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SRS Relat 19260 pair #381725134
details
property
value
status
complete
benchmark
zr01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n021.star.cs.uiowa.edu
space
Mixed_relative_SRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.07000803947 seconds
cpu usage
5.307054711
max memory
5.29412096E8
stage attributes
key
value
output-size
3740
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRS Reverse [EQUIVALENT, 0 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 24 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 33 ms] (6) RelTRS (7) RIsEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: n(s(x1)) -> s(x1) o(s(x1)) -> s(x1) The relative TRS consists of the following S rules: t(x1) -> t(c(n(x1))) c(n(x1)) -> n(c(x1)) c(o(x1)) -> o(c(x1)) c(o(x1)) -> o(x1) ---------------------------------------- (1) RelTRS Reverse (EQUIVALENT) We have reversed the following relative TRS [REVERSE]: The set of rules R is n(s(x1)) -> s(x1) o(s(x1)) -> s(x1) The set of rules S is t(x1) -> t(c(n(x1))) c(n(x1)) -> n(c(x1)) c(o(x1)) -> o(c(x1)) c(o(x1)) -> o(x1) We have obtained the following relative TRS: The set of rules R is s(n(x1)) -> s(x1) s(o(x1)) -> s(x1) The set of rules S is t(x1) -> n(c(t(x1))) n(c(x1)) -> c(n(x1)) o(c(x1)) -> c(o(x1)) o(c(x1)) -> o(x1) ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: s(n(x1)) -> s(x1) s(o(x1)) -> s(x1) The relative TRS consists of the following S rules: t(x1) -> n(c(t(x1))) n(c(x1)) -> c(n(x1)) o(c(x1)) -> c(o(x1)) o(c(x1)) -> o(x1) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(c(x_1)) = x_1 POL(n(x_1)) = x_1 POL(o(x_1)) = 1 + x_1 POL(s(x_1)) = x_1 POL(t(x_1)) = x_1 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R:
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return to SRS Relat 19260