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TRS Standard pair #516967275
details
property
value
status
complete
benchmark
ReverseLastInit.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n173.star.cs.uiowa.edu
space
Applicative_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.07926702499 seconds
cpu usage
5.295000259
max memory
4.70523904E8
stage attributes
key
value
output-size
2334
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 32 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(app(compose, f), g), x) -> app(g, app(f, x)) app(reverse, l) -> app(app(reverse2, l), nil) app(app(reverse2, nil), l) -> l app(app(reverse2, app(app(cons, x), xs)), l) -> app(app(reverse2, xs), app(app(cons, x), l)) app(hd, app(app(cons, x), xs)) -> x app(tl, app(app(cons, x), xs)) -> xs last -> app(app(compose, hd), reverse) init -> app(app(compose, reverse), app(app(compose, tl), reverse)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:init > last > tl > hd > cons > nil > reverse2 > reverse > compose > app_2 and weight map: compose=1 reverse=4 reverse2=1 nil=2 cons=1 hd=1 tl=1 last=6 init=11 app_2=0 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: app(app(app(compose, f), g), x) -> app(g, app(f, x)) app(reverse, l) -> app(app(reverse2, l), nil) app(app(reverse2, nil), l) -> l app(app(reverse2, app(app(cons, x), xs)), l) -> app(app(reverse2, xs), app(app(cons, x), l)) app(hd, app(app(cons, x), xs)) -> x app(tl, app(app(cons, x), xs)) -> xs last -> app(app(compose, hd), reverse) init -> app(app(compose, reverse), app(app(compose, tl), reverse)) ---------------------------------------- (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
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