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TRS Standard pair #487073394
details
property
value
status
complete
benchmark
026.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
AotoYamada_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0197569 seconds
cpu usage
0.020254
user time
0.01
system time
0.010254
max virtual memory
113188.0
max residence set size
5412.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S f:S g:S x:S xs:S) (RULES app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil 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(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil 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) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(cons,app(f:S,x:S)) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S) -> Rules: app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil 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) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(cons,app(f:S,x:S)) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S) -> Rules: app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil 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) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S) ->->-> Rules: app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil 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) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S) -> Rules: app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil app(twice,f:S) -> app(app(comp,f:S),f:S) ->Projection: pi(APP) = 1 Problem 1: SCC Processor: -> Pairs: APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S) -> Rules: app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil app(twice,f:S) -> app(app(comp,f:S),f:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S) ->->-> Rules: app(app(app(comp,f:S),g:S),x:S) -> app(f:S,app(g:S,x:S)) app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S))
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