details

property	value
status	complete
benchmark	4.53.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n179.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.6687 seconds
cpu usage	3.84271
user time	3.66764
system time	0.175073
max virtual memory	1.8408912E7
max residence set size	233440.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 79 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(a) -> b f(c) -> d f(g(x, y)) -> g(f(x), f(y)) f(h(x, y)) -> g(h(y, f(x)), h(x, f(y))) g(x, x) -> h(e, x) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: f_1 > b > h_2 f_1 > g_2 > e > h_2 a > b > h_2 c > d > h_2 Status: f_1: multiset status a: multiset status b: multiset status c: multiset status d: multiset status g_2: multiset status h_2: multiset status e: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(a) -> b f(c) -> d f(g(x, y)) -> g(f(x), f(y)) f(h(x, y)) -> g(h(y, f(x)), h(x, f(y))) g(x, x) -> h(e, x) ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES popout

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