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


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


WORST_CASE(?, O(1))
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(1, 1).

(0) CpxIntTrs
(1) Koat Proof [FINISHED, 20 ms]
(2) BOUNDS(1, 1)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A, B, C, D, E, F) -> Com_1(f17(H, G, I, D, E, F)) :|: 0 >= 2 + G
f0(A, B, C, D, E, F) -> Com_1(f17(H, G, I, D, E, F)) :|: G >= 0
f0(A, B, C, D, E, F) -> Com_1(f17(H, -(1), C, 0, G, I)) :|: TRUE

The start-symbols are:[f0_6]


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

(1) Koat Proof (FINISHED)
YES(?, 3)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(f17(h, g, i, ar_3, ar_4, ar_5)) [ 0 >= g + 2 ]

		(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(f17(h, g, i, ar_3, ar_4, ar_5)) [ g >= 0 ]

		(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(f17(h, -1, ar_2, 0, g, i))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(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 1 produces the following problem:

2:	T:

		(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(f17(h, g, i, ar_3, ar_4, ar_5)) [ 0 >= g + 2 ]

		(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(f17(h, g, i, ar_3, ar_4, ar_5)) [ g >= 0 ]

		(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(f17(h, -1, ar_2, 0, g, i))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 3



Time: 0.028 sec (SMT: 0.026 sec)


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

(2)
BOUNDS(1, 1)