TRS Context Sensitive pair #516978795

details

property	value
status	complete
benchmark	ExSec4_2_DLMMU04.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n009.star.cs.uiowa.edu
space	CSR_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.09988880157 seconds
cpu usage	5.639742552
max memory	4.82639872E8

stage attributes

key	value
output-size	10974
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination of the given CSR could be proven:

(0) CSR
(1) CSRInnermostProof [EQUIVALENT, 0 ms]
(2) CSR
(3) CSDependencyPairsProof [EQUIVALENT, 19 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) PIsEmptyProof [EQUIVALENT, 0 ms]
        (16) YES


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

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

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

The replacement map contains the following entries:

natsFrom: {1}
cons: {1}
s: {1}
fst: {1}
pair: {1, 2}
snd: {1}
splitAt: {1, 2}
0: empty set
nil: empty set
u: {1}
head: {1}
tail: {1}
sel: {1, 2}
afterNth: {1, 2}
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:

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

The replacement map contains the following entries:

natsFrom: {1}
cons: {1}
s: {1}
fst: {1}
pair: {1, 2}
snd: {1}

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