Complexity_ITS 2019-03-21 04.46 pair #429990962

details
property	value
status	complete
benchmark	exmini.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n051.star.cs.uiowa.edu
space	SAS10
run statistics
property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.03486 seconds
cpu usage	6.55447
user time	6.2085
system time	0.345973
max virtual memory	1.866302E7
max residence set size	230572.0
stage attributes
key	value
starexec-result	WORST_CASE(?, O(n^1))
output
6.37/3.99	WORST_CASE(?, O(n^1))
6.37/4.00	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.37/4.00	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.37/4.00	
6.37/4.00	
6.37/4.00	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(6, 6 + -1 * Arg_0 + 2 * Arg_4 + -1 * Arg_6)).
6.37/4.00	
6.37/4.00	(0) CpxIntTrs
6.37/4.00	(1) Koat2 Proof [FINISHED, 2295 ms]
6.37/4.00	(2) BOUNDS(1, max(6, 6 + -1 * Arg_0 + 2 * Arg_4 + -1 * Arg_6))
6.37/4.00	
6.37/4.00	
6.37/4.00	----------------------------------------
6.37/4.00	
6.37/4.00	(0)
6.37/4.00	Obligation:
6.37/4.00	Complexity Int TRS consisting of the following rules:
6.37/4.00	start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= 101 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
6.37/4.00	start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: G >= E + 1 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
6.37/4.00	start(A, B, C, D, E, F, G, H) -> Com_1(lbl71(A, H, C, D - 1, E, 1 + H, G, F)) :|: E >= G && 100 >= A && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
6.37/4.00	lbl71(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A + G + E >= B + 102 + D && E >= 1 + D && 100 >= A && E >= G && 2 * D + 2 + B >= A + G + E && 100 >= B && F >= B + 1 && F <= B + 1 && H + B + 1 + D >= A + G + E && H + B + 1 + D <= A + G + E
6.37/4.00	lbl71(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: B >= D && E >= 1 + D && 100 >= A && E >= G && 2 * D + 2 + B >= A + G + E && 100 >= B && F >= B + 1 && F <= B + 1 && H + B + 1 + D >= A + G + E && H + B + 1 + D <= A + G + E
6.37/4.00	lbl71(A, B, C, D, E, F, G, H) -> Com_1(lbl71(A, H, C, D - 1, E, 1 + H, G, F)) :|: D >= B + 1 && 101 + B + D >= A + G + E && E >= 1 + D && 100 >= A && E >= G && 2 * D + 2 + B >= A + G + E && 100 >= B && F >= B + 1 && F <= B + 1 && H + B + 1 + D >= A + G + E && H + B + 1 + D <= A + G + E
6.37/4.00	start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, E, E, G, G, A)) :|: TRUE
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6.37/4.00	The start-symbols are:[start0_8]
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6.37/4.00	----------------------------------------
6.37/4.00	
6.37/4.00	(1) Koat2 Proof (FINISHED)
6.37/4.00	YES( ?, max([6, 6+-(Arg_0)-Arg_6+2*Arg_4]) {O(n)})
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6.37/4.00	Initial Complexity Problem:
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6.37/4.00	  Start:  start0  
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6.37/4.00	  Program_Vars:  Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7  
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6.37/4.00	  Temp_Vars:    
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6.37/4.00	  Locations:  lbl71, start, start0, stop  
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6.37/4.00	  Transitions:
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6.37/4.00	  lbl71(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl71(Arg_0,Arg_7,Arg_2,Arg_3-1,Arg_4,1+Arg_7,Arg_6,Arg_5):|:Arg_7 <= Arg_4 && Arg_7 <= 1+Arg_3 && Arg_6 <= Arg_4 && Arg_5 <= 1+Arg_1 && 1+Arg_1 <= Arg_5 && 1+Arg_3 <= Arg_4 && Arg_0 <= 100 && Arg_1+1 <= Arg_3 && Arg_0+Arg_6+Arg_4 <= 101+Arg_1+Arg_3 && 1+Arg_3 <= Arg_4 && Arg_0 <= 100 && Arg_6 <= Arg_4 && Arg_0+Arg_6+Arg_4 <= (2)*Arg_3+2+Arg_1 && Arg_1 <= 100 && Arg_5 <= Arg_1+1 && Arg_1+1 <= Arg_5 && Arg_7+Arg_1+1+Arg_3 <= Arg_0+Arg_6+Arg_4 && Arg_0+Arg_6+Arg_4 <= Arg_7+Arg_1+1+Arg_3
6.37/4.00	
