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TRS Stand 20472 pair #381713262
details
property
value
status
complete
benchmark
023.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n081.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.55215597153 seconds
cpu usage
3.50174044
max memory
2.19336704E8
stage attributes
key
value
output-size
1567
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 62 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4)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(id, x) -> x app(plus, 0) -> id app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 1 POL(app(x_1, x_2)) = 1 + 2*x_1 + x_2 POL(id) = 1 POL(plus) = 1 POL(s) = 2 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: app(id, x) -> x app(plus, 0) -> id app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), 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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