TRS_Innermost 2019-03-28 22.12 pair #432271236

details

property	value
status	complete
benchmark	Ex4_7_56_Bor03_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n133.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.72104 seconds
cpu usage	3.67519
user time	3.52296
system time	0.152236
max virtual memory	1.8277816E7
max residence set size	234012.0

stage attributes

key	value
starexec-result	YES

output

3.60/1.68	YES
3.60/1.69	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.60/1.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.60/1.69	
3.60/1.69	
3.60/1.69	Termination w.r.t. Q of the given QTRS could be proven:
3.60/1.69	
3.60/1.69	(0) QTRS
3.60/1.69	(1) QTRSToCSRProof [SOUND, 0 ms]
3.60/1.69	(2) CSR
3.60/1.69	(3) CSRInnermostProof [EQUIVALENT, 0 ms]
3.60/1.69	(4) CSR
3.60/1.69	(5) CSDependencyPairsProof [EQUIVALENT, 0 ms]
3.60/1.69	(6) QCSDP
3.60/1.69	(7) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
3.60/1.69	(8) AND
3.60/1.69	    (9) QCSDP
3.60/1.69	        (10) QCSDPSubtermProof [EQUIVALENT, 0 ms]
3.60/1.69	        (11) QCSDP
3.60/1.69	        (12) PIsEmptyProof [EQUIVALENT, 0 ms]
3.60/1.69	        (13) YES
3.60/1.69	    (14) QCSDP
3.60/1.69	        (15) QCSDPSubtermProof [EQUIVALENT, 0 ms]
3.60/1.69	        (16) QCSDP
3.60/1.69	        (17) PIsEmptyProof [EQUIVALENT, 0 ms]
3.60/1.69	        (18) YES
3.60/1.69	
3.60/1.69	
3.60/1.69	----------------------------------------
3.60/1.69	
3.60/1.69	(0)
3.60/1.69	Obligation:
3.60/1.69	Q restricted rewrite system:
3.60/1.69	The TRS R consists of the following rules:
3.60/1.69	
3.60/1.69	   active(from(X)) -> mark(cons(X, from(s(X))))
3.60/1.69	   active(after(0, XS)) -> mark(XS)
3.60/1.69	   active(after(s(N), cons(X, XS))) -> mark(after(N, XS))
3.60/1.69	   active(from(X)) -> from(active(X))
3.60/1.69	   active(cons(X1, X2)) -> cons(active(X1), X2)
3.60/1.69	   active(s(X)) -> s(active(X))
3.60/1.69	   active(after(X1, X2)) -> after(active(X1), X2)
3.60/1.69	   active(after(X1, X2)) -> after(X1, active(X2))
3.60/1.69	   from(mark(X)) -> mark(from(X))
3.60/1.69	   cons(mark(X1), X2) -> mark(cons(X1, X2))
3.60/1.69	   s(mark(X)) -> mark(s(X))
3.60/1.69	   after(mark(X1), X2) -> mark(after(X1, X2))
3.60/1.69	   after(X1, mark(X2)) -> mark(after(X1, X2))
3.60/1.69	   proper(from(X)) -> from(proper(X))
3.60/1.69	   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
3.60/1.69	   proper(s(X)) -> s(proper(X))
3.60/1.69	   proper(after(X1, X2)) -> after(proper(X1), proper(X2))
3.60/1.69	   proper(0) -> ok(0)
3.60/1.69	   from(ok(X)) -> ok(from(X))
3.60/1.69	   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
3.60/1.69	   s(ok(X)) -> ok(s(X))
3.60/1.69	   after(ok(X1), ok(X2)) -> ok(after(X1, X2))
3.60/1.69	   top(mark(X)) -> top(proper(X))
3.60/1.69	   top(ok(X)) -> top(active(X))
3.60/1.69	
3.60/1.69	The set Q consists of the following terms:
3.60/1.69	
3.60/1.69	   active(from(x0))
3.60/1.69	   active(cons(x0, x1))
3.60/1.69	   active(s(x0))
3.60/1.69	   active(after(x0, x1))
3.60/1.69	   from(mark(x0))
3.60/1.69	   cons(mark(x0), x1)
3.60/1.69	   s(mark(x0))
3.60/1.69	   after(mark(x0), x1)
3.60/1.69	   after(x0, mark(x1))
3.60/1.69	   proper(from(x0))
3.60/1.69	   proper(cons(x0, x1))
3.60/1.69	   proper(s(x0))
3.60/1.69	   proper(after(x0, x1))
3.60/1.69	   proper(0)
3.60/1.69	   from(ok(x0))
3.60/1.69	   cons(ok(x0), ok(x1))
3.60/1.69	   s(ok(x0))
3.60/1.69	   after(ok(x0), ok(x1))
3.60/1.69	   top(mark(x0))
3.60/1.69	   top(ok(x0))
3.60/1.69	
3.60/1.69	
3.60/1.69	----------------------------------------
3.60/1.69	
3.60/1.69	(1) QTRSToCSRProof (SOUND)
3.60/1.69	The following Q TRS is given: Q restricted rewrite system:
3.60/1.69	The TRS R consists of the following rules:
3.60/1.69	
3.60/1.69	   active(from(X)) -> mark(cons(X, from(s(X))))
3.60/1.69	   active(after(0, XS)) -> mark(XS)
3.60/1.69	   active(after(s(N), cons(X, XS))) -> mark(after(N, XS))
3.60/1.69	   active(from(X)) -> from(active(X))
3.60/1.69	   active(cons(X1, X2)) -> cons(active(X1), X2)
3.60/1.69	   active(s(X)) -> s(active(X))
3.60/1.69	   active(after(X1, X2)) -> after(active(X1), X2)
3.60/1.69	   active(after(X1, X2)) -> after(X1, active(X2))
3.60/1.69	   from(mark(X)) -> mark(from(X))
3.60/1.69	   cons(mark(X1), X2) -> mark(cons(X1, X2))

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