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TRS Relat 75837 pair #381724843
details
property
value
status
complete
benchmark
rt1-2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n113.star.cs.uiowa.edu
space
Relative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.03987503052 seconds
cpu usage
5.013666498
max memory
3.39120128E8
stage attributes
key
value
output-size
1565
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 34 ms] (2) RelTRS (3) RIsEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: f(x) -> x g(x) -> x The relative TRS consists of the following S rules: f(x) -> g(x) g(x) -> f(x) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(f(x_1)) = 1 + x_1 POL(g(x_1)) = 1 + x_1 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: f(x) -> x g(x) -> x Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: R is empty. The relative TRS consists of the following S rules: f(x) -> g(x) g(x) -> f(x) ---------------------------------------- (3) RIsEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES
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