details

property	value
status	complete
benchmark	Ex1_2_AEL03_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n181.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.91835 seconds
cpu usage	4.43811
user time	4.26249
system time	0.175619
max virtual memory	1.8408912E7
max residence set size	258972.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 139 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4)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: from(X) -> cons(X, n__from(s(X))) 2ndspos(0, Z) -> rnil 2ndspos(s(N), cons(X, n__cons(Y, Z))) -> rcons(posrecip(activate(Y)), 2ndsneg(N, activate(Z))) 2ndsneg(0, Z) -> rnil 2ndsneg(s(N), cons(X, n__cons(Y, Z))) -> rcons(negrecip(activate(Y)), 2ndspos(N, activate(Z))) pi(X) -> 2ndspos(X, from(0)) plus(0, Y) -> Y plus(s(X), Y) -> s(plus(X, Y)) times(0, Y) -> 0 times(s(X), Y) -> plus(Y, times(X, Y)) square(X) -> times(X, X) from(X) -> n__from(X) cons(X1, X2) -> n__cons(X1, X2) activate(n__from(X)) -> from(X) activate(n__cons(X1, X2)) -> cons(X1, X2) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: from/1(YES) cons/2(YES,YES) n__from/1)YES( s/1(YES) 2ndspos/2(YES,YES) 0/0) rnil/0) n__cons/2(YES,YES) rcons/2(YES,YES) posrecip/1)YES( activate/1(YES) 2ndsneg/2(YES,YES) negrecip/1)YES( pi/1(YES) plus/2(YES,YES) times/2(YES,YES) square/1(YES) Quasi precedence: pi_1 > [2ndspos_2, 2ndsneg_2] > [from_1, activate_1] > cons_2 > n__cons_2 pi_1 > [2ndspos_2, 2ndsneg_2] > [from_1, activate_1] > s_1 > n__cons_2 pi_1 > [2ndspos_2, 2ndsneg_2] > rcons_2 > n__cons_2 pi_1 > [0, times_2] > rnil > n__cons_2 pi_1 > [0, times_2] > plus_2 > s_1 > n__cons_2 square_1 > [0, times_2] > rnil > n__cons_2 square_1 > [0, times_2] > plus_2 > s_1 > n__cons_2 Status: from_1: multiset status cons_2: multiset status s_1: multiset status 2ndspos_2: [1,2] 0: multiset status rnil: multiset status n__cons_2: multiset status rcons_2: multiset status activate_1: multiset status 2ndsneg_2: [1,2] pi_1: multiset status plus_2: multiset status times_2: multiset status square_1: [1] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: from(X) -> cons(X, n__from(s(X))) 2ndspos(0, Z) -> rnil 2ndspos(s(N), cons(X, n__cons(Y, Z))) -> rcons(posrecip(activate(Y)), 2ndsneg(N, activate(Z))) 2ndsneg(0, Z) -> rnil 2ndsneg(s(N), cons(X, n__cons(Y, Z))) -> rcons(negrecip(activate(Y)), 2ndspos(N, activate(Z))) pi(X) -> 2ndspos(X, from(0)) plus(0, Y) -> Y plus(s(X), Y) -> s(plus(X, Y)) popout

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

job log

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actions

all output return to TRS Standard