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SRS Relative pair #487521021
details
property
value
status
complete
benchmark
zr04new.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Mixed_relative_SRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.63590288162 seconds
cpu usage
15.031235429
max memory
2.173968384E9
stage attributes
key
value
output-size
8750
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 49 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 98 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 10 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 35 ms] (8) RelTRS (9) RelTRSRRRProof [EQUIVALENT, 53 ms] (10) RelTRS (11) RelTRSRRRProof [EQUIVALENT, 18 ms] (12) RelTRS (13) RIsEmptyProof [EQUIVALENT, 2 ms] (14) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: t(u(x1)) -> t(c(d(x1))) d(f(x1)) -> f(d(x1)) d(g(x1)) -> u(g(x1)) f(u(x1)) -> u(f(x1)) d(n(x1)) -> d(x1) d(o(x1)) -> d(x1) o(u(x1)) -> u(x1) The relative TRS consists of the following S rules: n(u(x1)) -> u(x1) f(x1) -> f(n(x1)) t(x1) -> t(c(n(x1))) c(n(x1)) -> n(c(x1)) c(o(x1)) -> o(c(x1)) c(o(x1)) -> o(x1) c(f(x1)) -> f(c(x1)) c(u(x1)) -> u(c(x1)) c(d(x1)) -> d(c(x1)) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(c(x_1)) = x_1 POL(d(x_1)) = x_1 POL(f(x_1)) = x_1 POL(g(x_1)) = x_1 POL(n(x_1)) = x_1 POL(o(x_1)) = 1 + x_1 POL(t(x_1)) = x_1 POL(u(x_1)) = x_1 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: d(o(x1)) -> d(x1) o(u(x1)) -> u(x1) Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: t(u(x1)) -> t(c(d(x1))) d(f(x1)) -> f(d(x1)) d(g(x1)) -> u(g(x1)) f(u(x1)) -> u(f(x1)) d(n(x1)) -> d(x1) The relative TRS consists of the following S rules: n(u(x1)) -> u(x1) f(x1) -> f(n(x1))
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