TRS_Innermost 2019-03-28 22.12 pair #432270904

details

property	value
status	complete
benchmark	Ex7_BLR02_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.888 seconds
cpu usage	3.94348
user time	3.78862
system time	0.154862
max virtual memory	1.8277816E7
max residence set size	247396.0

stage attributes

key	value
starexec-result	YES

output

3.67/1.83	YES
3.67/1.84	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.67/1.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.67/1.84	
3.67/1.84	
3.67/1.84	Termination w.r.t. Q of the given QTRS could be proven:
3.67/1.84	
3.67/1.84	(0) QTRS
3.67/1.84	(1) QTRSToCSRProof [SOUND, 0 ms]
3.67/1.84	(2) CSR
3.67/1.84	(3) CSRInnermostProof [EQUIVALENT, 0 ms]
3.67/1.84	(4) CSR
3.67/1.84	(5) CSDependencyPairsProof [EQUIVALENT, 11 ms]
3.67/1.84	(6) QCSDP
3.67/1.84	(7) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
3.67/1.84	(8) AND
3.67/1.84	    (9) QCSDP
3.67/1.84	        (10) QCSDPSubtermProof [EQUIVALENT, 0 ms]
3.67/1.84	        (11) QCSDP
3.67/1.84	        (12) PIsEmptyProof [EQUIVALENT, 0 ms]
3.67/1.84	        (13) YES
3.67/1.84	    (14) QCSDP
3.67/1.84	        (15) QCSDPSubtermProof [EQUIVALENT, 0 ms]
3.67/1.84	        (16) QCSDP
3.67/1.84	        (17) PIsEmptyProof [EQUIVALENT, 0 ms]
3.67/1.84	        (18) YES
3.67/1.84	
3.67/1.84	
3.67/1.84	----------------------------------------
3.67/1.84	
3.67/1.84	(0)
3.67/1.84	Obligation:
3.67/1.84	Q restricted rewrite system:
3.67/1.84	The TRS R consists of the following rules:
3.67/1.84	
3.67/1.84	   active(from(X)) -> mark(cons(X, from(s(X))))
3.67/1.84	   active(head(cons(X, XS))) -> mark(X)
3.67/1.84	   active(2nd(cons(X, XS))) -> mark(head(XS))
3.67/1.84	   active(take(0, XS)) -> mark(nil)
3.67/1.84	   active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS)))
3.67/1.84	   active(sel(0, cons(X, XS))) -> mark(X)
3.67/1.84	   active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS))
3.67/1.84	   active(from(X)) -> from(active(X))
3.67/1.84	   active(cons(X1, X2)) -> cons(active(X1), X2)
3.67/1.84	   active(s(X)) -> s(active(X))
3.67/1.84	   active(head(X)) -> head(active(X))
3.67/1.84	   active(2nd(X)) -> 2nd(active(X))
3.67/1.84	   active(take(X1, X2)) -> take(active(X1), X2)
3.67/1.84	   active(take(X1, X2)) -> take(X1, active(X2))
3.67/1.84	   active(sel(X1, X2)) -> sel(active(X1), X2)
3.67/1.84	   active(sel(X1, X2)) -> sel(X1, active(X2))
3.67/1.84	   from(mark(X)) -> mark(from(X))
3.67/1.84	   cons(mark(X1), X2) -> mark(cons(X1, X2))
3.67/1.84	   s(mark(X)) -> mark(s(X))
3.67/1.84	   head(mark(X)) -> mark(head(X))
3.67/1.84	   2nd(mark(X)) -> mark(2nd(X))
3.67/1.84	   take(mark(X1), X2) -> mark(take(X1, X2))
3.67/1.84	   take(X1, mark(X2)) -> mark(take(X1, X2))
3.67/1.84	   sel(mark(X1), X2) -> mark(sel(X1, X2))
3.67/1.84	   sel(X1, mark(X2)) -> mark(sel(X1, X2))
3.67/1.84	   proper(from(X)) -> from(proper(X))
3.67/1.84	   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
3.67/1.84	   proper(s(X)) -> s(proper(X))
3.67/1.84	   proper(head(X)) -> head(proper(X))
3.67/1.84	   proper(2nd(X)) -> 2nd(proper(X))
3.67/1.84	   proper(take(X1, X2)) -> take(proper(X1), proper(X2))
3.67/1.84	   proper(0) -> ok(0)
3.67/1.84	   proper(nil) -> ok(nil)
3.67/1.84	   proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
3.67/1.84	   from(ok(X)) -> ok(from(X))
3.67/1.84	   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
3.67/1.84	   s(ok(X)) -> ok(s(X))
3.67/1.84	   head(ok(X)) -> ok(head(X))
3.67/1.84	   2nd(ok(X)) -> ok(2nd(X))
3.67/1.84	   take(ok(X1), ok(X2)) -> ok(take(X1, X2))
3.67/1.84	   sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
3.67/1.84	   top(mark(X)) -> top(proper(X))
3.67/1.84	   top(ok(X)) -> top(active(X))
3.67/1.84	
3.67/1.84	The set Q consists of the following terms:
3.67/1.84	
3.67/1.84	   active(from(x0))
3.67/1.84	   active(cons(x0, x1))
3.67/1.84	   active(s(x0))
3.67/1.84	   active(head(x0))
3.67/1.84	   active(2nd(x0))
3.67/1.84	   active(take(x0, x1))
3.67/1.84	   active(sel(x0, x1))
3.67/1.84	   from(mark(x0))
3.67/1.84	   cons(mark(x0), x1)
3.67/1.84	   s(mark(x0))
3.67/1.84	   head(mark(x0))
3.67/1.84	   2nd(mark(x0))
3.67/1.84	   take(mark(x0), x1)
3.67/1.84	   take(x0, mark(x1))
3.67/1.84	   sel(mark(x0), x1)
3.67/1.84	   sel(x0, mark(x1))
3.67/1.84	   proper(from(x0))
3.67/1.84	   proper(cons(x0, x1))
3.67/1.84	   proper(s(x0))

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