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TRS Relat 75837 pair #381724845
details
property
value
status
complete
benchmark
#3.37_rand.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n088.star.cs.uiowa.edu
space
INVY_15
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.62436819077 seconds
cpu usage
7.496697922
max memory
7.46287104E8
stage attributes
key
value
output-size
5222
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 54 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 2 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 9 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 0 ms] (8) RelTRS (9) RIsEmptyProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: not(true) -> false not(false) -> true evenodd(x, 0) -> not(evenodd(x, s(0))) evenodd(0, s(0)) -> false evenodd(s(x), s(0)) -> evenodd(x, 0) The relative TRS consists of the following S rules: rand(x) -> x rand(x) -> rand(s(x)) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: not/1)YES( true/0) false/0) evenodd/2(YES,YES) 0/0) s/1)YES( rand/1(YES) Quasi precedence: [true, false, evenodd_2, 0, rand_1] Status: true: multiset status false: multiset status evenodd_2: multiset status 0: multiset status rand_1: multiset status With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: evenodd(0, s(0)) -> false Rules from S: rand(x) -> x ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: not(true) -> false not(false) -> true evenodd(x, 0) -> not(evenodd(x, s(0))) evenodd(s(x), s(0)) -> evenodd(x, 0) The relative TRS consists of the following S rules: rand(x) -> rand(s(x)) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal:
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