_3 >= 1 /\ ar_5 = ar_0 ]

		(Comp: 2*ar_0, Cost: 1)    lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_0 >= ar_3 /\ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)         start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_5, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)         start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_5, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)         start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_0))

		(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(lbl62) = V_2 + 1

and size complexities

	S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-0) = ar_0

	S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-1) = ar_1

	S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-2) = ar_2

	S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-3) = ar_3

	S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-4) = ar_4

	S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-5) = ar_5

	S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_0))", 0-0) = ar_0

	S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_0))", 0-1) = ar_2

	S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_0))", 0-2) = ar_2

	S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_0))", 0-3) = ar_4

	S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_0))", 0-4) = ar_4

	S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_0))", 0-5) = ar_0

	S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_5, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_0 ]", 0-0) = ar_0

	S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_5, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_0 ]", 0-1) = ar_2

	S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_5, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_0 ]", 0-2) = ar_2

	S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_5, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_0 ]", 0-3) = ar_0

	S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_5, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_0 ]", 0-4) = ar_4

	S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_5, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_0 ]", 0-5) = ar_0

	S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_5, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_0 ]", 0-0) = ar_0

	S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_5, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_0 ]", 0-1) = ar_0

	S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_5, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_0 ]", 0-2) = ar_2

	S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_5, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_0 ]", 0-3) = ar_0

	S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_5, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_0 ]", 0-4) = ar_4

	S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_5, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_4 /\\ ar_5 = ar_0 ]", 0-5) = ar_0

	S("lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_0 >= ar_3 /\\ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-0) = ar_0

	S("lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_0 >= ar_3 /\\ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-1) = 0

	S("lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_0 >= ar_3 /\\ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-2) = ar_2

	S("lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_0 >= ar_3 /\\ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-3) = ar_0

	S("lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_0 >= ar_3 /\\ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-4) = ar_4

	S("lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_0 >= ar_3 /\\ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-5) = ar_0

	S("lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\\ ar_0 >= ar_3 /\\ ar_0 >= ar_1 + 1 /\\ ar_1 >= 0 /\\ ar_3 >= 1 /\\ ar_5 = ar_0 ]", 0-0) = ar_0

	S("lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\\ ar_0 >= ar_3 /\\ ar_0 >= ar_1 + 1 /\\ ar_1 >= 0 /\\ ar_3 >= 1 /\\ ar_5 = ar_0 ]", 0-1) = ar_0

	S("lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\\ ar_0 >= ar_3 /\\ ar_0 >= ar_1 + 1 /\\ ar_1 >= 0 /\\ ar_3 >= 1 /\\ ar_5 = ar_0 ]", 0-2) = ar_2

	S("lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\\ ar_0 >= ar_3 /\\ ar_0 >= ar_1 + 1 /\\ ar_1 >= 0 /\\ ar_3 >= 1 /\\ ar_5 = ar_0 ]", 0-3) = ar_0

	S("lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\\ ar_0 >= ar_3 /\\ ar_0 >= ar_1 + 1 /\\ ar_1 >= 0 /\\ ar_3 >= 1 /\\ ar_5 = ar_0 ]", 0-4) = ar_4

	S("lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\\ ar_0 >= ar_3 /\\ ar_0 >= ar_1 + 1 /\\ ar_1 >= 0 /\\ ar_3 >= 1 /\\ ar_5 = ar_0 ]", 0-5) = ar_0

	S("lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_3 = 0 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-0) = ar_0

	S("lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_3 = 0 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-1) = 0

	S("lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_3 = 0 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-2) = ar_2

	S("lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_3 = 0 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-3) = 0

	S("lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_3 = 0 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-4) = ar_4

	S("lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_3 = 0 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-5) = ar_0

	S("lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_3 >= 0 /\\ ar_0 >= ar_3 + 1 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-0) = ar_0

	S("lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_3 >= 0 /\\ ar_0 >= ar_3 + 1 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-1) = ar_0

	S("lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_3 >= 0 /\\ ar_0 >= ar_3 + 1 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-2) = ar_2

	S("lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_3 >= 0 /\\ ar_0 >= ar_3 + 1 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-3) = ar_0

	S("lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_3 >= 0 /\\ ar_0 >= ar_3 + 1 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-4) = ar_4

	S("lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_3 >= 1 /\\ ar_3 >= 0 /\\ ar_0 >= ar_3 + 1 /\\ ar_1 = 0 /\\ ar_5 = ar_0 ]", 0-5) = ar_0

orients the transitions

	lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\ ar_0 >= ar_3 /\ ar_0 >= ar_1 + 1 /\ ar_1 >= 0 /\ ar_3 >= 1 /\ ar_5 = ar_0 ]

weakly and the transition

	lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\ ar_0 >= ar_3 /\ ar_0 >= ar_1 + 1 /\ ar_1 >= 0 /\ ar_3 >= 1 /\ ar_5 = ar_0 ]

strictly and produces the following problem:

6:	T:

