TRS Contextsensitive pair #487092647

details

property	value
status	complete
benchmark	LISTUTILITIES_nosorts-noand.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Maude_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.57568 seconds
cpu usage	4.01987
user time	3.864
system time	0.15587
max virtual memory	1.8343376E7
max residence set size	244684.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 37 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, XS) -> U12(tt, N, XS)
   U12(tt, N, XS) -> snd(splitAt(N, XS))
   U21(tt, X) -> U22(tt, X)
   U22(tt, X) -> X
   U31(tt, N) -> U32(tt, N)
   U32(tt, N) -> N
   U41(tt, N, XS) -> U42(tt, N, XS)
   U42(tt, N, XS) -> head(afterNth(N, XS))
   U51(tt, Y) -> U52(tt, Y)
   U52(tt, Y) -> Y
   U61(tt, N, X, XS) -> U62(tt, N, X, XS)
   U62(tt, N, X, XS) -> U63(tt, N, X, XS)
   U63(tt, N, X, XS) -> U64(splitAt(N, XS), X)
   U64(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
   U71(tt, XS) -> U72(tt, XS)
   U72(tt, XS) -> XS
   U81(tt, N, XS) -> U82(tt, N, XS)
   U82(tt, N, XS) -> fst(splitAt(N, XS))
   afterNth(N, XS) -> U11(tt, N, XS)
   fst(pair(X, Y)) -> U21(tt, X)
   head(cons(N, XS)) -> U31(tt, N)
   natsFrom(N) -> cons(N, natsFrom(s(N)))
   sel(N, XS) -> U41(tt, N, XS)
   snd(pair(X, Y)) -> U51(tt, Y)
   splitAt(0, XS) -> pair(nil, XS)
   splitAt(s(N), cons(X, XS)) -> U61(tt, N, X, XS)
   tail(cons(N, XS)) -> U71(tt, XS)
   take(N, XS) -> U81(tt, N, XS)

The replacement map contains the following entries:

U11: {1}
tt: empty set
U12: {1}
snd: {1}
splitAt: {1, 2}
U21: {1}
U22: {1}
U31: {1}
U32: {1}
U41: {1}
U42: {1}
head: {1}
afterNth: {1, 2}
U51: {1}
U52: {1}
U61: {1}
U62: {1}
U63: {1}
U64: {1}
pair: {1, 2}
cons: {1}
U71: {1}
U72: {1}
U81: {1}
U82: {1}
fst: {1}
natsFrom: {1}
s: {1}
sel: {1, 2}
0: empty set
nil: empty set
tail: {1}
take: {1, 2}

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