Complexity_ITS 2019-03-21 04.46 pair #429991006

details
property	value
status	complete
benchmark	insertsort.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n173.star.cs.uiowa.edu
space	SAS10
run statistics
property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	9.47774 seconds
cpu usage	11.5051
user time	11.0984
system time	0.406758
max virtual memory	1.8465516E7
max residence set size	230388.0
stage attributes
key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))
output
11.39/8.13	WORST_CASE(Omega(n^1), O(n^2))
11.39/8.14	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
11.39/8.14	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.39/8.14	
11.39/8.14	
11.39/8.14	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, nat(-2 + 2 * Arg_0) + nat(Arg_0) + max(2 * Arg_0, 4) + max(3, 3 + Arg_0 * max(2 * Arg_0, 4) + min(-4, -2 * Arg_0)) + max(1, Arg_0)).
11.39/8.14	
11.39/8.14	(0) CpxIntTrs
11.39/8.14	(1) Koat2 Proof [FINISHED, 6353 ms]
11.39/8.14	(2) BOUNDS(1, nat(-2 + 2 * Arg_0) + nat(Arg_0) + max(2 * Arg_0, 4) + max(3, 3 + Arg_0 * max(2 * Arg_0, 4) + min(-4, -2 * Arg_0)) + max(1, Arg_0))
11.39/8.14	(3) Loat Proof [FINISHED, 911 ms]
11.39/8.14	(4) BOUNDS(n^1, INF)
11.39/8.14	
11.39/8.14	
11.39/8.14	----------------------------------------
11.39/8.14	
11.39/8.14	(0)
11.39/8.14	Obligation:
11.39/8.14	Complexity Int TRS consisting of the following rules:
11.39/8.14	start(A, B, C, D, E, F, G, H, I, J) -> Com_1(stop(A, B, C, D, E, F, G, H, 1, J)) :|: 1 >= A && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A && G >= H && G <= H && I >= J && I <= J
11.39/8.14	start(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl31(A, K, C, D, E, F, G, H, 1, J)) :|: A >= 2 && B >= C && B <= C && D >= E && D <= E && F >= A && F <= A && G >= H && G <= H && I >= J && I <= J
11.39/8.14	lbl43(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl43(A, B, C, D, E, F, G - 1, H, I, J)) :|: G >= 0 && I >= G + 2 && G + 1 >= 0 && A >= I + 1 && F >= A && F <= A
11.39/8.14	lbl43(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl13(A, B, C, I, E, F, G, H, 1 + I, J)) :|: I >= G + 2 && G + 1 >= 0 && A >= I + 1 && F >= A && F <= A
11.39/8.14	lbl31(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl43(A, B, C, D, E, F, I - 2, H, I, J)) :|: I >= 1 && A >= I + 1 && F >= A && F <= A
11.39/8.14	lbl31(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl13(A, B, C, I, E, F, I - 1, H, 1 + I, J)) :|: I >= 1 && A >= I + 1 && F >= A && F <= A
11.39/8.14	lbl13(A, B, C, D, E, F, G, H, I, J) -> Com_1(stop(A, B, C, D, E, F, G, H, I, J)) :|: G + A >= 2 && G + 1 >= 0 && A >= 2 + G && F >= A && F <= A && I >= A && I <= A && D + 1 >= A && D + 1 <= A
11.39/8.14	lbl13(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl31(A, K, C, D, E, F, G, H, I, J)) :|: A >= D + 2 && G + D >= 1 && G + 1 >= 0 && A >= D + 1 && D >= G + 1 && F >= A && F <= A && I >= D + 1 && I <= D + 1
11.39/8.14	start0(A, B, C, D, E, F, G, H, I, J) -> Com_1(start(A, C, C, E, E, A, H, H, J, J)) :|: TRUE
11.39/8.14	
11.39/8.14	The start-symbols are:[start0_10]
11.39/8.14	
11.39/8.14	
11.39/8.14	----------------------------------------
11.39/8.14	
11.39/8.14	(1) Koat2 Proof (FINISHED)
11.39/8.14	YES( ?, 3+max([0, (-1+Arg_0)*max([4, 2*Arg_0])])+max([1, Arg_0])+max([0, -1+Arg_0])+max([0, Arg_0])+max([0, -1+Arg_0])+max([4, 2*Arg_0]) {O(n^2)})
