/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(?, O(1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) CpxIntTrs
(1) Koat Proof [FINISHED, 39 ms]
(2) BOUNDS(1, 1)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A, B, C, D, E, F, G, H, I) -> Com_1(f7(30, 30, 1, 0, 2, F, G, H, I)) :|: TRUE
f7(A, B, C, D, E, F, G, H, I) -> Com_1(f7(A, B, C + D, C, E + 1, C, G, H, I)) :|: B >= E
f7(A, B, C, D, E, F, G, H, I) -> Com_1(f19(A, B, C, D, E, F, C, C, C)) :|: E >= 1 + B

The start-symbols are:[f0_9]


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(1) Koat Proof (FINISHED)
YES(?, 31)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(30, 30, 1, 0, 2, Ar_5, Ar_6, Ar_7, Ar_8))

		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_2, Ar_4 + 1, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_1 >= Ar_4 ]

		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2, Ar_2, Ar_2)) [ Ar_4 >= Ar_1 + 1 ]

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 1 produces the following problem:

2:	T:

		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(30, 30, 1, 0, 2, Ar_5, Ar_6, Ar_7, Ar_8))

		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_2, Ar_4 + 1, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_1 >= Ar_4 ]

		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2, Ar_2, Ar_2)) [ Ar_4 >= Ar_1 + 1 ]

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(f0) = 1

	Pol(f7) = 1

	Pol(f19) = 0

	Pol(koat_start) = 1

orients all transitions weakly and the transition

	f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2, Ar_2, Ar_2)) [ Ar_4 >= Ar_1 + 1 ]

strictly and produces the following problem:

3:	T:

		(Comp: 1, Cost: 1)    f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(30, 30, 1, 0, 2, Ar_5, Ar_6, Ar_7, Ar_8))

		(Comp: ?, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_2, Ar_4 + 1, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_1 >= Ar_4 ]

		(Comp: 1, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2, Ar_2, Ar_2)) [ Ar_4 >= Ar_1 + 1 ]

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(f0) = 29

	Pol(f7) = V_2 - V_5 + 1

	Pol(f19) = V_2 - V_5

	Pol(koat_start) = 29

orients all transitions weakly and the transition

	f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_2, Ar_4 + 1, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_1 >= Ar_4 ]

strictly and produces the following problem:

4:	T:

		(Comp: 1, Cost: 1)     f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(30, 30, 1, 0, 2, Ar_5, Ar_6, Ar_7, Ar_8))

		(Comp: 29, Cost: 1)    f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f7(Ar_0, Ar_1, Ar_2 + Ar_3, Ar_2, Ar_4 + 1, Ar_2, Ar_6, Ar_7, Ar_8)) [ Ar_1 >= Ar_4 ]

		(Comp: 1, Cost: 1)     f7(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f19(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_2, Ar_2, Ar_2)) [ Ar_4 >= Ar_1 + 1 ]

		(Comp: 1, Cost: 0)     koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8) -> Com_1(f0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6, Ar_7, Ar_8)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 31



Time: 0.074 sec (SMT: 0.063 sec)


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(2)
BOUNDS(1, 1)