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TRS Standard pair #516965081
details
property
value
status
complete
benchmark
019.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n170.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.125042915344 seconds
cpu usage
0.019192179
max memory
1544192.0
stage attributes
key
value
output-size
2040
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S f:S g:S x:S) (RULES app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(twice,f:S) -> app(app(comp,f:S),f:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(twice,f:S) -> app(app(comp,f:S),f:S) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: APP(app(app(comp,f:S),g:S),x:S) -> APP(f:S,app(g:S,x:S)) APP(app(app(comp,f:S),g:S),x:S) -> APP(g:S,x:S) -> Rules: app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(twice,f:S) -> app(app(comp,f:S),f:S) Problem 1: SCC Processor: -> Pairs: APP(app(app(comp,f:S),g:S),x:S) -> APP(f:S,app(g:S,x:S)) APP(app(app(comp,f:S),g:S),x:S) -> APP(g:S,x:S) -> Rules: app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(twice,f:S) -> app(app(comp,f:S),f:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(app(comp,f:S),g:S),x:S) -> APP(f:S,app(g:S,x:S)) APP(app(app(comp,f:S),g:S),x:S) -> APP(g:S,x:S) ->->-> Rules: app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(twice,f:S) -> app(app(comp,f:S),f:S) Problem 1: Subterm Processor: -> Pairs: APP(app(app(comp,f:S),g:S),x:S) -> APP(f:S,app(g:S,x:S)) APP(app(app(comp,f:S),g:S),x:S) -> APP(g:S,x:S) -> Rules: app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(twice,f:S) -> app(app(comp,f:S),f:S) ->Projection: pi(APP) = 1 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(twice,f:S) -> app(app(comp,f:S),f:S) ->Strongly Connected Components: There is no strongly connected component The problem is finite.
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