TRS Context Sensitive pair #487523853

details

property	value
status	complete
benchmark	LISTUTILITIES_nosorts.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Maude_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.59308099747 seconds
cpu usage	3.6080929
max memory	2.197504E8

stage attributes

key	value
output-size	11953
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 of the given CSR could be proven:

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


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

(0)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, N, X, XS) -> U12(splitAt(N, XS), X)
   U12(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
   afterNth(N, XS) -> snd(splitAt(N, XS))
   and(tt, X) -> X
   fst(pair(X, Y)) -> X
   head(cons(N, XS)) -> N
   natsFrom(N) -> cons(N, natsFrom(s(N)))
   sel(N, XS) -> head(afterNth(N, XS))
   snd(pair(X, Y)) -> Y
   splitAt(0, XS) -> pair(nil, XS)
   splitAt(s(N), cons(X, XS)) -> U11(tt, N, X, XS)
   tail(cons(N, XS)) -> XS
   take(N, XS) -> fst(splitAt(N, XS))

The replacement map contains the following entries:

U11: {1}
tt: empty set
U12: {1}
splitAt: {1, 2}
pair: {1, 2}
cons: {1}
afterNth: {1, 2}
snd: {1}
and: {1}
fst: {1}
head: {1}
natsFrom: {1}
s: {1}
sel: {1, 2}
0: empty set
nil: empty set
tail: {1}
take: {1, 2}

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

(1) CSRInnermostProof (EQUIVALENT)
The CSR is orthogonal. By [CS_Inn] we can switch to innermost.
----------------------------------------

(2)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, N, X, XS) -> U12(splitAt(N, XS), X)
   U12(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
   afterNth(N, XS) -> snd(splitAt(N, XS))
   and(tt, X) -> X
   fst(pair(X, Y)) -> X
   head(cons(N, XS)) -> N
   natsFrom(N) -> cons(N, natsFrom(s(N)))
   sel(N, XS) -> head(afterNth(N, XS))
   snd(pair(X, Y)) -> Y
   splitAt(0, XS) -> pair(nil, XS)
   splitAt(s(N), cons(X, XS)) -> U11(tt, N, X, XS)
   tail(cons(N, XS)) -> XS
   take(N, XS) -> fst(splitAt(N, XS))

The replacement map contains the following entries:

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job log

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actions all output return to TRS Context Sensitive