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TRS Relative pair #487520730
details
property
value
status
complete
benchmark
rt1-5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
Relative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.98491883278 seconds
cpu usage
4.619817805
max memory
3.38010112E8
stage attributes
key
value
output-size
2607
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 41 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 0 ms] (4) RelTRS (5) RIsEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: s(a(x)) -> s(b(x)) b(b(x)) -> a(x) The relative TRS consists of the following S rules: f(s(x), y) -> f(x, s(y)) s(a(x)) -> a(s(x)) s(b(x)) -> b(s(x)) a(s(x)) -> s(a(x)) b(s(x)) -> s(b(x)) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(a(x_1)) = 1 + x_1 POL(b(x_1)) = 1 + x_1 POL(f(x_1, x_2)) = x_1 + x_2 POL(s(x_1)) = x_1 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: b(b(x)) -> a(x) Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: s(a(x)) -> s(b(x)) The relative TRS consists of the following S rules: f(s(x), y) -> f(x, s(y)) s(a(x)) -> a(s(x)) s(b(x)) -> b(s(x)) a(s(x)) -> s(a(x)) b(s(x)) -> s(b(x)) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(a(x_1)) = 1 + x_1 POL(b(x_1)) = x_1 POL(f(x_1, x_2)) = x_1 + x_2 POL(s(x_1)) = x_1 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: s(a(x)) -> s(b(x)) Rules from S: none ----------------------------------------
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