details

property	value
status	complete
benchmark	ExProp7_Luc06_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.13392 seconds
cpu usage	4.59434
user time	4.35151
system time	0.242825
max virtual memory	1.8474676E7
max residence set size	291872.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 74 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 11 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 0 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 8 ms] (10) QTRS (11) QTRSRRRProof [EQUIVALENT, 0 ms] (12) QTRS (13) DependencyPairsProof [EQUIVALENT, 8 ms] (14) QDP (15) DependencyGraphProof [EQUIVALENT, 0 ms] (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(0) -> cons(0, f(s(0))) a__f(s(0)) -> a__f(a__p(s(0))) a__p(s(X)) -> mark(X) mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(0) -> 0 mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__p(X) -> p(X) The set Q consists of the following terms: mark(f(x0)) mark(p(x0)) mark(0) mark(cons(x0, x1)) mark(s(x0)) a__f(x0) a__p(x0) ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(a__f(x_1)) = 2 + 2*x_1 POL(a__p(x_1)) = 2*x_1 POL(cons(x_1, x_2)) = 2*x_1 + x_2 POL(f(x_1)) = 2 + 2*x_1 POL(mark(x_1)) = 2*x_1 POL(p(x_1)) = 2*x_1 POL(s(x_1)) = 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: mark(f(X)) -> a__f(mark(X)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(0) -> cons(0, f(s(0))) a__f(s(0)) -> a__f(a__p(s(0))) a__p(s(X)) -> mark(X) mark(p(X)) -> a__p(mark(X)) mark(0) -> 0 mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__p(X) -> p(X) The set Q consists of the following terms: popout

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

job log

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actions

all output return to TRS Innermost