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TRS Stand 20472 pair #381714677
details
property
value
status
complete
benchmark
4.21.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n048.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.72966003418 seconds
cpu usage
3.958541287
max memory
1.98795264E8
stage attributes
key
value
output-size
1965
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 49 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: and(x, or(y, z)) -> or(and(x, y), and(x, z)) and(x, and(y, y)) -> and(x, y) or(or(x, y), and(y, z)) -> or(x, y) or(x, and(x, y)) -> x or(true, y) -> true or(x, false) -> x or(x, x) -> x or(x, or(y, y)) -> or(x, y) and(x, true) -> x and(false, y) -> false and(x, x) -> x Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: and_2 > or_2 true > or_2 false > or_2 Status: and_2: [2,1] or_2: [1,2] true: multiset status false: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: and(x, or(y, z)) -> or(and(x, y), and(x, z)) and(x, and(y, y)) -> and(x, y) or(or(x, y), and(y, z)) -> or(x, y) or(x, and(x, y)) -> x or(true, y) -> true or(x, false) -> x or(x, x) -> x or(x, or(y, y)) -> or(x, y) and(x, true) -> x and(false, y) -> false and(x, x) -> x ---------------------------------------- (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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