11.39/8.14	
11.39/8.14	
11.39/8.14	
11.39/8.14	Initial Complexity Problem:
11.39/8.14	
11.39/8.14	  Start:  start0  
11.39/8.14	
11.39/8.14	  Program_Vars:  Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7, Arg_8, Arg_9  
11.39/8.14	
11.39/8.14	  Temp_Vars:  K  
11.39/8.14	
11.39/8.14	  Locations:  lbl13, lbl31, lbl43, start, start0, stop  
11.39/8.14	
11.39/8.14	  Transitions:
11.39/8.14	
11.39/8.14	  lbl13(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9) -> lbl31(Arg_0,K,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9):|:Arg_8 <= Arg_5 && Arg_8 <= 1+Arg_3 && Arg_8 <= Arg_0 && 2 <= Arg_8 && 2+Arg_6 <= Arg_8 && 4 <= Arg_5+Arg_8 && 3 <= Arg_3+Arg_8 && 1+Arg_3 <= Arg_8 && 4 <= Arg_0+Arg_8 && 2+Arg_6 <= Arg_5 && 1+Arg_6 <= Arg_3 && 2+Arg_6 <= Arg_0 && Arg_5 <= Arg_0 && 2 <= Arg_5 && 3 <= Arg_3+Arg_5 && 1+Arg_3 <= Arg_5 && 4 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 1+Arg_3 <= Arg_0 && 1 <= Arg_3 && 3 <= Arg_0+Arg_3 && 2 <= Arg_0 && Arg_3+2 <= Arg_0 && 1 <= Arg_6+Arg_3 && 0 <= 1+Arg_6 && Arg_3+1 <= Arg_0 && Arg_6+1 <= Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_8 <= Arg_3+1 && Arg_3+1 <= Arg_8
11.39/8.14	
11.39/8.14	  lbl13(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9):|:Arg_8 <= Arg_5 && Arg_8 <= 1+Arg_3 && Arg_8 <= Arg_0 && 2 <= Arg_8 && 2+Arg_6 <= Arg_8 && 4 <= Arg_5+Arg_8 && 3 <= Arg_3+Arg_8 && 1+Arg_3 <= Arg_8 && 4 <= Arg_0+Arg_8 && 2+Arg_6 <= Arg_5 && 1+Arg_6 <= Arg_3 && 2+Arg_6 <= Arg_0 && Arg_5 <= Arg_0 && 2 <= Arg_5 && 3 <= Arg_3+Arg_5 && 1+Arg_3 <= Arg_5 && 4 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 1+Arg_3 <= Arg_0 && 1 <= Arg_3 && 3 <= Arg_0+Arg_3 && 2 <= Arg_0 && 2 <= Arg_6+Arg_0 && 0 <= 1+Arg_6 && 2+Arg_6 <= Arg_0 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_8 <= Arg_0 && Arg_0 <= Arg_8 && Arg_3+1 <= Arg_0 && Arg_0 <= Arg_3+1
11.39/8.14	
11.39/8.14	  lbl31(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9) -> lbl13(Arg_0,Arg_1,Arg_2,Arg_8,Arg_4,Arg_5,Arg_8-1,Arg_7,1+Arg_8,Arg_9):|:1+Arg_8 <= Arg_5 && 1+Arg_8 <= Arg_0 && 1 <= Arg_8 && 3 <= Arg_5+Arg_8 && 3 <= Arg_0+Arg_8 && Arg_5 <= Arg_0 && 2 <= Arg_5 && 4 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 2 <= Arg_0 && 1 <= Arg_8 && Arg_8+1 <= Arg_0 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5
11.39/8.14	
11.39/8.14	  lbl31(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9) -> lbl43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_8-2,Arg_7,Arg_8,Arg_9):|:1+Arg_8 <= Arg_5 && 1+Arg_8 <= Arg_0 && 1 <= Arg_8 && 3 <= Arg_5+Arg_8 && 3 <= Arg_0+Arg_8 && Arg_5 <= Arg_0 && 2 <= Arg_5 && 4 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 2 <= Arg_0 && 1 <= Arg_8 && Arg_8+1 <= Arg_0 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5
11.39/8.14	
11.39/8.14	  lbl43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9) -> lbl13(Arg_0,Arg_1,Arg_2,Arg_8,Arg_4,Arg_5,Arg_6,Arg_7,1+Arg_8,Arg_9):|:1+Arg_8 <= Arg_5 && 1+Arg_8 <= Arg_0 && 1 <= Arg_8 && 0 <= Arg_6+Arg_8 && 2+Arg_6 <= Arg_8 && 3 <= Arg_5+Arg_8 && 3 <= Arg_0+Arg_8 && 3+Arg_6 <= Arg_5 && 3+Arg_6 <= Arg_0 && 0 <= 1+Arg_6 && 1 <= Arg_5+Arg_6 && 1 <= Arg_0+Arg_6 && Arg_5 <= Arg_0 && 2 <= Arg_5 && 4 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 2 <= Arg_0 && Arg_6+2 <= Arg_8 && 0 <= 1+Arg_6 && Arg_8+1 <= Arg_0 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5
