details

property	value
status	complete
benchmark	ExSec11_1_Luc02a_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.89105 seconds
cpu usage	4.05018
user time	3.87012
system time	0.180054
max virtual memory	1.8408912E7
max residence set size	251148.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 122 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: terms(N) -> cons(recip(sqr(N)), n__terms(s(N))) sqr(0) -> 0 sqr(s(X)) -> s(add(sqr(X), dbl(X))) dbl(0) -> 0 dbl(s(X)) -> s(s(dbl(X))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) half(0) -> 0 half(s(0)) -> 0 half(s(s(X))) -> s(half(X)) half(dbl(X)) -> X terms(X) -> n__terms(X) first(X1, X2) -> n__first(X1, X2) activate(n__terms(X)) -> terms(X) activate(n__first(X1, X2)) -> first(X1, X2) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: terms/1(YES) cons/2(YES,YES) recip/1)YES( sqr/1(YES) n__terms/1)YES( s/1(YES) 0/0) add/2(YES,YES) dbl/1(YES) first/2(YES,YES) nil/0) n__first/2(YES,YES) activate/1(YES) half/1)YES( Quasi precedence: [terms_1, first_2, activate_1] > [cons_2, n__first_2] > nil [terms_1, first_2, activate_1] > [sqr_1, dbl_1] > add_2 > s_1 > 0 > nil Status: terms_1: multiset status cons_2: multiset status sqr_1: multiset status s_1: multiset status 0: multiset status add_2: [2,1] dbl_1: multiset status first_2: multiset status nil: multiset status n__first_2: multiset status activate_1: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: terms(N) -> cons(recip(sqr(N)), n__terms(s(N))) sqr(0) -> 0 sqr(s(X)) -> s(add(sqr(X), dbl(X))) dbl(0) -> 0 dbl(s(X)) -> s(s(dbl(X))) add(0, X) -> X add(s(X), Y) -> s(add(X, Y)) first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z))) half(s(0)) -> 0 half(s(s(X))) -> s(half(X)) half(dbl(X)) -> X terms(X) -> n__terms(X) first(X1, X2) -> n__first(X1, X2) activate(n__first(X1, X2)) -> first(X1, X2) activate(X) -> X popout

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

job log

popout

actions

all output return to TRS Standard