6.37/4.00	  lbl71(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_7 <= Arg_4 && Arg_7 <= 1+Arg_3 && Arg_6 <= Arg_4 && Arg_5 <= 1+Arg_1 && 1+Arg_1 <= Arg_5 && 1+Arg_3 <= Arg_4 && Arg_0 <= 100 && Arg_1+102+Arg_3 <= Arg_0+Arg_6+Arg_4 && 1+Arg_3 <= Arg_4 && Arg_0 <= 100 && Arg_6 <= Arg_4 && Arg_0+Arg_6+Arg_4 <= (2)*Arg_3+2+Arg_1 && Arg_1 <= 100 && Arg_5 <= Arg_1+1 && Arg_1+1 <= Arg_5 && Arg_7+Arg_1+1+Arg_3 <= Arg_0+Arg_6+Arg_4 && Arg_0+Arg_6+Arg_4 <= Arg_7+Arg_1+1+Arg_3
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6.37/4.00	  lbl71(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_7 <= Arg_4 && Arg_7 <= 1+Arg_3 && Arg_6 <= Arg_4 && Arg_5 <= 1+Arg_1 && 1+Arg_1 <= Arg_5 && 1+Arg_3 <= Arg_4 && Arg_0 <= 100 && Arg_3 <= Arg_1 && 1+Arg_3 <= Arg_4 && Arg_0 <= 100 && Arg_6 <= Arg_4 && Arg_0+Arg_6+Arg_4 <= (2)*Arg_3+2+Arg_1 && Arg_1 <= 100 && Arg_5 <= Arg_1+1 && Arg_1+1 <= Arg_5 && Arg_7+Arg_1+1+Arg_3 <= Arg_0+Arg_6+Arg_4 && Arg_0+Arg_6+Arg_4 <= Arg_7+Arg_1+1+Arg_3
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6.37/4.00	  start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> lbl71(Arg_0,Arg_7,Arg_2,Arg_3-1,Arg_4,1+Arg_7,Arg_6,Arg_5):|:Arg_7 <= Arg_0 && Arg_0 <= Arg_7 && Arg_6 <= Arg_5 && Arg_5 <= Arg_6 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && Arg_6 <= Arg_4 && Arg_0 <= 100 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_6 && Arg_6 <= Arg_5 && Arg_7 <= Arg_0 && Arg_0 <= Arg_7
6.37/4.00	
6.37/4.00	  start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_7 <= Arg_0 && Arg_0 <= Arg_7 && Arg_6 <= Arg_5 && Arg_5 <= Arg_6 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 101 <= Arg_0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_6 && Arg_6 <= Arg_5 && Arg_7 <= Arg_0 && Arg_0 <= Arg_7
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6.37/4.00	  start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_7 <= Arg_0 && Arg_0 <= Arg_7 && Arg_6 <= Arg_5 && Arg_5 <= Arg_6 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && Arg_4+1 <= Arg_6 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_6 && Arg_6 <= Arg_5 && Arg_7 <= Arg_0 && Arg_0 <= Arg_7
6.37/4.00	
6.37/4.00	  start0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> start(Arg_0,Arg_2,Arg_2,Arg_4,Arg_4,Arg_6,Arg_6,Arg_0):|:  
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6.37/4.00	Timebounds: 
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6.37/4.00	  Overall timebound: max([6, 6+-(Arg_0)-Arg_6+2*Arg_4]) {O(n)}
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6.37/4.00	  3: lbl71->stop: 1 {O(1)}
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6.37/4.00	  4: lbl71->stop: 1 {O(1)}
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6.37/4.00	  5: lbl71->lbl71: max([0, -(Arg_0)-Arg_6+2*Arg_4]) {O(n)}
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6.37/4.00	  0: start->stop: 1 {O(1)}
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6.37/4.00	  1: start->stop: 1 {O(1)}
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6.37/4.00	  2: start->lbl71: 1 {O(1)}
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6.37/4.00	  6: start0->start: 1 {O(1)}
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6.37/4.00	Costbounds:
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6.37/4.00	  Overall costbound: max([6, 6+-(Arg_0)-Arg_6+2*Arg_4]) {O(n)}
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6.37/4.00	  3: lbl71->stop: 1 {O(1)}
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6.37/4.00	  4: lbl71->stop: 1 {O(1)}
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6.37/4.00	  5: lbl71->lbl71: max([0, -(Arg_0)-Arg_6+2*Arg_4]) {O(n)}
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6.37/4.00	  0: start->stop: 1 {O(1)}
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6.37/4.00	  1: start->stop: 1 {O(1)}
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6.37/4.00	  2: start->lbl71: 1 {O(1)}
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6.37/4.00	  6: start0->start: 1 {O(1)}
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