TRS Innermost pair #487524541

details

property	value
status	complete
benchmark	ExSec4_2_DLMMU04_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.02389192581 seconds
cpu usage	4.364575524
max memory	2.45403648E8

stage attributes

key	value
output-size	21536
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) QTRSToCSRProof [SOUND, 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, 10 ms]
        (11) QCSDP
        (12) PIsEmptyProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QCSDP
        (15) QCSDPSubtermProof [EQUIVALENT, 19 ms]
        (16) QCSDP
        (17) PIsEmptyProof [EQUIVALENT, 0 ms]
        (18) YES


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

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

   active(natsFrom(N)) -> mark(cons(N, natsFrom(s(N))))
   active(fst(pair(XS, YS))) -> mark(XS)
   active(snd(pair(XS, YS))) -> mark(YS)
   active(splitAt(0, XS)) -> mark(pair(nil, XS))
   active(splitAt(s(N), cons(X, XS))) -> mark(u(splitAt(N, XS), N, X, XS))
   active(u(pair(YS, ZS), N, X, XS)) -> mark(pair(cons(X, YS), ZS))
   active(head(cons(N, XS))) -> mark(N)
   active(tail(cons(N, XS))) -> mark(XS)
   active(sel(N, XS)) -> mark(head(afterNth(N, XS)))
   active(take(N, XS)) -> mark(fst(splitAt(N, XS)))
   active(afterNth(N, XS)) -> mark(snd(splitAt(N, XS)))
   active(natsFrom(X)) -> natsFrom(active(X))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(s(X)) -> s(active(X))
   active(fst(X)) -> fst(active(X))
   active(pair(X1, X2)) -> pair(active(X1), X2)
   active(pair(X1, X2)) -> pair(X1, active(X2))
   active(snd(X)) -> snd(active(X))
   active(splitAt(X1, X2)) -> splitAt(active(X1), X2)
   active(splitAt(X1, X2)) -> splitAt(X1, active(X2))
   active(u(X1, X2, X3, X4)) -> u(active(X1), X2, X3, X4)
   active(head(X)) -> head(active(X))
   active(tail(X)) -> tail(active(X))
   active(sel(X1, X2)) -> sel(active(X1), X2)
   active(sel(X1, X2)) -> sel(X1, active(X2))
   active(afterNth(X1, X2)) -> afterNth(active(X1), X2)
   active(afterNth(X1, X2)) -> afterNth(X1, active(X2))
   active(take(X1, X2)) -> take(active(X1), X2)
   active(take(X1, X2)) -> take(X1, active(X2))
   natsFrom(mark(X)) -> mark(natsFrom(X))
   cons(mark(X1), X2) -> mark(cons(X1, X2))
   s(mark(X)) -> mark(s(X))
   fst(mark(X)) -> mark(fst(X))
   pair(mark(X1), X2) -> mark(pair(X1, X2))
   pair(X1, mark(X2)) -> mark(pair(X1, X2))
   snd(mark(X)) -> mark(snd(X))
   splitAt(mark(X1), X2) -> mark(splitAt(X1, X2))
   splitAt(X1, mark(X2)) -> mark(splitAt(X1, X2))
   u(mark(X1), X2, X3, X4) -> mark(u(X1, X2, X3, X4))
   head(mark(X)) -> mark(head(X))
   tail(mark(X)) -> mark(tail(X))
   sel(mark(X1), X2) -> mark(sel(X1, X2))
   sel(X1, mark(X2)) -> mark(sel(X1, X2))
   afterNth(mark(X1), X2) -> mark(afterNth(X1, X2))
   afterNth(X1, mark(X2)) -> mark(afterNth(X1, X2))
   take(mark(X1), X2) -> mark(take(X1, X2))
   take(X1, mark(X2)) -> mark(take(X1, X2))
   proper(natsFrom(X)) -> natsFrom(proper(X))
   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
   proper(s(X)) -> s(proper(X))
   proper(fst(X)) -> fst(proper(X))
   proper(pair(X1, X2)) -> pair(proper(X1), proper(X2))
   proper(snd(X)) -> snd(proper(X))
   proper(splitAt(X1, X2)) -> splitAt(proper(X1), proper(X2))
   proper(0) -> ok(0)
   proper(nil) -> ok(nil)
   proper(u(X1, X2, X3, X4)) -> u(proper(X1), proper(X2), proper(X3), proper(X4))
   proper(head(X)) -> head(proper(X))
   proper(tail(X)) -> tail(proper(X))

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actions all output return to TRS Innermost