Integer_TRS_Innermost 2019-03-21 04.53 pair #429995036

details

property	value
status	complete
benchmark	A06.itrs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n036.star.cs.uiowa.edu
space	Mixed_ITRS_2014

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.80389 seconds
cpu usage	7.0998
user time	6.70134
system time	0.398465
max virtual memory	1.8609752E7
max residence set size	401740.0

stage attributes

key	value
starexec-result	YES

output

6.89/2.73	YES
6.89/2.76	proof of /export/starexec/sandbox/benchmark/theBenchmark.itrs
6.89/2.76	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.89/2.76	
6.89/2.76	
6.89/2.76	Termination of the given ITRS could be proven:
6.89/2.76	
6.89/2.76	(0) ITRS
6.89/2.76	(1) ITRStoIDPProof [EQUIVALENT, 0 ms]
6.89/2.76	(2) IDP
6.89/2.76	(3) UsableRulesProof [EQUIVALENT, 0 ms]
6.89/2.76	(4) IDP
6.89/2.76	(5) IDPNonInfProof [SOUND, 748 ms]
6.89/2.76	(6) IDP
6.89/2.76	(7) PisEmptyProof [EQUIVALENT, 0 ms]
6.89/2.76	(8) YES
6.89/2.76	
6.89/2.76	
6.89/2.76	----------------------------------------
6.89/2.76	
6.89/2.76	(0)
6.89/2.76	Obligation:
6.89/2.76	ITRS problem:
6.89/2.76	
6.89/2.76	The following function symbols are pre-defined:
6.89/2.76	<<<
6.89/2.76	 & 	~ 	Bwand: (Integer, Integer) -> Integer
6.89/2.76	 >= 	~ 	Ge: (Integer, Integer) -> Boolean
6.89/2.76	 | 	~ 	Bwor: (Integer, Integer) -> Integer
6.89/2.76	 / 	~ 	Div: (Integer, Integer) -> Integer
6.89/2.76	 != 	~ 	Neq: (Integer, Integer) -> Boolean
6.89/2.76	 && 	~ 	Land: (Boolean, Boolean) -> Boolean
6.89/2.76	 ! 	~ 	Lnot: (Boolean) -> Boolean
6.89/2.76	 = 	~ 	Eq: (Integer, Integer) -> Boolean
6.89/2.76	 <= 	~ 	Le: (Integer, Integer) -> Boolean
6.89/2.76	 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
6.89/2.76	 % 	~ 	Mod: (Integer, Integer) -> Integer
6.89/2.76	 > 	~ 	Gt: (Integer, Integer) -> Boolean
6.89/2.77	 + 	~ 	Add: (Integer, Integer) -> Integer
6.89/2.77	 -1 	~ 	UnaryMinus: (Integer) -> Integer
6.89/2.77	 < 	~ 	Lt: (Integer, Integer) -> Boolean
6.89/2.77	 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
6.89/2.77	 - 	~ 	Sub: (Integer, Integer) -> Integer
6.89/2.77	 ~ 	~ 	Bwnot: (Integer) -> Integer
6.89/2.77	 * 	~ 	Mul: (Integer, Integer) -> Integer
6.89/2.77	>>>
6.89/2.77	
6.89/2.77	The TRS R consists of the following rules:
6.89/2.77	f(TRUE, x, y, z) -> f(x > y + z, x, y + 1, z)
6.89/2.77	f(TRUE, x, y, z) -> f(x > y + z, x, y, z + 1)
6.89/2.77	The set Q consists of the following terms:
6.89/2.77	f(TRUE, x0, x1, x2)
6.89/2.77	
6.89/2.77	----------------------------------------
6.89/2.77	
6.89/2.77	(1) ITRStoIDPProof (EQUIVALENT)
6.89/2.77	Added dependency pairs
6.89/2.77	----------------------------------------
6.89/2.77	
6.89/2.77	(2)
6.89/2.77	Obligation:
6.89/2.77	IDP problem:
6.89/2.77	The following function symbols are pre-defined:
6.89/2.77	<<<
6.89/2.77	 & 	~ 	Bwand: (Integer, Integer) -> Integer
6.89/2.77	 >= 	~ 	Ge: (Integer, Integer) -> Boolean
6.89/2.77	 | 	~ 	Bwor: (Integer, Integer) -> Integer
6.89/2.77	 / 	~ 	Div: (Integer, Integer) -> Integer
6.89/2.77	 != 	~ 	Neq: (Integer, Integer) -> Boolean
6.89/2.77	 && 	~ 	Land: (Boolean, Boolean) -> Boolean
6.89/2.77	 ! 	~ 	Lnot: (Boolean) -> Boolean
6.89/2.77	 = 	~ 	Eq: (Integer, Integer) -> Boolean
6.89/2.77	 <= 	~ 	Le: (Integer, Integer) -> Boolean
6.89/2.77	 ^ 	~ 	Bwxor: (Integer, Integer) -> Integer
6.89/2.77	 % 	~ 	Mod: (Integer, Integer) -> Integer
6.89/2.77	 > 	~ 	Gt: (Integer, Integer) -> Boolean
6.89/2.77	 + 	~ 	Add: (Integer, Integer) -> Integer
6.89/2.77	 -1 	~ 	UnaryMinus: (Integer) -> Integer
6.89/2.77	 < 	~ 	Lt: (Integer, Integer) -> Boolean
6.89/2.77	 || 	~ 	Lor: (Boolean, Boolean) -> Boolean
6.89/2.77	 - 	~ 	Sub: (Integer, Integer) -> Integer
6.89/2.77	 ~ 	~ 	Bwnot: (Integer) -> Integer
6.89/2.77	 * 	~ 	Mul: (Integer, Integer) -> Integer
6.89/2.77	>>>
6.89/2.77	
6.89/2.77	
6.89/2.77	The following domains are used:
6.89/2.77	   Integer
6.89/2.77	
6.89/2.77	The ITRS R consists of the following rules:
6.89/2.77	f(TRUE, x, y, z) -> f(x > y + z, x, y + 1, z)
6.89/2.77	f(TRUE, x, y, z) -> f(x > y + z, x, y, z + 1)
6.89/2.77	
6.89/2.77	The integer pair graph contains the following rules and edges:
6.89/2.77	(0): F(TRUE, x[0], y[0], z[0]) -> F(x[0] > y[0] + z[0], x[0], y[0] + 1, z[0])
6.89/2.77	(1): F(TRUE, x[1], y[1], z[1]) -> F(x[1] > y[1] + z[1], x[1], y[1], z[1] + 1)
6.89/2.77	
6.89/2.77	   (0) -> (0), if (x[0] > y[0] + z[0]  & x[0] ->^* x[0]' & y[0] + 1 ->^* y[0]' & z[0] ->^* z[0]')
6.89/2.77	   (0) -> (1), if (x[0] > y[0] + z[0]  & x[0] ->^* x[1] & y[0] + 1 ->^* y[1] & z[0] ->^* z[1])
6.89/2.77	   (1) -> (0), if (x[1] > y[1] + z[1]  & x[1] ->^* x[0] & y[1] ->^* y[0] & z[1] + 1 ->^* z[0])

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