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SRS Relative pair #487521621
details
property
value
status
complete
benchmark
rel13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n084.star.cs.uiowa.edu
space
Zantema_06_relative
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.88383102417 seconds
cpu usage
7.956297403
max memory
9.6534528E8
stage attributes
key
value
output-size
4987
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 39 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 107 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 55 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: o(l(x1)) -> r(x1) n(l(o(x1))) -> r(o(x1)) L(l(o(x1))) -> L(r(o(x1))) r(o(x1)) -> l(x1) o(r(n(x1))) -> o(l(x1)) o(r(R(x1))) -> o(l(R(x1))) The relative TRS consists of the following S rules: L(x1) -> L(n(x1)) R(x1) -> n(R(x1)) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(L(x_1)) = x_1 POL(R(x_1)) = x_1 POL(l(x_1)) = x_1 POL(n(x_1)) = x_1 POL(o(x_1)) = 1 + x_1 POL(r(x_1)) = x_1 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: o(l(x1)) -> r(x1) r(o(x1)) -> l(x1) Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: n(l(o(x1))) -> r(o(x1)) L(l(o(x1))) -> L(r(o(x1))) o(r(n(x1))) -> o(l(x1)) o(r(R(x1))) -> o(l(R(x1))) The relative TRS consists of the following S rules: L(x1) -> L(n(x1)) R(x1) -> n(R(x1)) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(n(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 >>> <<< POL(l(x_1)) = [[0], [0]] + [[1, 0], [0, 2]] * x_1 >>>
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