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TRS Standard pair #516966500
details
property
value
status
complete
benchmark
4.20.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
SK90
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.17261314392 seconds
cpu usage
5.60594123
max memory
4.75090944E8
stage attributes
key
value
output-size
2069
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 87 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: not(x) -> xor(x, true) or(x, y) -> xor(and(x, y), xor(x, y)) implies(x, y) -> xor(and(x, y), xor(x, true)) and(x, true) -> x and(x, false) -> false and(x, x) -> x xor(x, false) -> x xor(x, x) -> false and(xor(x, y), z) -> xor(and(x, z), and(y, z)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: or_2 > and_2 > [xor_2, false] implies_2 > [not_1, true] > [xor_2, false] implies_2 > and_2 > [xor_2, false] Status: not_1: multiset status xor_2: multiset status true: multiset status or_2: multiset status and_2: multiset status implies_2: 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: not(x) -> xor(x, true) or(x, y) -> xor(and(x, y), xor(x, y)) implies(x, y) -> xor(and(x, y), xor(x, true)) and(x, true) -> x and(x, false) -> false and(x, x) -> x xor(x, false) -> x xor(x, x) -> false and(xor(x, y), z) -> xor(and(x, z), and(y, z)) ---------------------------------------- (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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