Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Stand 20472 pair #381711632
details
property
value
status
complete
benchmark
23.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n109.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.59093117714 seconds
cpu usage
3.686983806
max memory
2.29384192E8
stage attributes
key
value
output-size
2231
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 66 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(0, f(x, x)) -> x g(x, s(y)) -> g(f(x, y), 0) g(s(x), y) -> g(f(x, y), 0) g(f(x, y), 0) -> f(g(x, 0), g(y, 0)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(f(x_1, x_2)) = 1 + x_1 + x_2 POL(g(x_1, x_2)) = 2*x_1 + 2*x_2 POL(s(x_1)) = 1 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g(0, f(x, x)) -> x g(f(x, y), 0) -> f(g(x, 0), g(y, 0)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(x, s(y)) -> g(f(x, y), 0) g(s(x), y) -> g(f(x, y), 0) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:0 > f_2 > s_1 > g_2 and weight map: 0=2 s_1=3 f_2=0 g_2=0 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g(x, s(y)) -> g(f(x, y), 0) g(s(x), y) -> g(f(x, y), 0) ---------------------------------------- (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. ----------------------------------------
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Stand 20472