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TRS Standard pair #516967291
details
property
value
status
complete
benchmark
Ex8Polymorphic.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
Applicative_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0907549858093 seconds
cpu usage
0.024981932
max memory
2011136.0
stage attributes
key
value
output-size
6100
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S f:S h:S t:S x:S) (RULES app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S)) app(app(fmap,nil),x:S) -> nil app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S)) app(app(map,f:S),nil) -> nil app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S)) app(app(fmap,nil),x:S) -> nil app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S)) app(app(map,f:S),nil) -> nil app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x: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(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S)) APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(cons,app(f:S,x:S)) APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(f:S,x:S) APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S)) APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(map,f:S),t:S) APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(cons,app(f:S,h:S)) APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(f:S,h:S) APP(app(twice,f:S),x:S) -> APP(f:S,app(f:S,x:S)) APP(app(twice,f:S),x:S) -> APP(f:S,x:S) -> Rules: app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S)) app(app(fmap,nil),x:S) -> nil app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S)) app(app(map,f:S),nil) -> nil app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x:S)) Problem 1: SCC Processor: -> Pairs: APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S)) APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(cons,app(f:S,x:S)) APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(f:S,x:S) APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S)) APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(map,f:S),t:S) APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(cons,app(f:S,h:S)) APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(f:S,h:S) APP(app(twice,f:S),x:S) -> APP(f:S,app(f:S,x:S)) APP(app(twice,f:S),x:S) -> APP(f:S,x:S) -> Rules: app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S)) app(app(fmap,nil),x:S) -> nil app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S)) app(app(map,f:S),nil) -> nil app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(f:S,x:S) APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(map,f:S),t:S) APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(f:S,h:S) APP(app(twice,f:S),x:S) -> APP(f:S,app(f:S,x:S)) APP(app(twice,f:S),x:S) -> APP(f:S,x:S) ->->-> Rules: app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S)) app(app(fmap,nil),x:S) -> nil app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S)) app(app(map,f:S),nil) -> nil app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x:S)) Problem 1: Subterm Processor: -> Pairs: APP(app(fmap,app(app(cons,f:S),t_f)),x:S) -> APP(f:S,x:S) APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(app(map,f:S),t:S) APP(app(map,f:S),app(app(cons,h:S),t:S)) -> APP(f:S,h:S) APP(app(twice,f:S),x:S) -> APP(f:S,app(f:S,x:S)) APP(app(twice,f:S),x:S) -> APP(f:S,x:S) -> Rules: app(app(fmap,app(app(cons,f:S),t_f)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t_f),x:S)) app(app(fmap,nil),x:S) -> nil app(app(map,f:S),app(app(cons,h:S),t:S)) -> app(app(cons,app(f:S,h:S)),app(app(map,f:S),t:S)) app(app(map,f:S),nil) -> nil app(app(twice,f:S),x:S) -> app(f:S,app(f:S,x:S))
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