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TRS Standard pair #487067088
details
property
value
status
complete
benchmark
pair2simple1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n192.star.cs.uiowa.edu
space
Endrullis_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.6167 seconds
cpu usage
3.61845
user time
3.45075
system time
0.167697
max virtual memory
1.8408912E7
max residence set size
227536.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 61 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: p(a(x0), p(a(b(x1)), x2)) -> p(a(b(a(x2))), p(a(a(x1)), x2)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: [p_2, b_1] > a_1 Status: p_2: [2,1] a_1: multiset status b_1: [1] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: p(a(x0), p(a(b(x1)), x2)) -> p(a(b(a(x2))), p(a(a(x1)), x2)) ---------------------------------------- (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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