details

property	value
status	complete
benchmark	polo2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n192.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.90415 seconds
cpu usage	4.35281
user time	4.18025
system time	0.172557
max virtual memory	1.8343376E7
max residence set size	258888.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 132 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4)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: dx(X) -> one dx(a) -> zero dx(plus(ALPHA, BETA)) -> plus(dx(ALPHA), dx(BETA)) dx(times(ALPHA, BETA)) -> plus(times(BETA, dx(ALPHA)), times(ALPHA, dx(BETA))) dx(minus(ALPHA, BETA)) -> minus(dx(ALPHA), dx(BETA)) dx(neg(ALPHA)) -> neg(dx(ALPHA)) dx(div(ALPHA, BETA)) -> minus(div(dx(ALPHA), BETA), times(ALPHA, div(dx(BETA), exp(BETA, two)))) dx(ln(ALPHA)) -> div(dx(ALPHA), ALPHA) dx(exp(ALPHA, BETA)) -> plus(times(BETA, times(exp(ALPHA, minus(BETA, one)), dx(ALPHA))), times(exp(ALPHA, BETA), times(ln(ALPHA), dx(BETA)))) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: dx/1(YES) one/0) a/0) zero/0) plus/2(YES,YES) times/2(YES,YES) minus/2(YES,YES) neg/1)YES( div/2(YES,YES) exp/2(YES,YES) two/0) ln/1(YES) Quasi precedence: [dx_1, one] > [a, zero] [dx_1, one] > two [dx_1, one] > ln_1 > [div_2, exp_2] > [plus_2, times_2] [dx_1, one] > ln_1 > [div_2, exp_2] > minus_2 Status: dx_1: multiset status one: multiset status a: multiset status zero: multiset status plus_2: [2,1] times_2: multiset status minus_2: multiset status div_2: multiset status exp_2: multiset status two: multiset status ln_1: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: dx(X) -> one dx(a) -> zero dx(plus(ALPHA, BETA)) -> plus(dx(ALPHA), dx(BETA)) dx(times(ALPHA, BETA)) -> plus(times(BETA, dx(ALPHA)), times(ALPHA, dx(BETA))) dx(minus(ALPHA, BETA)) -> minus(dx(ALPHA), dx(BETA)) dx(div(ALPHA, BETA)) -> minus(div(dx(ALPHA), BETA), times(ALPHA, div(dx(BETA), exp(BETA, two)))) dx(ln(ALPHA)) -> div(dx(ALPHA), ALPHA) dx(exp(ALPHA, BETA)) -> plus(times(BETA, times(exp(ALPHA, minus(BETA, one)), dx(ALPHA))), times(exp(ALPHA, BETA), times(ln(ALPHA), dx(BETA)))) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: dx(neg(ALPHA)) -> neg(dx(ALPHA)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) popout

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