Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Standard pair #487066728
details
property
value
status
complete
benchmark
07.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n189.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.6451 seconds
cpu usage
3.54868
user time
3.37999
system time
0.168691
max virtual memory
1.8475908E7
max residence set size
234496.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 3 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, y) -> h(x, y) f(x, y) -> h(y, x) h(x, x) -> x Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(f(x_1, x_2)) = 2 + x_1 + x_2 POL(h(x_1, x_2)) = 2 + x_1 + x_2 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: h(x, x) -> x ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x, y) -> h(x, y) f(x, y) -> h(y, x) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: f_2 > h_2 Status: f_2: [1,2] h_2: [2,1] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(x, y) -> h(x, y) f(x, y) -> h(y, x) ---------------------------------------- (4) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (5) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (6) YES
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Standard