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TRS Standard pair #516966495
details
property
value
status
complete
benchmark
2.45.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n078.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.24142003059 seconds
cpu usage
5.906747954
max memory
4.81165312E8
stage attributes
key
value
output-size
1879
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 161 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: admit(x, nil) -> nil admit(x, .(u, .(v, .(w, z)))) -> cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z))))) cond(true, y) -> y Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: [admit_2, ._2] > nil > [w, carry_3] [admit_2, ._2] > cond_2 > [w, carry_3] [admit_2, ._2] > =_2 > [w, carry_3] [admit_2, ._2] > sum_3 > [w, carry_3] true > [w, carry_3] Status: admit_2: [2,1] nil: multiset status ._2: [1,2] w: multiset status cond_2: [2,1] =_2: multiset status sum_3: [1,3,2] carry_3: multiset status true: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: admit(x, nil) -> nil admit(x, .(u, .(v, .(w, z)))) -> cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z))))) cond(true, y) -> 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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