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SRS Relative pair #487521026
details
property
value
status
complete
benchmark
zr10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
Mixed_relative_SRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.2391500473 seconds
cpu usage
12.733377868
max memory
1.76996352E9
stage attributes
key
value
output-size
6939
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RootLabelingProof [EQUIVALENT, 0 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 182 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 106 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 58 ms] (8) RelTRS (9) RelTRSRRRProof [EQUIVALENT, 10 ms] (10) RelTRS (11) RIsEmptyProof [EQUIVALENT, 5 ms] (12) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: a(b(a(x1))) -> a(b(b(a(x1)))) b(a(b(x1))) -> b(a(a(b(x1)))) The relative TRS consists of the following S rules: a(x1) -> a(a(a(x1))) b(x1) -> b(b(b(x1))) ---------------------------------------- (1) RootLabelingProof (EQUIVALENT) We used plain root labeling [ROOTLAB] with the following heuristic: LabelAll: All function symbols get labeled ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: a_{b_1}(b_{a_1}(a_{a_1}(x1))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) a_{b_1}(b_{a_1}(a_{b_1}(x1))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) b_{a_1}(a_{b_1}(b_{a_1}(x1))) -> b_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) b_{a_1}(a_{b_1}(b_{b_1}(x1))) -> b_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) The relative TRS consists of the following S rules: a_{a_1}(x1) -> a_{a_1}(a_{a_1}(a_{a_1}(x1))) a_{b_1}(x1) -> a_{a_1}(a_{a_1}(a_{b_1}(x1))) b_{a_1}(x1) -> b_{b_1}(b_{b_1}(b_{a_1}(x1))) b_{b_1}(x1) -> b_{b_1}(b_{b_1}(b_{b_1}(x1))) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(a_{b_1}(x_1)) = [[0], [1]] + [[1, 2], [2, 0]] * x_1 >>> <<< POL(b_{a_1}(x_1)) = [[0], [0]] + [[2, 0], [1, 1]] * x_1 >>> <<< POL(a_{a_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 >>> <<< POL(b_{b_1}(x_1)) = [[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: a_{b_1}(b_{a_1}(a_{b_1}(x1))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) Rules from S: none
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