		(Comp: 2*ar_0, Cost: 1)                   lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_3 >= 0 /\ ar_0 >= ar_3 + 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)                        lbl72(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_3 = 0 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: 2*ar_0^2 + 3*ar_0 + 1, Cost: 1)    lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_1 - 1, ar_2, ar_3, ar_4, ar_5)) [ ar_1 >= 1 /\ ar_0 >= ar_3 /\ ar_0 >= ar_1 + 1 /\ ar_1 >= 0 /\ ar_3 >= 1 /\ ar_5 = ar_0 ]

		(Comp: 2*ar_0, Cost: 1)                   lbl62(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl72(ar_0, ar_1, ar_2, ar_3 - 1, ar_4, ar_5)) [ ar_0 >= ar_3 /\ ar_0 >= 1 /\ ar_3 >= 1 /\ ar_1 = 0 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)                        start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl62(ar_0, ar_5 - 1, ar_2, ar_5, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)                        start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_5, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_4 /\ ar_5 = ar_0 ]

		(Comp: 1, Cost: 1)                        start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_4, ar_4, ar_0))

		(Comp: 1, Cost: 0)                        koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 7*ar_0 + 2*ar_0^2 + 5



Time: 0.232 sec (SMT: 0.196 sec)


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

(2)
BOUNDS(1, n^2)

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

(3) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: start0

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

      1: start -> lbl62 : B'=-1+F, D'=F, [ A>=1 && B==C && D==E && F==A ], cost: 1

      2: lbl72 -> stop : [ A>=1 && D==0 && B==0 && F==A ], cost: 1

      3: lbl72 -> lbl72 : B'=F, D'=-1+D, [ D>=1 && 0>=A && D>=0 && A>=1+D && B==0 && F==A ], cost: 1

      4: lbl72 -> lbl62 : B'=-1+F, [ A>=1 && D>=1 && D>=0 && A>=1+D && B==0 && F==A ], cost: 1

      5: lbl62 -> lbl72 : D'=-1+D, [ A>=D && A>=1 && D>=1 && B==0 && F==A ], cost: 1

      6: lbl62 -> lbl62 : B'=-1+B, [ B>=1 && A>=D && A>=1+B && B>=0 && D>=1 && F==A ], cost: 1

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



Removed unreachable and leaf rules:

   Start location: start0

      1: start -> lbl62 : B'=-1+F, D'=F, [ A>=1 && B==C && D==E && F==A ], cost: 1

      3: lbl72 -> lbl72 : B'=F, D'=-1+D, [ D>=1 && 0>=A && D>=0 && A>=1+D && B==0 && F==A ], cost: 1

      4: lbl72 -> lbl62 : B'=-1+F, [ A>=1 && D>=1 && D>=0 && A>=1+D && B==0 && F==A ], cost: 1

      5: lbl62 -> lbl72 : D'=-1+D, [ A>=D && A>=1 && D>=1 && B==0 && F==A ], cost: 1

      6: lbl62 -> lbl62 : B'=-1+B, [ B>=1 && A>=D && A>=1+B && B>=0 && D>=1 && F==A ], cost: 1

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



Removed rules with unsatisfiable guard:

   Start location: start0

      1: start -> lbl62 : B'=-1+F, D'=F, [ A>=1 && B==C && D==E && F==A ], cost: 1

      4: lbl72 -> lbl62 : B'=-1+F, [ A>=1 && D>=1 && D>=0 && A>=1+D && B==0 && F==A ], cost: 1

      5: lbl62 -> lbl72 : D'=-1+D, [ A>=D && A>=1 && D>=1 && B==0 && F==A ], cost: 1

      6: lbl62 -> lbl62 : B'=-1+B, [ B>=1 && A>=D && A>=1+B && B>=0 && D>=1 && F==A ], cost: 1

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



Simplified all rules, resulting in:

   Start location: start0

      1: start -> lbl62 : B'=-1+F, D'=F, [ A>=1 && B==C && D==E && F==A ], cost: 1

      4: lbl72 -> lbl62 : B'=-1+F, [ D>=1 && A>=1+D && B==0 && F==A ], cost: 1

      5: lbl62 -> lbl72 : D'=-1+D, [ A>=D && A>=1 && D>=1 && B==0 && F==A ], cost: 1

      6: lbl62 -> lbl62 : B'=-1+B, [ B>=1 && A>=D && A>=1+B && D>=1 && F==A ], cost: 1

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



### Simplification by acceleration and chaining ###



Accelerating simple loops of location 2.

   Accelerating the following rules:

      6: lbl62 -> lbl62 : B'=-1+B, [ B>=1 && A>=D && A>=1+B && D>=1 && F==A ], cost: 1



   Accelerated rule 6 with metering function B, yielding the new rule 8.

   Removing the simple loops: 6.



