details

property	value
status	complete
benchmark	TreeHeight.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n181.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.026471 seconds
cpu usage	0.026993
user time	0.013371
system time	0.013622
max virtual memory	113188.0
max residence set size	5804.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S f:S x:S xs:S y:S ys:S) (RULES app(app(le,app(s,x:S)),app(s,y:S)) -> app(app(le,x:S),y:S) app(app(le,app(s,x:S)),0) -> ffalse app(app(le,0),y:S) -> ttrue 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(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> app(app(if,app(app(le,x:S),y:S)),app(app(maxlist,y:S),ys:S)) app(app(maxlist,x:S),nil) -> x:S app(height,app(app(node,x:S),xs:S)) -> app(s,app(app(maxlist,0),app(app(map,height),xs:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: app(app(le,app(s,x:S)),app(s,y:S)) -> app(app(le,x:S),y:S) app(app(le,app(s,x:S)),0) -> ffalse app(app(le,0),y:S) -> ttrue 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(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> app(app(if,app(app(le,x:S),y:S)),app(app(maxlist,y:S),ys:S)) app(app(maxlist,x:S),nil) -> x:S app(height,app(app(node,x:S),xs:S)) -> app(s,app(app(maxlist,0),app(app(map,height),xs: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(le,app(s,x:S)),app(s,y:S)) -> APP(app(le,x:S),y: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) APP(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> APP(app(if,app(app(le,x:S),y:S)),app(app(maxlist,y:S),ys:S)) APP(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> APP(app(le,x:S),y:S) APP(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> APP(app(maxlist,y:S),ys:S) APP(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> APP(if,app(app(le,x:S),y:S)) APP(height,app(app(node,x:S),xs:S)) -> APP(app(map,height),xs:S) APP(height,app(app(node,x:S),xs:S)) -> APP(app(maxlist,0),app(app(map,height),xs:S)) APP(height,app(app(node,x:S),xs:S)) -> APP(s,app(app(maxlist,0),app(app(map,height),xs:S))) -> Rules: app(app(le,app(s,x:S)),app(s,y:S)) -> app(app(le,x:S),y:S) app(app(le,app(s,x:S)),0) -> ffalse app(app(le,0),y:S) -> ttrue 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(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> app(app(if,app(app(le,x:S),y:S)),app(app(maxlist,y:S),ys:S)) app(app(maxlist,x:S),nil) -> x:S app(height,app(app(node,x:S),xs:S)) -> app(s,app(app(maxlist,0),app(app(map,height),xs:S))) Problem 1: SCC Processor: -> Pairs: APP(app(le,app(s,x:S)),app(s,y:S)) -> APP(app(le,x:S),y: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) APP(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> APP(app(if,app(app(le,x:S),y:S)),app(app(maxlist,y:S),ys:S)) APP(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> APP(app(le,x:S),y:S) APP(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> APP(app(maxlist,y:S),ys:S) APP(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> APP(if,app(app(le,x:S),y:S)) APP(height,app(app(node,x:S),xs:S)) -> APP(app(map,height),xs:S) APP(height,app(app(node,x:S),xs:S)) -> APP(app(maxlist,0),app(app(map,height),xs:S)) APP(height,app(app(node,x:S),xs:S)) -> APP(s,app(app(maxlist,0),app(app(map,height),xs:S))) -> Rules: app(app(le,app(s,x:S)),app(s,y:S)) -> app(app(le,x:S),y:S) app(app(le,app(s,x:S)),0) -> ffalse app(app(le,0),y:S) -> ttrue 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(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> app(app(if,app(app(le,x:S),y:S)),app(app(maxlist,y:S),ys:S)) app(app(maxlist,x:S),nil) -> x:S app(height,app(app(node,x:S),xs:S)) -> app(s,app(app(maxlist,0),app(app(map,height),xs:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(le,app(s,x:S)),app(s,y:S)) -> APP(app(le,x:S),y:S) ->->-> Rules: app(app(le,app(s,x:S)),app(s,y:S)) -> app(app(le,x:S),y:S) app(app(le,app(s,x:S)),0) -> ffalse app(app(le,0),y:S) -> ttrue 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(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> app(app(if,app(app(le,x:S),y:S)),app(app(maxlist,y:S),ys:S)) app(app(maxlist,x:S),nil) -> x:S app(height,app(app(node,x:S),xs:S)) -> app(s,app(app(maxlist,0),app(app(map,height),xs:S))) ->->Cycle: ->->-> Pairs: APP(app(maxlist,x:S),app(app(cons,y:S),ys:S)) -> APP(app(maxlist,y:S),ys:S) ->->-> Rules: app(app(le,app(s,x:S)),app(s,y:S)) -> app(app(le,x:S),y:S) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to TRS Standard