Complexity_ITS 2019-03-21 04.46 pair #429990060

details

property	value
status	complete
benchmark	randomwalk.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n019.star.cs.uiowa.edu
space	T2

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.72463 seconds
cpu usage	14.1218
user time	13.6185
system time	0.503306
max virtual memory	1.8719536E7
max residence set size	221648.0

stage attributes

key	value
starexec-result	MAYBE

output

14.06/5.68	MAYBE
14.06/5.69	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
14.06/5.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
14.06/5.69	
14.06/5.69	
14.06/5.69	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
14.06/5.69	
14.06/5.69	(0) CpxIntTrs
14.06/5.69	(1) Loat Proof [FINISHED, 3835 ms]
14.06/5.69	(2) BOUNDS(1, INF)
14.06/5.69	
14.06/5.69	
14.06/5.69	----------------------------------------
14.06/5.69	
14.06/5.69	(0)
14.06/5.69	Obligation:
14.06/5.69	Complexity Int TRS consisting of the following rules:
14.06/5.69	f0(A, B, C, D, E, F, G) -> Com_1(f10(1, 1, H, 0, 2, 1, G)) :|: H >= 0
14.06/5.69	f10(A, B, C, D, E, F, G) -> Com_1(f21(A, B - 1, C, D, E, F, 0)) :|: F >= 1 && E >= F && B >= 1 && 0 >= C
14.06/5.69	f10(A, B, C, D, E, F, G) -> Com_1(f21(A + 1, A + 1, H, D, E, F, I)) :|: I >= 0 && 1 >= I && H >= 0 && F >= 1 && E >= F && 0 >= B && 0 >= C
14.06/5.69	f10(A, B, C, D, E, F, G) -> Com_1(f21(A, B, C - 1, D, E, F, H)) :|: H >= 0 && 1 >= H && F >= 1 && C >= 1 && E >= F
14.06/5.69	f21(A, B, C, D, E, F, G) -> Com_1(f10(A, B, C, D, E, F - 1, G)) :|: 0 >= G
14.06/5.69	f21(A, B, C, D, E, F, G) -> Com_1(f10(A, B, C, D, E, F + 1, G)) :|: G >= 1
14.06/5.69	f10(A, B, C, D, E, F, G) -> Com_1(f31(A, B, C, D, E, F, G)) :|: 0 >= F && E >= F
14.06/5.69	f10(A, B, C, D, E, F, G) -> Com_1(f31(A, B, C, D, E, F, G)) :|: F >= 1 + E
14.06/5.69	
14.06/5.69	The start-symbols are:[f0_7]
14.06/5.69	
14.06/5.69	
14.06/5.69	----------------------------------------
14.06/5.69	
14.06/5.69	(1) Loat Proof (FINISHED)
14.06/5.69	
14.06/5.69	
14.06/5.69	### Pre-processing the ITS problem ###
14.06/5.69	
14.06/5.69	
14.06/5.69	
14.06/5.69	Initial linear ITS problem
14.06/5.69	
14.06/5.69	   Start location: f0
14.06/5.69	
14.06/5.69	      0: f0 -> f10 : A'=1, B'=1, C'=free, D'=0, E'=2, F'=1, [ free>=0 ], cost: 1
14.06/5.69	
14.06/5.69	      1: f10 -> f21 : B'=-1+B, G'=0, [ F>=1 && E>=F && B>=1 && 0>=C ], cost: 1
14.06/5.69	
14.06/5.69	      2: f10 -> f21 : A'=1+A, B'=1+A, C'=free_2, G'=free_1, [ free_1>=0 && 1>=free_1 && free_2>=0 && F>=1 && E>=F && 0>=B && 0>=C ], cost: 1
14.06/5.69	
14.06/5.69	      3: f10 -> f21 : C'=-1+C, G'=free_3, [ free_3>=0 && 1>=free_3 && F>=1 && C>=1 && E>=F ], cost: 1
14.06/5.69	
14.06/5.69	      6: f10 -> f31 : [ 0>=F && E>=F ], cost: 1
14.06/5.69	
14.06/5.69	      7: f10 -> f31 : [ F>=1+E ], cost: 1
14.06/5.69	
14.06/5.69	      4: f21 -> f10 : F'=-1+F, [ 0>=G ], cost: 1
14.06/5.69	
14.06/5.69	      5: f21 -> f10 : F'=1+F, [ G>=1 ], cost: 1
14.06/5.69	
14.06/5.69	
14.06/5.69	
14.06/5.69	Removed unreachable and leaf rules:
14.06/5.69	
14.06/5.69	   Start location: f0
14.06/5.69	
14.06/5.69	      0: f0 -> f10 : A'=1, B'=1, C'=free, D'=0, E'=2, F'=1, [ free>=0 ], cost: 1
14.06/5.69	
14.06/5.69	      1: f10 -> f21 : B'=-1+B, G'=0, [ F>=1 && E>=F && B>=1 && 0>=C ], cost: 1
14.06/5.69	
14.06/5.69	      2: f10 -> f21 : A'=1+A, B'=1+A, C'=free_2, G'=free_1, [ free_1>=0 && 1>=free_1 && free_2>=0 && F>=1 && E>=F && 0>=B && 0>=C ], cost: 1
14.06/5.69	
14.06/5.69	      3: f10 -> f21 : C'=-1+C, G'=free_3, [ free_3>=0 && 1>=free_3 && F>=1 && C>=1 && E>=F ], cost: 1
14.06/5.69	
14.06/5.69	      4: f21 -> f10 : F'=-1+F, [ 0>=G ], cost: 1
14.06/5.69	
14.06/5.69	      5: f21 -> f10 : F'=1+F, [ G>=1 ], cost: 1
14.06/5.69	
14.06/5.69	
14.06/5.69	
14.06/5.69	### Simplification by acceleration and chaining ###
14.06/5.69	
14.06/5.69	
14.06/5.69	
14.06/5.69	Eliminated locations (on tree-shaped paths):
14.06/5.69	
14.06/5.69	   Start location: f0
14.06/5.69	
14.06/5.69	      0: f0 -> f10 : A'=1, B'=1, C'=free, D'=0, E'=2, F'=1, [ free>=0 ], cost: 1
14.06/5.69	
14.06/5.69	      8: f10 -> f10 : B'=-1+B, F'=-1+F, G'=0, [ F>=1 && E>=F && B>=1 && 0>=C ], cost: 2
14.06/5.69	
14.06/5.69	      9: f10 -> f10 : A'=1+A, B'=1+A, C'=free_2, F'=-1+F, G'=free_1, [ free_1>=0 && free_2>=0 && F>=1 && E>=F && 0>=B && 0>=C && 0>=free_1 ], cost: 2
14.06/5.69	
14.06/5.69	     10: f10 -> f10 : A'=1+A, B'=1+A, C'=free_2, F'=1+F, G'=free_1, [ 1>=free_1 && free_2>=0 && F>=1 && E>=F && 0>=B && 0>=C && free_1>=1 ], cost: 2
14.06/5.69	
14.06/5.69	     11: f10 -> f10 : C'=-1+C, F'=-1+F, G'=free_3, [ free_3>=0 && F>=1 && C>=1 && E>=F && 0>=free_3 ], cost: 2
14.06/5.69	
14.06/5.69	     12: f10 -> f10 : C'=-1+C, F'=1+F, G'=free_3, [ 1>=free_3 && F>=1 && C>=1 && E>=F && free_3>=1 ], cost: 2
14.06/5.69	
14.06/5.69	
14.06/5.69

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