Compl Integ Trans Syste 26843 pair #381744230

details
property	value
status	complete
benchmark	sipma91.c.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n034.star.cs.uiowa.edu
space	Flores-Montoya_16
run statistics
property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.94895601273 seconds
cpu usage	9.200781039
max memory	4.96832512E8
stage attributes
key	value
output-size	358515
starexec-result	WORST_CASE(Omega(n^1), O(n^1))
output
/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 2211 ms]
(2) BOUNDS(1, n^1)
(3) Loat Proof [FINISHED, 699 ms]
(4) BOUNDS(n^1, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
eval_sipma91_start(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb0_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: TRUE
eval_sipma91_bb0_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_0(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: TRUE
eval_sipma91_0(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_1(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: TRUE
eval_sipma91_1(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_2(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: TRUE
eval_sipma91_2(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_3(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: TRUE
eval_sipma91_3(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb8_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: v_x > 100
eval_sipma91_3(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb1_in(v_5, v_6, v_x, v_x, v_y1_1, v_y1_2, 1, v_y2_1, v_y2_2)) :|: v_x <= 100
eval_sipma91_bb1_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb2_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: v_y1_0 <= 100
eval_sipma91_bb1_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb3_in(v_5, v_6, v_x, v_y1_0, v_y1_0, v_y1_2, v_y2_0, v_y2_0, v_y2_2)) :|: v_y1_0 > 100
eval_sipma91_bb2_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb1_in(v_5, v_6, v_x, v_y1_0 + 11, v_y1_1, v_y1_2, v_y2_0 + 1, v_y2_1, v_y2_2)) :|: TRUE
eval_sipma91_bb3_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb4_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: v_y2_1 > 1
eval_sipma91_bb3_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb8_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: v_y2_1 <= 1
eval_sipma91_bb4_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb3_in(v_5, v_6, v_x, v_y1_0, v_y1_1 - 10, v_y1_2, v_y2_0, v_y2_1 - 1, v_y2_2)) :|: v_y1_1 - 10 > 100 && v_y2_1 - 1 >= 1 && v_y2_1 - 1 <= 1
eval_sipma91_bb4_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb5_in(v_y1_1 - 10, v_y2_1 - 1, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: v_y1_1 - 10 <= 100
eval_sipma91_bb4_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb5_in(v_y1_1 - 10, v_y2_1 - 1, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: v_y2_1 - 1 < 1
eval_sipma91_bb4_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb5_in(v_y1_1 - 10, v_y2_1 - 1, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: v_y2_1 - 1 > 1
eval_sipma91_bb5_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb6_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: v_5 > 100
eval_sipma91_bb5_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb7_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_5, v_y2_0, v_y2_1, v_6)) :|: v_5 <= 100
eval_sipma91_bb6_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb7_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_5 - 10, v_y2_0, v_y2_1, v_6 - 1)) :|: TRUE
eval_sipma91_bb7_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_bb3_in(v_5, v_6, v_x, v_y1_0, v_y1_2 + 11, v_y1_2, v_y2_0, v_y2_2 + 1, v_y2_2)) :|: TRUE
eval_sipma91_bb8_in(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2) -> Com_1(eval_sipma91_stop(v_5, v_6, v_x, v_y1_0, v_y1_1, v_y1_2, v_y2_0, v_y2_1, v_y2_2)) :|: TRUE

The start-symbols are:[eval_sipma91_start_9]


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(1) Koat Proof (FINISHED)
YES(?, 365*ar_0 + 40280)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    evalsipma91start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8))

		(Comp: ?, Cost: 1)    evalsipma91bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma910(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8))

		(Comp: ?, Cost: 1)    evalsipma910(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma911(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8))

		(Comp: ?, Cost: 1)    evalsipma911(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma912(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8))

		(Comp: ?, Cost: 1)    evalsipma912(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma913(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8))

		(Comp: ?, Cost: 1)    evalsipma913(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_0 >= 101 ]

		(Comp: ?, Cost: 1)    evalsipma913(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb1in(ar_0, ar_0, 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 100 >= ar_0 ]

		(Comp: ?, Cost: 1)    evalsipma91bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 100 >= ar_1 ]

		(Comp: ?, Cost: 1)    evalsipma91bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb3in(ar_0, ar_1, ar_2, ar_1, ar_2, ar_5, ar_6, ar_7, ar_8)) [ ar_1 >= 101 ]

		(Comp: ?, Cost: 1)    evalsipma91bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb1in(ar_0, ar_1 + 11, ar_2 + 1, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8))

		(Comp: ?, Cost: 1)    evalsipma91bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_4 >= 2 ]

		(Comp: ?, Cost: 1)    evalsipma91bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 1 >= ar_4 ]

		(Comp: ?, Cost: 1)    evalsipma91bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb3in(ar_0, ar_1, ar_2, ar_3 - 10, ar_4 - 1, ar_5, ar_6, ar_7, ar_8)) [ ar_3 >= 111 /\ ar_4 = 2 ]

		(Comp: ?, Cost: 1)    evalsipma91bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_3 - 10, ar_4 - 1, ar_7, ar_8)) [ 110 >= ar_3 ]

		(Comp: ?, Cost: 1)    evalsipma91bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_3 - 10, ar_4 - 1, ar_7, ar_8)) [ 1 >= ar_4 ]

		(Comp: ?, Cost: 1)    evalsipma91bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_3 - 10, ar_4 - 1, ar_7, ar_8)) [ ar_4 >= 3 ]

		(Comp: ?, Cost: 1)    evalsipma91bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ ar_5 >= 101 ]

		(Comp: ?, Cost: 1)    evalsipma91bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_5, ar_6)) [ 100 >= ar_5 ]

		(Comp: ?, Cost: 1)    evalsipma91bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_5 - 10, ar_6 - 1))

		(Comp: ?, Cost: 1)    evalsipma91bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(evalsipma91bb3in(ar_0, ar_1, ar_2, ar_7 + 11, ar_8 + 1, ar_5, ar_6, ar_7, ar_8))
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