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TRS Relative pair #487520625
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
n146.star.cs.uiowa.edu
space
INVY_15
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.6493139267 seconds
cpu usage
7.305312043
max memory
6.90864128E8
stage attributes
key
value
output-size
6064
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 30 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 7 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 12 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 0 ms] (8) RelTRS (9) RelTRSRRRProof [EQUIVALENT, 5 ms] (10) RelTRS (11) RIsEmptyProof [EQUIVALENT, 0 ms] (12) 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: Polynomial interpretation [POLO]: POL(0) = 0 POL(evenodd(x_1, x_2)) = 1 + x_1 + x_2 POL(false) = 1 POL(not(x_1)) = x_1 POL(rand(x_1)) = 1 + x_1 POL(s(x_1)) = x_1 POL(true) = 1 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: none 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(0, s(0)) -> false 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: Polynomial interpretation [POLO]: POL(0) = 1 POL(evenodd(x_1, x_2)) = 1 + x_1 + x_2 POL(false) = 1 POL(not(x_1)) = x_1 POL(rand(x_1)) = x_1 POL(s(x_1)) = x_1
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