SRS_Standard 2019-03-29 03.29 pair #432292315

details

property	value
status	complete
benchmark	z094.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n053.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.97319 seconds
cpu usage	11.5539
user time	10.931
system time	0.622894
max virtual memory	4.0173484E7
max residence set size	1704104.0

stage attributes

key	value
starexec-result	YES

output

10.96/3.71	YES
10.96/3.77	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
10.96/3.77	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.96/3.77	
10.96/3.77	
10.96/3.77	Termination w.r.t. Q of the given QTRS could be proven:
10.96/3.77	
10.96/3.77	(0) QTRS
10.96/3.77	(1) QTRS Reverse [EQUIVALENT, 0 ms]
10.96/3.77	(2) QTRS
10.96/3.77	(3) DependencyPairsProof [EQUIVALENT, 25 ms]
10.96/3.77	(4) QDP
10.96/3.77	(5) DependencyGraphProof [EQUIVALENT, 0 ms]
10.96/3.77	(6) AND
10.96/3.77	    (7) QDP
10.96/3.77	        (8) UsableRulesProof [EQUIVALENT, 2 ms]
10.96/3.77	        (9) QDP
10.96/3.77	        (10) QDPSizeChangeProof [EQUIVALENT, 1 ms]
10.96/3.77	        (11) YES
10.96/3.77	    (12) QDP
10.96/3.77	        (13) QDPOrderProof [EQUIVALENT, 44 ms]
10.96/3.77	        (14) QDP
10.96/3.77	        (15) PisEmptyProof [EQUIVALENT, 0 ms]
10.96/3.77	        (16) YES
10.96/3.77	
10.96/3.77	
10.96/3.77	----------------------------------------
10.96/3.77	
10.96/3.77	(0)
10.96/3.77	Obligation:
10.96/3.77	Q restricted rewrite system:
10.96/3.77	The TRS R consists of the following rules:
10.96/3.77	
10.96/3.77	   f(x1) -> n(c(c(x1)))
10.96/3.77	   c(f(x1)) -> f(c(c(x1)))
10.96/3.77	   c(c(x1)) -> c(x1)
10.96/3.77	   n(s(x1)) -> f(s(s(x1)))
10.96/3.77	   n(f(x1)) -> f(n(x1))
10.96/3.77	
10.96/3.77	Q is empty.
10.96/3.77	
10.96/3.77	----------------------------------------
10.96/3.77	
10.96/3.77	(1) QTRS Reverse (EQUIVALENT)
10.96/3.77	We applied the QTRS Reverse Processor [REVERSE].
10.96/3.77	----------------------------------------
10.96/3.77	
10.96/3.77	(2)
10.96/3.77	Obligation:
10.96/3.77	Q restricted rewrite system:
10.96/3.77	The TRS R consists of the following rules:
10.96/3.77	
10.96/3.77	   f(x1) -> c(c(n(x1)))
10.96/3.77	   f(c(x1)) -> c(c(f(x1)))
10.96/3.77	   c(c(x1)) -> c(x1)
10.96/3.77	   s(n(x1)) -> s(s(f(x1)))
10.96/3.77	   f(n(x1)) -> n(f(x1))
10.96/3.77	
10.96/3.77	Q is empty.
10.96/3.77	
10.96/3.77	----------------------------------------
10.96/3.77	
10.96/3.77	(3) DependencyPairsProof (EQUIVALENT)
10.96/3.77	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
10.96/3.77	----------------------------------------
10.96/3.77	
10.96/3.77	(4)
10.96/3.77	Obligation:
10.96/3.77	Q DP problem:
10.96/3.77	The TRS P consists of the following rules:
10.96/3.77	
10.96/3.77	   F(x1) -> C(c(n(x1)))
10.96/3.77	   F(x1) -> C(n(x1))
10.96/3.77	   F(c(x1)) -> C(c(f(x1)))
10.96/3.77	   F(c(x1)) -> C(f(x1))
10.96/3.77	   F(c(x1)) -> F(x1)
10.96/3.77	   S(n(x1)) -> S(s(f(x1)))
10.96/3.77	   S(n(x1)) -> S(f(x1))
10.96/3.77	   S(n(x1)) -> F(x1)
10.96/3.77	   F(n(x1)) -> F(x1)
10.96/3.77	
10.96/3.77	The TRS R consists of the following rules:
10.96/3.77	
10.96/3.77	   f(x1) -> c(c(n(x1)))
10.96/3.77	   f(c(x1)) -> c(c(f(x1)))
10.96/3.77	   c(c(x1)) -> c(x1)
10.96/3.77	   s(n(x1)) -> s(s(f(x1)))
10.96/3.77	   f(n(x1)) -> n(f(x1))
10.96/3.77	
10.96/3.77	Q is empty.
10.96/3.77	We have to consider all minimal (P,Q,R)-chains.
10.96/3.77	----------------------------------------
10.96/3.77	
10.96/3.77	(5) DependencyGraphProof (EQUIVALENT)
10.96/3.77	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 5 less nodes.
10.96/3.77	----------------------------------------
10.96/3.77	
10.96/3.77	(6)
10.96/3.77	Complex Obligation (AND)
10.96/3.77

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