Complexity_C_Integer 2019-03-21 04.38 pair #429988818

details

property	value
status	complete
benchmark	speed_pldi09_fig4_4.c
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	C4B_examples

run statistics

property	value
solver	AProVE
configuration	c_complexity
runtime (wallclock)	1.45306 seconds
cpu usage	2.47913
user time	2.26505
system time	0.214082
max virtual memory	1.8408828E7
max residence set size	187948.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^1))

output

2.30/1.42	WORST_CASE(?, O(n^1))
2.43/1.43	proof of /export/starexec/sandbox/output/output_files/bench.koat
2.43/1.43	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.43/1.43	
2.43/1.43	
2.43/1.43	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1).
2.43/1.43	
2.43/1.43	(0) CpxIntTrs
2.43/1.43	(1) Koat Proof [FINISHED, 178 ms]
2.43/1.43	(2) BOUNDS(1, n^1)
2.43/1.43	
2.43/1.43	
2.43/1.43	----------------------------------------
2.43/1.43	
2.43/1.43	(0)
2.43/1.43	Obligation:
2.43/1.43	Complexity Int TRS consisting of the following rules:
2.43/1.43	eval_peed_pldi09_fig4_4_start(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb0_in(v_i.0, v_m, v_n)) :|: TRUE
2.43/1.43	eval_peed_pldi09_fig4_4_bb0_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb3_in(v_i.0, v_m, v_n)) :|: 0 >= v_m
2.43/1.43	eval_peed_pldi09_fig4_4_bb0_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb1_in(v_n, v_m, v_n)) :|: 0 < v_m
2.43/1.43	eval_peed_pldi09_fig4_4_bb1_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb2_in(v_i.0, v_m, v_n)) :|: v_i.0 > 0
2.43/1.43	eval_peed_pldi09_fig4_4_bb1_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb3_in(v_i.0, v_m, v_n)) :|: v_i.0 <= 0
2.43/1.43	eval_peed_pldi09_fig4_4_bb2_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb1_in(v_i.0 - 1, v_m, v_n)) :|: v_i.0 < v_m
2.43/1.43	eval_peed_pldi09_fig4_4_bb2_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_bb1_in(v_i.0 - v_m, v_m, v_n)) :|: v_i.0 >= v_m
2.43/1.43	eval_peed_pldi09_fig4_4_bb3_in(v_i.0, v_m, v_n) -> Com_1(eval_peed_pldi09_fig4_4_stop(v_i.0, v_m, v_n)) :|: TRUE
2.43/1.43	
2.43/1.43	The start-symbols are:[eval_peed_pldi09_fig4_4_start_3]
2.43/1.43	
2.43/1.43	
2.43/1.43	----------------------------------------
2.43/1.43	
2.43/1.43	(1) Koat Proof (FINISHED)
2.43/1.43	YES(?, 6*ar_2 + 7)
2.43/1.43	
2.43/1.43	
2.43/1.43	
2.43/1.43	Initial complexity problem:
2.43/1.43	
2.43/1.43	1:	T:
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - ar_0, ar_2)) [ ar_1 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44stop(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.43/1.43	
2.43/1.43		start location:	koat_start
2.43/1.43	
2.43/1.43		leaf cost:	0
2.43/1.43	
2.43/1.43	
2.43/1.43	
2.43/1.43	Repeatedly propagating knowledge in problem 1 produces the following problem:
2.43/1.43	
2.43/1.43	2:	T:
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)    evalpeedpldi09fig44start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)    evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 1)    evalpeedpldi09fig44bb0in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_2, ar_2)) [ ar_0 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2)) [ ar_1 >= 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb1in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2)) [ 0 >= ar_1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - 1, ar_2)) [ ar_0 >= ar_1 + 1 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb2in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44bb1in(ar_0, ar_1 - ar_0, ar_2)) [ ar_1 >= ar_0 ]
2.43/1.43	
2.43/1.43			(Comp: ?, Cost: 1)    evalpeedpldi09fig44bb3in(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44stop(ar_0, ar_1, ar_2))
2.43/1.43	
2.43/1.43			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalpeedpldi09fig44start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
2.43/1.43	
2.43/1.43		start location:	koat_start
2.43/1.43	
2.43/1.43		leaf cost:	0
2.43/1.43	
2.43/1.43	
2.43/1.43	
2.43/1.43	A polynomial rank function with
2.43/1.43	
2.43/1.43		Pol(evalpeedpldi09fig44start) = 2
2.43/1.43	
2.43/1.43		Pol(evalpeedpldi09fig44bb0in) = 2
2.43/1.43	
2.43/1.43		Pol(evalpeedpldi09fig44bb3in) = 1
2.43/1.43

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actions all output return to Complexity_C_Integer 2019-03-21 04.38