TRS Stand 20472 pair #381714998

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	n113.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.74534392357 seconds
cpu usage	4.098219476
max memory	2.1393408E8

stage attributes

key	value
output-size	12952
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRSToCSRProof [EQUIVALENT, 0 ms]
(2) CSR
(3) CSRInnermostProof [EQUIVALENT, 0 ms]
(4) CSR
(5) CSDependencyPairsProof [EQUIVALENT, 0 ms]
(6) QCSDP
(7) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QCSDP
        (10) QCSDPSubtermProof [EQUIVALENT, 5 ms]
        (11) QCSDP
        (12) PIsEmptyProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QCSDP
        (15) QCSDPSubtermProof [EQUIVALENT, 4 ms]
        (16) QCSDP
        (17) PIsEmptyProof [EQUIVALENT, 0 ms]
        (18) YES


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(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   active(from(X)) -> mark(cons(X, from(s(X))))
   active(head(cons(X, XS))) -> mark(X)
   active(2nd(cons(X, XS))) -> mark(head(XS))
   active(take(0, XS)) -> mark(nil)
   active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS)))
   active(sel(0, cons(X, XS))) -> mark(X)
   active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS))
   active(from(X)) -> from(active(X))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(s(X)) -> s(active(X))
   active(head(X)) -> head(active(X))
   active(2nd(X)) -> 2nd(active(X))
   active(take(X1, X2)) -> take(active(X1), X2)
   active(take(X1, X2)) -> take(X1, active(X2))
   active(sel(X1, X2)) -> sel(active(X1), X2)
   active(sel(X1, X2)) -> sel(X1, active(X2))
   from(mark(X)) -> mark(from(X))
   cons(mark(X1), X2) -> mark(cons(X1, X2))
   s(mark(X)) -> mark(s(X))
   head(mark(X)) -> mark(head(X))
   2nd(mark(X)) -> mark(2nd(X))
   take(mark(X1), X2) -> mark(take(X1, X2))
   take(X1, mark(X2)) -> mark(take(X1, X2))
   sel(mark(X1), X2) -> mark(sel(X1, X2))
   sel(X1, mark(X2)) -> mark(sel(X1, X2))
   proper(from(X)) -> from(proper(X))
   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
   proper(s(X)) -> s(proper(X))
   proper(head(X)) -> head(proper(X))
   proper(2nd(X)) -> 2nd(proper(X))
   proper(take(X1, X2)) -> take(proper(X1), proper(X2))
   proper(0) -> ok(0)
   proper(nil) -> ok(nil)
   proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
   from(ok(X)) -> ok(from(X))
   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
   s(ok(X)) -> ok(s(X))
   head(ok(X)) -> ok(head(X))
   2nd(ok(X)) -> ok(2nd(X))
   take(ok(X1), ok(X2)) -> ok(take(X1, X2))
   sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))

Q is empty.

----------------------------------------

(1) QTRSToCSRProof (EQUIVALENT)
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:

   active(from(X)) -> mark(cons(X, from(s(X))))
   active(head(cons(X, XS))) -> mark(X)
   active(2nd(cons(X, XS))) -> mark(head(XS))
   active(take(0, XS)) -> mark(nil)
   active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS)))
   active(sel(0, cons(X, XS))) -> mark(X)
   active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS))

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