TRS_Innermost 2019-03-28 22.12 pair #432271246

details

property	value
status	complete
benchmark	Ex49_GM04_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n065.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.47582 seconds
cpu usage	6.34445
user time	6.07294
system time	0.271508
max virtual memory	1.8489504E7
max residence set size	417408.0

stage attributes

key	value
starexec-result	YES

output

6.06/2.41	YES
6.06/2.42	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
6.06/2.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.06/2.42	
6.06/2.42	
6.06/2.42	Termination w.r.t. Q of the given QTRS could be proven:
6.06/2.42	
6.06/2.42	(0) QTRS
6.06/2.42	(1) DependencyPairsProof [EQUIVALENT, 42 ms]
6.06/2.42	(2) QDP
6.06/2.42	(3) DependencyGraphProof [EQUIVALENT, 0 ms]
6.06/2.42	(4) AND
6.06/2.42	    (5) QDP
6.06/2.42	        (6) UsableRulesProof [EQUIVALENT, 0 ms]
6.06/2.42	        (7) QDP
6.06/2.42	        (8) QReductionProof [EQUIVALENT, 0 ms]
6.06/2.42	        (9) QDP
6.06/2.42	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
6.06/2.42	        (11) YES
6.06/2.42	    (12) QDP
6.06/2.42	        (13) UsableRulesProof [EQUIVALENT, 0 ms]
6.06/2.42	        (14) QDP
6.06/2.42	        (15) QReductionProof [EQUIVALENT, 0 ms]
6.06/2.42	        (16) QDP
6.06/2.42	        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
6.06/2.42	        (18) YES
6.06/2.42	    (19) QDP
6.06/2.42	        (20) QDPOrderProof [EQUIVALENT, 59 ms]
6.06/2.42	        (21) QDP
6.06/2.42	        (22) DependencyGraphProof [EQUIVALENT, 0 ms]
6.06/2.42	        (23) QDP
6.06/2.42	        (24) QDPSizeChangeProof [EQUIVALENT, 0 ms]
6.06/2.42	        (25) YES
6.06/2.42	
6.06/2.42	
6.06/2.42	----------------------------------------
6.06/2.42	
6.06/2.42	(0)
6.06/2.42	Obligation:
6.06/2.42	Q restricted rewrite system:
6.06/2.42	The TRS R consists of the following rules:
6.06/2.42	
6.06/2.42	   a__minus(0, Y) -> 0
6.06/2.42	   a__minus(s(X), s(Y)) -> a__minus(X, Y)
6.06/2.42	   a__geq(X, 0) -> true
6.06/2.42	   a__geq(0, s(Y)) -> false
6.06/2.42	   a__geq(s(X), s(Y)) -> a__geq(X, Y)
6.06/2.42	   a__div(0, s(Y)) -> 0
6.06/2.42	   a__div(s(X), s(Y)) -> a__if(a__geq(X, Y), s(div(minus(X, Y), s(Y))), 0)
6.06/2.42	   a__if(true, X, Y) -> mark(X)
6.06/2.42	   a__if(false, X, Y) -> mark(Y)
6.06/2.42	   mark(minus(X1, X2)) -> a__minus(X1, X2)
6.06/2.42	   mark(geq(X1, X2)) -> a__geq(X1, X2)
6.06/2.42	   mark(div(X1, X2)) -> a__div(mark(X1), X2)
6.06/2.42	   mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
6.06/2.42	   mark(0) -> 0
6.06/2.42	   mark(s(X)) -> s(mark(X))
6.06/2.42	   mark(true) -> true
6.06/2.42	   mark(false) -> false
6.06/2.42	   a__minus(X1, X2) -> minus(X1, X2)
6.06/2.42	   a__geq(X1, X2) -> geq(X1, X2)
6.06/2.42	   a__div(X1, X2) -> div(X1, X2)
6.06/2.42	   a__if(X1, X2, X3) -> if(X1, X2, X3)
6.06/2.42	
6.06/2.42	The set Q consists of the following terms:
6.06/2.42	
6.06/2.42	   mark(minus(x0, x1))
6.06/2.42	   mark(geq(x0, x1))
6.06/2.42	   mark(div(x0, x1))
6.06/2.42	   mark(if(x0, x1, x2))
6.06/2.42	   mark(0)
6.06/2.42	   mark(s(x0))
6.06/2.42	   mark(true)
6.06/2.42	   mark(false)
6.06/2.42	   a__minus(x0, x1)
6.06/2.42	   a__geq(x0, x1)
6.06/2.42	   a__div(x0, x1)
6.06/2.42	   a__if(x0, x1, x2)
6.06/2.42	
6.06/2.42	
6.06/2.42	----------------------------------------
6.06/2.42	
6.06/2.42	(1) DependencyPairsProof (EQUIVALENT)
6.06/2.42	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
6.06/2.42	----------------------------------------
6.06/2.42	
6.06/2.42	(2)
6.06/2.42	Obligation:
6.06/2.42	Q DP problem:
6.06/2.42	The TRS P consists of the following rules:
6.06/2.42	
6.06/2.42	   A__MINUS(s(X), s(Y)) -> A__MINUS(X, Y)
6.06/2.42	   A__GEQ(s(X), s(Y)) -> A__GEQ(X, Y)
6.06/2.42	   A__DIV(s(X), s(Y)) -> A__IF(a__geq(X, Y), s(div(minus(X, Y), s(Y))), 0)
6.06/2.42	   A__DIV(s(X), s(Y)) -> A__GEQ(X, Y)
6.06/2.42	   A__IF(true, X, Y) -> MARK(X)
6.06/2.42	   A__IF(false, X, Y) -> MARK(Y)
6.06/2.42	   MARK(minus(X1, X2)) -> A__MINUS(X1, X2)
6.06/2.42	   MARK(geq(X1, X2)) -> A__GEQ(X1, X2)
6.06/2.42	   MARK(div(X1, X2)) -> A__DIV(mark(X1), X2)

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actions all output return to TRS_Innermost 2019-03-28 22.12