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SRS Relative pair #487521086
details
property
value
status
complete
benchmark
r10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
Waldmann_06_relative
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
122.852678061 seconds
cpu usage
487.840003302
max memory
9.465737216E9
stage attributes
key
value
output-size
2006
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 67.5 s] (2) RelTRS (3) RIsEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: b(a(a(b(x1)))) -> a(a(a(a(x1)))) a(b(b(a(x1)))) -> b(b(b(b(x1)))) The relative TRS consists of the following S rules: b(x1) -> b(b(b(x1))) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^6, +, *, >=, >) : <<< POL(b(x_1)) = [[0], [0], [1], [0], [0], [0]] + [[1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0]] * x_1 >>> <<< POL(a(x_1)) = [[0], [0], [0], [0], [1], [0]] + [[1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0]] * x_1 >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: b(a(a(b(x1)))) -> a(a(a(a(x1)))) a(b(b(a(x1)))) -> b(b(b(b(x1)))) Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: R is empty. The relative TRS consists of the following S rules: b(x1) -> b(b(b(x1))) ---------------------------------------- (3) RIsEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES
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