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	n031.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.28580093384 seconds
cpu usage	5.915833
max memory	4.78580736E8

stage attributes

key	value
output-size	3548
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 153 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS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)) popout

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

job log

popout

actions

all output return to TRS Standard