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TRS Standard pair #516964685
details
property
value
status
complete
benchmark
koen.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n085.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.14252400398 seconds
cpu usage
5.352360256
max memory
4.75373568E8
stage attributes
key
value
output-size
1507
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 31 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES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: f(s(X), X) -> f(X, a(X)) f(X, c(X)) -> f(s(X), X) f(X, X) -> c(X) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:f_2 > c_1 > a_1 > s_1 and weight map: s_1=1 a_1=1 c_1=2 f_2=1 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(s(X), X) -> f(X, a(X)) f(X, c(X)) -> f(s(X), X) f(X, X) -> c(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
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