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TRS Stand 20472 pair #381717032
details
property
value
status
complete
benchmark
Ex26_Luc03b_L.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n008.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.53082704544 seconds
cpu usage
3.3612672
max memory
2.22941184E8
stage attributes
key
value
output-size
1862
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 31 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: terms(N) -> cons(recip(sqr(N))) sqr(0) -> 0 sqr(s) -> s dbl(0) -> 0 dbl(s) -> s add(0, X) -> X add(s, Y) -> s first(0, X) -> nil first(s, cons(Y)) -> cons(Y) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:dbl_1 > first_2 > nil > add_2 > s > 0 > recip_1 > sqr_1 > terms_1 > cons_1 and weight map: 0=1 s=1 nil=2 terms_1=3 cons_1=1 recip_1=1 sqr_1=1 dbl_1=0 add_2=0 first_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: terms(N) -> cons(recip(sqr(N))) sqr(0) -> 0 sqr(s) -> s dbl(0) -> 0 dbl(s) -> s add(0, X) -> X add(s, Y) -> s first(0, X) -> nil first(s, cons(Y)) -> cons(Y) ---------------------------------------- (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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