details

property	value
status	complete
benchmark	quicksort.itrs
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Mixed_ITRS_2014

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.70778 seconds
cpu usage	6.86094
user time	6.51351
system time	0.347425
max virtual memory	1.9348776E7
max residence set size	465456.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/benchmark/theBenchmark.itrs # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given ITRS could be proven: (0) ITRS (1) ITRStoIDPProof [EQUIVALENT, 0 ms] (2) IDP (3) ItpfGraphProof [EQUIVALENT, 12 ms] (4) IDP (5) IDependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) IDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) IDP (10) IDPtoQDPProof [SOUND, 34 ms] (11) QDP (12) QReductionProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] (15) YES (16) IDP (17) UsableRulesProof [EQUIVALENT, 3 ms] (18) IDP (19) IDPNonInfProof [SOUND, 87 ms] (20) IDP (21) PisEmptyProof [EQUIVALENT, 0 ms] (22) YES (23) IDP (24) UsableRulesProof [EQUIVALENT, 0 ms] (25) IDP (26) IDPNonInfProof [SOUND, 197 ms] (27) IDP (28) IDependencyGraphProof [EQUIVALENT, 0 ms] (29) TRUE ---------------------------------------- (0) Obligation: ITRS problem: The following function symbols are pre-defined: <<< & ~ Bwand: (Integer, Integer) -> Integer >= ~ Ge: (Integer, Integer) -> Boolean | ~ Bwor: (Integer, Integer) -> Integer / ~ Div: (Integer, Integer) -> Integer != ~ Neq: (Integer, Integer) -> Boolean && ~ Land: (Boolean, Boolean) -> Boolean ! ~ Lnot: (Boolean) -> Boolean = ~ Eq: (Integer, Integer) -> Boolean <= ~ Le: (Integer, Integer) -> Boolean ^ ~ Bwxor: (Integer, Integer) -> Integer % ~ Mod: (Integer, Integer) -> Integer > ~ Gt: (Integer, Integer) -> Boolean + ~ Add: (Integer, Integer) -> Integer -1 ~ UnaryMinus: (Integer) -> Integer < ~ Lt: (Integer, Integer) -> Boolean || ~ Lor: (Boolean, Boolean) -> Boolean - ~ Sub: (Integer, Integer) -> Integer ~ ~ Bwnot: (Integer) -> Integer * ~ Mul: (Integer, Integer) -> Integer >>> The TRS R consists of the following rules: app(nil, zs) -> zs app(cons(x, ys), zs) -> cons(x, app(ys, zs)) split(x, e) -> pair(e, e) split(x, ins(y, zs)) -> Cond_split(x > y, x, ins(y, zs)) Cond_split(TRUE, x, ins(y, zs)) -> if_1(split(x, zs), x, y, zs) if_1(pair(zl, zh), x, y, zs) -> Cond_if_1(x > y, pair(zl, zh), x, y, zs) Cond_if_1(TRUE, pair(zl, zh), x, y, zs) -> pair(ins(y, zl), zh) split(x, ins(y, zs)) -> Cond_split1(y >= x, x, ins(y, zs)) Cond_split1(TRUE, x, ins(y, zs)) -> if_2(split(x, zs), x, y, zs) if_2(pair(zl, zh), x, y, zs) -> Cond_if_2(y >= x, pair(zl, zh), x, y, zs) Cond_if_2(TRUE, pair(zl, zh), x, y, zs) -> pair(zl, ins(y, zh)) qsort(e) -> nil qsort(ins(x, ys)) -> if_3(split(x, ys), x, ys) if_3(pair(yl, yh), x, ys) -> app(qsort(yl), cons(x, qsort(yh))) The set Q consists of the following terms: app(nil, x0) app(cons(x0, x1), x2) split(x0, e) split(x0, ins(x1, x2)) Cond_split(TRUE, x0, ins(x1, x2)) if_1(pair(x0, x1), x2, x3, x4) Cond_if_1(TRUE, pair(x0, x1), x2, x3, x4) Cond_split1(TRUE, x0, ins(x1, x2)) if_2(pair(x0, x1), x2, x3, x4) Cond_if_2(TRUE, pair(x0, x1), x2, x3, x4) qsort(e) qsort(ins(x0, x1)) if_3(pair(x0, x1), x2, x3) ---------------------------------------- popout

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

job log

popout

actions

all output return to Integer TRS Innermost