Complexity_ITS 2019-03-21 04.46 pair #429990008

details

property	value
status	complete
benchmark	Loopus2011_ex3.c.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n084.star.cs.uiowa.edu
space	Flores-Montoya_16

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.20798 seconds
cpu usage	7.06654
user time	6.64897
system time	0.41757
max virtual memory	1.8711504E7
max residence set size	228604.0

stage attributes

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

output

6.96/3.17	WORST_CASE(?, O(n^1))
6.96/3.18	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.96/3.18	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.96/3.18	
6.96/3.18	
6.96/3.18	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, nat(-65280 * Arg_1 + -16646400 * Arg_2) + nat(256 * Arg_1) + nat(-1 * Arg_1 + 255 * Arg_2) + max(10 + -1 * Arg_1 + -255 * Arg_2, 10) + nat(255 + -1 * Arg_1) + nat(-65280 * Arg_1 + 16646400 * Arg_2)).
6.96/3.18	
6.96/3.18	(0) CpxIntTrs
6.96/3.18	(1) Koat2 Proof [FINISHED, 1255 ms]
6.96/3.18	(2) BOUNDS(1, nat(-65280 * Arg_1 + -16646400 * Arg_2) + nat(256 * Arg_1) + nat(-1 * Arg_1 + 255 * Arg_2) + max(10 + -1 * Arg_1 + -255 * Arg_2, 10) + nat(255 + -1 * Arg_1) + nat(-65280 * Arg_1 + 16646400 * Arg_2))
6.96/3.18	
6.96/3.18	
6.96/3.18	----------------------------------------
6.96/3.18	
6.96/3.18	(0)
6.96/3.18	Obligation:
6.96/3.18	Complexity Int TRS consisting of the following rules:
6.96/3.18	eval_ex3_start(v__0, v_b, v_x) -> Com_1(eval_ex3_bb0_in(v__0, v_b, v_x)) :|: TRUE
6.96/3.18	eval_ex3_bb0_in(v__0, v_b, v_x) -> Com_1(eval_ex3_0(v__0, v_b, v_x)) :|: TRUE
6.96/3.18	eval_ex3_0(v__0, v_b, v_x) -> Com_1(eval_ex3_1(v__0, v_b, v_x)) :|: TRUE
6.96/3.18	eval_ex3_1(v__0, v_b, v_x) -> Com_1(eval_ex3_2(v__0, v_b, v_x)) :|: TRUE
6.96/3.18	eval_ex3_2(v__0, v_b, v_x) -> Com_1(eval_ex3_3(v__0, v_b, v_x)) :|: TRUE
6.96/3.18	eval_ex3_3(v__0, v_b, v_x) -> Com_1(eval_ex3_4(v__0, v_b, v_x)) :|: TRUE
6.96/3.18	eval_ex3_4(v__0, v_b, v_x) -> Com_1(eval_ex3_bb1_in(v_x, v_b, v_x)) :|: TRUE
6.96/3.18	eval_ex3_bb1_in(v__0, v_b, v_x) -> Com_1(eval_ex3_bb2_in(v__0, v_b, v_x)) :|: 0 < v__0 && v__0 < 255
6.96/3.18	eval_ex3_bb1_in(v__0, v_b, v_x) -> Com_1(eval_ex3_bb3_in(v__0, v_b, v_x)) :|: 0 >= v__0
6.96/3.18	eval_ex3_bb1_in(v__0, v_b, v_x) -> Com_1(eval_ex3_bb3_in(v__0, v_b, v_x)) :|: v__0 >= 255
6.96/3.18	eval_ex3_bb2_in(v__0, v_b, v_x) -> Com_1(eval_ex3_bb1_in(v__0 + 1, v_b, v_x)) :|: v_b < 0
6.96/3.18	eval_ex3_bb2_in(v__0, v_b, v_x) -> Com_1(eval_ex3_bb1_in(v__0 + 1, v_b, v_x)) :|: v_b > 0
6.96/3.18	eval_ex3_bb2_in(v__0, v_b, v_x) -> Com_1(eval_ex3_bb1_in(v__0 - 1, v_b, v_x)) :|: v_b >= 0 && v_b <= 0
6.96/3.18	eval_ex3_bb3_in(v__0, v_b, v_x) -> Com_1(eval_ex3_stop(v__0, v_b, v_x)) :|: TRUE
6.96/3.18	
6.96/3.18	The start-symbols are:[eval_ex3_start_3]
6.96/3.18	
6.96/3.18	
6.96/3.18	----------------------------------------
6.96/3.18	
6.96/3.18	(1) Koat2 Proof (FINISHED)
