details

property	value
status	complete
benchmark	ExSec11_1_Luc02a_L.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.90238 seconds
cpu usage	3.845
user time	3.66507
system time	0.179935
max virtual memory	1.8408912E7
max residence set size	232376.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 37 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 1 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: terms(N) -> cons(recip(sqr(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)) -> cons(Y) half(0) -> 0 half(s(0)) -> 0 half(s(s(X))) -> s(half(X)) half(dbl(X)) -> X The set Q consists of the following terms: terms(x0) sqr(0) sqr(s(x0)) dbl(0) dbl(s(x0)) add(0, x0) add(s(x0), x1) first(0, x0) first(s(x0), cons(x1)) half(0) half(s(0)) half(s(s(x0))) half(dbl(x0)) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: terms_1 > cons_1 > s_1 terms_1 > recip_1 > s_1 terms_1 > [sqr_1, dbl_1] > [0, nil, half_1] > s_1 terms_1 > [sqr_1, dbl_1] > add_2 > s_1 first_2 > s_1 Status: terms_1: multiset status cons_1: multiset status recip_1: multiset status sqr_1: multiset status 0: multiset status s_1: multiset status add_2: [1,2] dbl_1: multiset status first_2: multiset status nil: multiset status half_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))) 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)) -> cons(Y) half(0) -> 0 half(s(0)) -> 0 half(s(s(X))) -> s(half(X)) half(dbl(X)) -> X ---------------------------------------- (2) Obligation: popout

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

job log

popout

actions

all output return to TRS Innermost