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TRS Stand 20472 pair #381710155
details
property
value
status
complete
benchmark
polycounter-5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n016.star.cs.uiowa.edu
space
TCT_12
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.68071317673 seconds
cpu usage
3.712067559
max memory
2.265088E8
stage attributes
key
value
output-size
1883
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 101 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4)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(x1), x2, x3, x4, x5) -> f(x1, x2, x3, x4, x5) f(0, s(x2), x3, x4, x5) -> f(x2, x2, x3, x4, x5) f(0, 0, s(x3), x4, x5) -> f(x3, x3, x3, x4, x5) f(0, 0, 0, s(x4), x5) -> f(x4, x4, x4, x4, x5) f(0, 0, 0, 0, s(x5)) -> f(x5, x5, x5, x5, x5) f(0, 0, 0, 0, 0) -> 0 Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: [f_5, s_1, 0] Status: f_5: [5,4,3,2,1] s_1: multiset status 0: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(s(x1), x2, x3, x4, x5) -> f(x1, x2, x3, x4, x5) f(0, s(x2), x3, x4, x5) -> f(x2, x2, x3, x4, x5) f(0, 0, s(x3), x4, x5) -> f(x3, x3, x3, x4, x5) f(0, 0, 0, s(x4), x5) -> f(x4, x4, x4, x4, x5) f(0, 0, 0, 0, s(x5)) -> f(x5, x5, x5, x5, x5) f(0, 0, 0, 0, 0) -> 0 ---------------------------------------- (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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