Complexity_ITS 2019-03-21 04.46 pair #429991184

details

property	value
status	complete
benchmark	Example3.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n007.star.cs.uiowa.edu
space	Loopus

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	3.02244 seconds
cpu usage	6.95357
user time	6.55695
system time	0.396618
max virtual memory	1.8769164E7
max residence set size	225692.0

stage attributes

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

output

6.83/2.99	WORST_CASE(?, O(n^1))
6.83/3.00	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.83/3.00	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.83/3.00	
6.83/3.00	
6.83/3.00	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(5 + -16948680941280 * Arg_0 + 4304981706793560 * Arg_1, 5) + nat(-4253917943760 * Arg_0 + -1080511905423480 * Arg_1) + nat(32967930 * Arg_0) + nat(510 + -2 * Arg_0) + nat(-1012 * Arg_0 + 257049 * Arg_1) + nat(-254 * Arg_0 + -64517 * Arg_1)).
6.83/3.00	
6.83/3.00	(0) CpxIntTrs
6.83/3.00	(1) Koat2 Proof [FINISHED, 926 ms]
6.83/3.00	(2) BOUNDS(1, max(5 + -16948680941280 * Arg_0 + 4304981706793560 * Arg_1, 5) + nat(-4253917943760 * Arg_0 + -1080511905423480 * Arg_1) + nat(32967930 * Arg_0) + nat(510 + -2 * Arg_0) + nat(-1012 * Arg_0 + 257049 * Arg_1) + nat(-254 * Arg_0 + -64517 * Arg_1))
6.83/3.00	
6.83/3.00	
6.83/3.00	----------------------------------------
6.83/3.00	
6.83/3.00	(0)
6.83/3.00	Obligation:
6.83/3.00	Complexity Int TRS consisting of the following rules:
6.83/3.00	evalfstart(A, B) -> Com_1(evalfentryin(A, B)) :|: TRUE
6.83/3.00	evalfentryin(A, B) -> Com_1(evalfbb3in(B, A)) :|: TRUE
6.83/3.00	evalfbb3in(A, B) -> Com_1(evalfbbin(A, B)) :|: B >= 1 && 254 >= B
6.83/3.00	evalfbb3in(A, B) -> Com_1(evalfreturnin(A, B)) :|: 0 >= B
6.83/3.00	evalfbb3in(A, B) -> Com_1(evalfreturnin(A, B)) :|: B >= 255
6.83/3.00	evalfbbin(A, B) -> Com_1(evalfbb1in(A, B)) :|: 0 >= A + 1
6.83/3.00	evalfbbin(A, B) -> Com_1(evalfbb1in(A, B)) :|: A >= 1
6.83/3.00	evalfbbin(A, B) -> Com_1(evalfbb2in(A, B)) :|: A >= 0 && A <= 0
6.83/3.00	evalfbb1in(A, B) -> Com_1(evalfbb3in(A, B + 1)) :|: TRUE
6.83/3.00	evalfbb2in(A, B) -> Com_1(evalfbb3in(A, B - 1)) :|: TRUE
6.83/3.00	evalfreturnin(A, B) -> Com_1(evalfstop(A, B)) :|: TRUE
6.83/3.00	
6.83/3.00	The start-symbols are:[evalfstart_2]
6.83/3.00	
6.83/3.00	
6.83/3.00	----------------------------------------
6.83/3.00	
6.83/3.00	(1) Koat2 Proof (FINISHED)
6.83/3.00	YES( ?, 5+2*64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+254*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 255-Arg_0])+max([0, 257049*Arg_1+-1012*Arg_0])+max([0, 255-Arg_0])+max([0, -64517*Arg_1+-254*Arg_0])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]) {O(n)})
6.83/3.00	
6.83/3.00	
6.83/3.00	
6.83/3.00	Initial Complexity Problem:
6.83/3.00	
6.83/3.00	  Start:  evalfstart  
6.83/3.00	
6.83/3.00	  Program_Vars:  Arg_0, Arg_1  
