TRS Context Sensitive pair #487523915

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	n054.star.cs.uiowa.edu
space	Maude_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.91083884239 seconds
cpu usage	4.112949732
max memory	2.56176128E8

stage attributes

key	value
output-size	19093
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 16 ms]
(4) QCSDP
(5) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QCSDP
        (8) QCSDPSubtermProof [EQUIVALENT, 28 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

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Context Sensitive