TRS Standard pair #516961975

details

property	value
status	complete
benchmark	LISTUTILITIES_nosorts_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n078.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.62814307213 seconds
cpu usage	6.687638235
max memory	4.86719488E8

stage attributes

key	value
output-size	9371
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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 w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) QDPOrderProof [EQUIVALENT, 24 ms]
        (12) QDP
        (13) DependencyGraphProof [EQUIVALENT, 0 ms]
        (14) TRUE


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

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

   U11(tt, N, X, XS) -> U12(splitAt(activate(N), activate(XS)), activate(X))
   U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
   afterNth(N, XS) -> snd(splitAt(N, XS))
   and(tt, X) -> activate(X)
   fst(pair(X, Y)) -> X
   head(cons(N, XS)) -> N
   natsFrom(N) -> cons(N, n__natsFrom(n__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, activate(XS))
   tail(cons(N, XS)) -> activate(XS)
   take(N, XS) -> fst(splitAt(N, XS))
   natsFrom(X) -> n__natsFrom(X)
   s(X) -> n__s(X)
   activate(n__natsFrom(X)) -> natsFrom(activate(X))
   activate(n__s(X)) -> s(activate(X))
   activate(X) -> X

Q is empty.

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

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   U11^1(tt, N, X, XS) -> U12^1(splitAt(activate(N), activate(XS)), activate(X))
   U11^1(tt, N, X, XS) -> SPLITAT(activate(N), activate(XS))
   U11^1(tt, N, X, XS) -> ACTIVATE(N)
   U11^1(tt, N, X, XS) -> ACTIVATE(XS)
   U11^1(tt, N, X, XS) -> ACTIVATE(X)
   U12^1(pair(YS, ZS), X) -> ACTIVATE(X)
   AFTERNTH(N, XS) -> SND(splitAt(N, XS))
   AFTERNTH(N, XS) -> SPLITAT(N, XS)
   AND(tt, X) -> ACTIVATE(X)
   SEL(N, XS) -> HEAD(afterNth(N, XS))
   SEL(N, XS) -> AFTERNTH(N, XS)
   SPLITAT(s(N), cons(X, XS)) -> U11^1(tt, N, X, activate(XS))
   SPLITAT(s(N), cons(X, XS)) -> ACTIVATE(XS)
   TAIL(cons(N, XS)) -> ACTIVATE(XS)
   TAKE(N, XS) -> FST(splitAt(N, XS))
   TAKE(N, XS) -> SPLITAT(N, XS)
   ACTIVATE(n__natsFrom(X)) -> NATSFROM(activate(X))
   ACTIVATE(n__natsFrom(X)) -> ACTIVATE(X)
   ACTIVATE(n__s(X)) -> S(activate(X))
   ACTIVATE(n__s(X)) -> ACTIVATE(X)

The TRS R consists of the following rules:

   U11(tt, N, X, XS) -> U12(splitAt(activate(N), activate(XS)), activate(X))
   U12(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
   afterNth(N, XS) -> snd(splitAt(N, XS))
   and(tt, X) -> activate(X)
   fst(pair(X, Y)) -> X
   head(cons(N, XS)) -> N
   natsFrom(N) -> cons(N, n__natsFrom(n__s(N)))
   sel(N, XS) -> head(afterNth(N, XS))

popout

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

job log

popout

actions all output return to TRS Standard