11.39/8.14	
11.39/8.14	  lbl43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9) -> lbl43(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6-1,Arg_7,Arg_8,Arg_9):|:1+Arg_8 <= Arg_5 && 1+Arg_8 <= Arg_0 && 1 <= Arg_8 && 0 <= Arg_6+Arg_8 && 2+Arg_6 <= Arg_8 && 3 <= Arg_5+Arg_8 && 3 <= Arg_0+Arg_8 && 3+Arg_6 <= Arg_5 && 3+Arg_6 <= Arg_0 && 0 <= 1+Arg_6 && 1 <= Arg_5+Arg_6 && 1 <= Arg_0+Arg_6 && Arg_5 <= Arg_0 && 2 <= Arg_5 && 4 <= Arg_0+Arg_5 && Arg_0 <= Arg_5 && 2 <= Arg_0 && 0 <= Arg_6 && Arg_6+2 <= Arg_8 && 0 <= 1+Arg_6 && Arg_8+1 <= Arg_0 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5
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11.39/8.14	  start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9) -> lbl31(Arg_0,K,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,1,Arg_9):|:Arg_9 <= Arg_8 && Arg_8 <= Arg_9 && Arg_7 <= Arg_6 && Arg_6 <= Arg_7 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && 2 <= Arg_0 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_6 <= Arg_7 && Arg_7 <= Arg_6 && Arg_8 <= Arg_9 && Arg_9 <= Arg_8
11.39/8.14	
11.39/8.14	  start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,1,Arg_9):|:Arg_9 <= Arg_8 && Arg_8 <= Arg_9 && Arg_7 <= Arg_6 && Arg_6 <= Arg_7 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_4 <= Arg_3 && Arg_3 <= Arg_4 && Arg_2 <= Arg_1 && Arg_1 <= Arg_2 && Arg_0 <= 1 && Arg_1 <= Arg_2 && Arg_2 <= Arg_1 && Arg_3 <= Arg_4 && Arg_4 <= Arg_3 && Arg_5 <= Arg_0 && Arg_0 <= Arg_5 && Arg_6 <= Arg_7 && Arg_7 <= Arg_6 && Arg_8 <= Arg_9 && Arg_9 <= Arg_8
11.39/8.14	
11.39/8.14	  start0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7,Arg_8,Arg_9) -> start(Arg_0,Arg_2,Arg_2,Arg_4,Arg_4,Arg_0,Arg_7,Arg_7,Arg_9,Arg_9):|:  
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11.39/8.14	Timebounds: 
11.39/8.14	
11.39/8.14	  Overall timebound: 3+max([0, (-1+Arg_0)*max([4, 2*Arg_0])])+max([1, Arg_0])+max([0, -1+Arg_0])+max([0, Arg_0])+max([0, -1+Arg_0])+max([4, 2*Arg_0]) {O(n^2)}
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11.39/8.14	  6: lbl13->stop: 1 {O(1)}
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11.39/8.14	  7: lbl13->lbl31: max([0, -1+Arg_0]) {O(n)}
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11.39/8.14	  4: lbl31->lbl43: max([0, Arg_0]) {O(n)}
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11.39/8.14	  5: lbl31->lbl13: max([0, -1+Arg_0]) {O(n)}
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11.39/8.14	  2: lbl43->lbl43: max([0, (-1+Arg_0)*max([4, 2*Arg_0])])+max([4, 2*Arg_0]) {O(n^2)}
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11.39/8.14	  3: lbl43->lbl13: max([0, -1+Arg_0]) {O(n)}
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11.39/8.14	  0: start->stop: 1 {O(1)}
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11.39/8.14	  1: start->lbl31: 1 {O(1)}
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11.39/8.14	  8: start0->start: 1 {O(1)}
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11.39/8.14	
11.39/8.14	Costbounds:
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11.39/8.14	  Overall costbound: 3+max([0, (-1+Arg_0)*max([4, 2*Arg_0])])+max([1, Arg_0])+max([0, -1+Arg_0])+max([0, Arg_0])+max([0, -1+Arg_0])+max([4, 2*Arg_0]) {O(n^2)}
11.39/8.14	
11.39/8.14	  6: lbl13->stop: 1 {O(1)}
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