TRS_Relative 2019-03-21 03.54 pair #429988623

details

property	value
status	complete
benchmark	#3.26_rand.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n182.star.cs.uiowa.edu
space	INVY_15

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.53658 seconds
cpu usage	6.51686
user time	6.13912
system time	0.377739
max virtual memory	1.9878288E7
max residence set size	834280.0

stage attributes

key	value
starexec-result	YES

output

6.33/2.49	YES
6.33/2.50	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
6.33/2.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.33/2.50	
6.33/2.50	
6.33/2.50	Termination of the given RelTRS could be proven:
6.33/2.50	
6.33/2.50	(0) RelTRS
6.33/2.50	(1) RelTRSRRRProof [EQUIVALENT, 51 ms]
6.33/2.50	(2) RelTRS
6.33/2.50	(3) RelTRSRRRProof [EQUIVALENT, 23 ms]
6.33/2.50	(4) RelTRS
6.33/2.50	(5) RelTRSRRRProof [EQUIVALENT, 3 ms]
6.33/2.50	(6) RelTRS
6.33/2.50	(7) RIsEmptyProof [EQUIVALENT, 5 ms]
6.33/2.50	(8) YES
6.33/2.50	
6.33/2.50	
6.33/2.50	----------------------------------------
6.33/2.50	
6.33/2.50	(0)
6.33/2.50	Obligation:
6.33/2.50	Relative term rewrite system:
6.33/2.50	The relative TRS consists of the following R rules:
6.33/2.50	
6.33/2.50	   f(x) -> s(x)
6.33/2.50	   f(s(s(x))) -> s(f(f(x)))
6.33/2.50	
6.33/2.50	The relative TRS consists of the following S rules:
6.33/2.50	
6.33/2.50	   rand(x) -> x
6.33/2.50	   rand(x) -> rand(s(x))
6.33/2.50	
6.33/2.50	
6.33/2.50	----------------------------------------
6.33/2.50	
6.33/2.50	(1) RelTRSRRRProof (EQUIVALENT)
6.33/2.50	We used the following monotonic ordering for rule removal:
6.33/2.50	Polynomial interpretation [POLO]:
6.33/2.50	
6.33/2.50	   POL(f(x_1)) = x_1
6.33/2.50	   POL(rand(x_1)) = 1 + x_1
6.33/2.50	   POL(s(x_1)) = x_1
6.33/2.50	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
6.33/2.50	Rules from R:
6.33/2.50	none
6.33/2.50	Rules from S:
6.33/2.50	
6.33/2.50	   rand(x) -> x
6.33/2.50	
6.33/2.50	
6.33/2.50	
6.33/2.50	
6.33/2.50	----------------------------------------
6.33/2.50	
6.33/2.50	(2)
6.33/2.50	Obligation:
6.33/2.50	Relative term rewrite system:
6.33/2.50	The relative TRS consists of the following R rules:
6.33/2.50	
6.33/2.50	   f(x) -> s(x)
6.33/2.50	   f(s(s(x))) -> s(f(f(x)))
6.33/2.50	
6.33/2.50	The relative TRS consists of the following S rules:
6.33/2.50	
6.33/2.50	   rand(x) -> rand(s(x))
6.33/2.50	
6.33/2.50	
6.33/2.50	----------------------------------------
6.33/2.50	
6.33/2.50	(3) RelTRSRRRProof (EQUIVALENT)
6.33/2.50	We used the following monotonic ordering for rule removal:
6.33/2.50	Matrix interpretation [MATRO] to (N^2, +, *, >=, >) :
6.33/2.50	
6.33/2.50	   <<<
6.33/2.50	 POL(f(x_1)) =  	[[0], [1]] 	 +  	[[1, 1], [0, 2]] 	* 	x_1
6.33/2.50	>>>
6.33/2.50	
6.33/2.50	   <<<
6.33/2.50	 POL(s(x_1)) =  	[[0], [1]] 	 +  	[[1, 0], [0, 2]] 	* 	x_1
6.33/2.50	>>>
6.33/2.50	
6.33/2.50	   <<<
6.33/2.50	 POL(rand(x_1)) =  	[[1], [2]] 	 +  	[[1, 0], [0, 0]] 	* 	x_1
6.33/2.50	>>>
6.33/2.50	
6.33/2.50	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
6.33/2.50	Rules from R:
6.33/2.50	
6.33/2.50	   f(s(s(x))) -> s(f(f(x)))
6.33/2.50	Rules from S:
6.33/2.50	none
6.33/2.50	
6.33/2.50	
6.33/2.50	
6.33/2.50	
6.33/2.50	----------------------------------------
6.33/2.50	
6.33/2.50	(4)
6.33/2.50	Obligation:

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