6.83/3.00	
6.83/3.00	  Temp_Vars:    
6.83/3.00	
6.83/3.00	  Locations:  evalfbb1in, evalfbb2in, evalfbb3in, evalfbbin, evalfentryin, evalfreturnin, evalfstart, evalfstop  
6.83/3.00	
6.83/3.00	  Transitions:
6.83/3.00	
6.83/3.00	  evalfbb1in(Arg_0,Arg_1) -> evalfbb3in(Arg_0,Arg_1+1):|:Arg_1 <= 254 && 1 <= Arg_1
6.83/3.00	
6.83/3.00	  evalfbb2in(Arg_0,Arg_1) -> evalfbb3in(Arg_0,Arg_1-1):|:Arg_1 <= 254 && Arg_1 <= 254+Arg_0 && Arg_0+Arg_1 <= 254 && 1 <= Arg_1 && 1 <= Arg_0+Arg_1 && 1+Arg_0 <= Arg_1 && Arg_0 <= 0 && 0 <= Arg_0
6.83/3.00	
6.83/3.00	  evalfbb3in(Arg_0,Arg_1) -> evalfbbin(Arg_0,Arg_1):|:1 <= Arg_1 && Arg_1 <= 254
6.83/3.00	
6.83/3.00	  evalfbb3in(Arg_0,Arg_1) -> evalfreturnin(Arg_0,Arg_1):|:Arg_1 <= 0
6.83/3.00	
6.83/3.00	  evalfbb3in(Arg_0,Arg_1) -> evalfreturnin(Arg_0,Arg_1):|:255 <= Arg_1
6.83/3.00	
6.83/3.00	  evalfbbin(Arg_0,Arg_1) -> evalfbb1in(Arg_0,Arg_1):|:Arg_1 <= 254 && 1 <= Arg_1 && Arg_0+1 <= 0
6.83/3.00	
6.83/3.00	  evalfbbin(Arg_0,Arg_1) -> evalfbb1in(Arg_0,Arg_1):|:Arg_1 <= 254 && 1 <= Arg_1 && 1 <= Arg_0
6.83/3.00	
6.83/3.00	  evalfbbin(Arg_0,Arg_1) -> evalfbb2in(Arg_0,Arg_1):|:Arg_1 <= 254 && 1 <= Arg_1 && Arg_0 <= 0 && 0 <= Arg_0
6.83/3.00	
6.83/3.00	  evalfentryin(Arg_0,Arg_1) -> evalfbb3in(Arg_1,Arg_0):|:
6.83/3.00	
6.83/3.00	  evalfreturnin(Arg_0,Arg_1) -> evalfstop(Arg_0,Arg_1):|:
6.83/3.00	
6.83/3.00	  evalfstart(Arg_0,Arg_1) -> evalfentryin(Arg_0,Arg_1):|:  
6.83/3.00	
6.83/3.00	
6.83/3.00	
6.83/3.00	Timebounds: 
6.83/3.00	
6.83/3.00	  Overall timebound: 5+2*64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+254*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 255-Arg_0])+max([0, 257049*Arg_1+-1012*Arg_0])+max([0, 255-Arg_0])+max([0, -64517*Arg_1+-254*Arg_0])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]) {O(n)}
6.83/3.00	
6.83/3.00	  8: evalfbb1in->evalfbb3in: 64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 255-Arg_0]) {O(n)}
6.83/3.00	
6.83/3.00	  9: evalfbb2in->evalfbb3in: 254*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0])) {O(n)}
6.83/3.00	
6.83/3.00	  2: evalfbb3in->evalfbbin: 64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 255-Arg_0]) {O(n)}
6.83/3.00	
6.83/3.00	  3: evalfbb3in->evalfreturnin: 1 {O(1)}
6.83/3.00	
6.83/3.00	  4: evalfbb3in->evalfreturnin: 1 {O(1)}
6.83/3.00	
6.83/3.00	  5: evalfbbin->evalfbb1in: max([0, -64517*Arg_1+-254*Arg_0]) {O(n)}
6.83/3.00	
6.83/3.00	  6: evalfbbin->evalfbb1in: max([0, 257049*Arg_1+-1012*Arg_0]) {O(n)}
6.83/3.00	
6.83/3.00	  7: evalfbbin->evalfbb2in: max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]) {O(n)}
6.83/3.00	
6.83/3.00	  1: evalfentryin->evalfbb3in: 1 {O(1)}
6.83/3.00	
6.83/3.00	  10: evalfreturnin->evalfstop: 1 {O(1)}
6.83/3.00	
6.83/3.00	  0: evalfstart->evalfentryin: 1 {O(1)}

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to Complexity_ITS 2019-03-21 04.46