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

   Start location: start0

      1: start -> lbl62 : B'=-1+F, D'=F, [ A>=1 && B==C && D==E && F==A ], cost: 1

      4: lbl72 -> lbl62 : B'=-1+F, [ D>=1 && A>=1+D && B==0 && F==A ], cost: 1

      5: lbl62 -> lbl72 : D'=-1+D, [ A>=D && A>=1 && D>=1 && B==0 && F==A ], cost: 1

      8: lbl62 -> lbl62 : B'=0, [ B>=1 && A>=D && A>=1+B && D>=1 && F==A ], cost: B

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



Chained accelerated rules (with incoming rules):

   Start location: start0

      1: start -> lbl62 : B'=-1+F, D'=F, [ A>=1 && B==C && D==E && F==A ], cost: 1

      9: start -> lbl62 : B'=0, D'=F, [ A>=1 && B==C && D==E && F==A && -1+F>=1 ], cost: F

      4: lbl72 -> lbl62 : B'=-1+F, [ D>=1 && A>=1+D && B==0 && F==A ], cost: 1

     10: lbl72 -> lbl62 : B'=0, [ D>=1 && A>=1+D && B==0 && F==A && -1+F>=1 ], cost: F

      5: lbl62 -> lbl72 : D'=-1+D, [ A>=D && A>=1 && D>=1 && B==0 && F==A ], cost: 1

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



Eliminated locations (on tree-shaped paths):

   Start location: start0

     13: lbl62 -> lbl62 : B'=-1+F, D'=-1+D, [ A>=D && A>=1 && B==0 && F==A && -1+D>=1 ], cost: 2

     14: lbl62 -> lbl62 : B'=0, D'=-1+D, [ A>=D && A>=1 && B==0 && F==A && -1+D>=1 && -1+F>=1 ], cost: 1+F

     11: start0 -> lbl62 : B'=-1+A, D'=A, F'=A, [ A>=1 ], cost: 2

     12: start0 -> lbl62 : B'=0, D'=A, F'=A, [ -1+A>=1 ], cost: 1+A



Accelerating simple loops of location 2.

   Accelerating the following rules:

     13: lbl62 -> lbl62 : B'=-1+F, D'=-1+D, [ A>=D && A>=1 && B==0 && F==A && -1+D>=1 ], cost: 2

     14: lbl62 -> lbl62 : B'=0, D'=-1+D, [ A>=D && A>=1 && B==0 && F==A && -1+D>=1 && -1+F>=1 ], cost: 1+F



   Accelerated rule 13 with NONTERM (after strengthening guard), yielding the new rule 15.

   Accelerated rule 14 with metering function -1+D, yielding the new rule 16.

   Removing the simple loops: 14.



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

   Start location: start0

     13: lbl62 -> lbl62 : B'=-1+F, D'=-1+D, [ A>=D && A>=1 && B==0 && F==A && -1+D>=1 ], cost: 2

     15: lbl62 -> [6] : [ A>=D && A>=1 && B==0 && F==A && -1+D>=1 && -1+F==0 ], cost: INF

     16: lbl62 -> lbl62 : B'=0, D'=1, [ A>=D && A>=1 && B==0 && F==A && -1+D>=1 && -1+F>=1 ], cost: -1+D+F*(-1+D)

     11: start0 -> lbl62 : B'=-1+A, D'=A, F'=A, [ A>=1 ], cost: 2

     12: start0 -> lbl62 : B'=0, D'=A, F'=A, [ -1+A>=1 ], cost: 1+A



Chained accelerated rules (with incoming rules):

   Start location: start0

     11: start0 -> lbl62 : B'=-1+A, D'=A, F'=A, [ A>=1 ], cost: 2

     12: start0 -> lbl62 : B'=0, D'=A, F'=A, [ -1+A>=1 ], cost: 1+A

     17: start0 -> lbl62 : B'=-1+A, D'=-1+A, F'=A, [ -1+A>=1 ], cost: 3+A

     18: start0 -> lbl62 : B'=0, D'=1, F'=A, [ -1+A>=1 ], cost: (-1+A)*A+2*A



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

   Start location: start0

     12: start0 -> lbl62 : B'=0, D'=A, F'=A, [ -1+A>=1 ], cost: 1+A

     17: start0 -> lbl62 : B'=-1+A, D'=-1+A, F'=A, [ -1+A>=1 ], cost: 3+A

     18: start0 -> lbl62 : B'=0, D'=1, F'=A, [ -1+A>=1 ], cost: (-1+A)*A+2*A



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: start0

     17: start0 -> lbl62 : B'=-1+A, D'=-1+A, F'=A, [ -1+A>=1 ], cost: 3+A

     18: start0 -> lbl62 : B'=0, D'=1, F'=A, [ -1+A>=1 ], cost: (-1+A)*A+2*A



Computing asymptotic complexity for rule 17

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      -1+A (+/+!), 3+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 3+n has complexity: Poly(n^1)



Found new complexity Poly(n^1).



Computing asymptotic complexity for rule 18

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      -1+A (+/+!), A+A^2 (+) [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 n^2+n has complexity: Poly(n^2)



Found new complexity Poly(n^2).



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

   Complexity:  Poly(n^2)

   Cpx degree:  2

   Solved cost: n^2+n

   Rule cost:   (-1+A)*A+2*A

   Rule guard:  [ -1+A>=1 ]



WORST_CASE(Omega(n^2),?)


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

(4)
BOUNDS(n^2, INF)