6.96/3.18	YES( ?, 4+6+max([0, -(Arg_1)+-255*Arg_2])+max([0, 255-Arg_1])+255*(max([0, 255*(-(Arg_1)+255*Arg_2)])+max([0, 255*(-(Arg_1)+-255*Arg_2)])+max([0, Arg_1]))+max([0, 255*(-(Arg_1)+255*Arg_2)])+max([0, -(Arg_1)+255*Arg_2])+max([0, 255*(-(Arg_1)+-255*Arg_2)])+max([0, Arg_1]) {O(n)})
6.96/3.18	
6.96/3.18	
6.96/3.18	
6.96/3.18	Initial Complexity Problem:
6.96/3.18	
6.96/3.18	  Start:  evalex3start  
6.96/3.18	
6.96/3.18	  Program_Vars:  Arg_0, Arg_1, Arg_2  
6.96/3.18	
6.96/3.18	  Temp_Vars:    
6.96/3.18	
6.96/3.18	  Locations:  evalex30, evalex31, evalex32, evalex33, evalex34, evalex3bb0in, evalex3bb1in, evalex3bb2in, evalex3bb3in, evalex3start, evalex3stop  
6.96/3.18	
6.96/3.18	  Transitions:
6.96/3.18	
6.96/3.18	  evalex30(Arg_0,Arg_1,Arg_2) -> evalex31(Arg_0,Arg_1,Arg_2):|:
6.96/3.18	
6.96/3.18	  evalex31(Arg_0,Arg_1,Arg_2) -> evalex32(Arg_0,Arg_1,Arg_2):|:
6.96/3.18	
6.96/3.18	  evalex32(Arg_0,Arg_1,Arg_2) -> evalex33(Arg_0,Arg_1,Arg_2):|:
6.96/3.18	
6.96/3.18	  evalex33(Arg_0,Arg_1,Arg_2) -> evalex34(Arg_0,Arg_1,Arg_2):|:
6.96/3.18	
6.96/3.18	  evalex34(Arg_0,Arg_1,Arg_2) -> evalex3bb1in(Arg_1,Arg_1,Arg_2):|:
6.96/3.18	
6.96/3.18	  evalex3bb0in(Arg_0,Arg_1,Arg_2) -> evalex30(Arg_0,Arg_1,Arg_2):|:
6.96/3.18	
6.96/3.18	  evalex3bb1in(Arg_0,Arg_1,Arg_2) -> evalex3bb2in(Arg_0,Arg_1,Arg_2):|:1 <= Arg_0 && Arg_0 <= 254
6.96/3.18	
6.96/3.18	  evalex3bb1in(Arg_0,Arg_1,Arg_2) -> evalex3bb3in(Arg_0,Arg_1,Arg_2):|:Arg_0 <= 0
6.96/3.18	
6.96/3.18	  evalex3bb1in(Arg_0,Arg_1,Arg_2) -> evalex3bb3in(Arg_0,Arg_1,Arg_2):|:255 <= Arg_0
6.96/3.18	
6.96/3.18	  evalex3bb2in(Arg_0,Arg_1,Arg_2) -> evalex3bb1in(Arg_0+1,Arg_1,Arg_2):|:Arg_0 <= 254 && 1 <= Arg_0 && Arg_2+1 <= 0
6.96/3.18	
6.96/3.18	  evalex3bb2in(Arg_0,Arg_1,Arg_2) -> evalex3bb1in(Arg_0+1,Arg_1,Arg_2):|:Arg_0 <= 254 && 1 <= Arg_0 && 1 <= Arg_2
6.96/3.18	
6.96/3.18	  evalex3bb2in(Arg_0,Arg_1,Arg_2) -> evalex3bb1in(Arg_0-1,Arg_1,Arg_2):|:Arg_0 <= 254 && 1 <= Arg_0 && Arg_2 <= 0 && 0 <= Arg_2
6.96/3.18	
6.96/3.18	  evalex3bb3in(Arg_0,Arg_1,Arg_2) -> evalex3stop(Arg_0,Arg_1,Arg_2):|:
6.96/3.18	
6.96/3.18	  evalex3start(Arg_0,Arg_1,Arg_2) -> evalex3bb0in(Arg_0,Arg_1,Arg_2):|:  
6.96/3.18	
6.96/3.18	
6.96/3.18	
6.96/3.18	Timebounds: 
6.96/3.18	
6.96/3.18	  Overall timebound: 4+6+max([0, -(Arg_1)+-255*Arg_2])+max([0, 255-Arg_1])+255*(max([0, 255*(-(Arg_1)+255*Arg_2)])+max([0, 255*(-(Arg_1)+-255*Arg_2)])+max([0, Arg_1]))+max([0, 255*(-(Arg_1)+255*Arg_2)])+max([0, -(Arg_1)+255*Arg_2])+max([0, 255*(-(Arg_1)+-255*Arg_2)])+max([0, Arg_1]) {O(n)}
6.96/3.18	
6.96/3.18	  2: evalex30->evalex31: 1 {O(1)}
6.96/3.18	
6.96/3.18	  3: evalex31->evalex32: 1 {O(1)}
6.96/3.18	
6.96/3.18	  4: evalex32->evalex33: 1 {O(1)}
6.96/3.18	
6.96/3.18	  5: evalex33->evalex34: 1 {O(1)}
6.96/3.18	
6.96/3.18	  6: evalex34->evalex3bb1in: 1 {O(1)}
6.96/3.18	
6.96/3.18	  1: evalex3bb0in->evalex30: 1 {O(1)}
6.96/3.18

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