details

property	value
status	complete
benchmark	TreeMap.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)	0.021105 seconds
cpu usage	0.021596
user time	0.009471
system time	0.012125
max virtual memory	113188.0
max residence set size	5408.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S f:S x:S xs:S) (RULES 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(treemap,f:S),app(app(node,x:S),xs:S)) -> app(app(node,app(f:S,x:S)),app(app(map,app(treemap,f:S)),xs:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: 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(treemap,f:S),app(app(node,x:S),xs:S)) -> app(app(node,app(f:S,x:S)),app(app(map,app(treemap,f:S)),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(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(treemap,f:S),app(app(node,x:S),xs:S)) -> APP(app(map,app(treemap,f:S)),xs:S) APP(app(treemap,f:S),app(app(node,x:S),xs:S)) -> APP(app(node,app(f:S,x:S)),app(app(map,app(treemap,f:S)),xs:S)) APP(app(treemap,f:S),app(app(node,x:S),xs:S)) -> APP(node,app(f:S,x:S)) APP(app(treemap,f:S),app(app(node,x:S),xs:S)) -> APP(f:S,x:S) -> Rules: 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(treemap,f:S),app(app(node,x:S),xs:S)) -> app(app(node,app(f:S,x:S)),app(app(map,app(treemap,f:S)),xs:S)) Problem 1: SCC Processor: -> Pairs: 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(treemap,f:S),app(app(node,x:S),xs:S)) -> APP(app(map,app(treemap,f:S)),xs:S) APP(app(treemap,f:S),app(app(node,x:S),xs:S)) -> APP(app(node,app(f:S,x:S)),app(app(map,app(treemap,f:S)),xs:S)) APP(app(treemap,f:S),app(app(node,x:S),xs:S)) -> APP(node,app(f:S,x:S)) APP(app(treemap,f:S),app(app(node,x:S),xs:S)) -> APP(f:S,x:S) -> Rules: 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(treemap,f:S),app(app(node,x:S),xs:S)) -> app(app(node,app(f:S,x:S)),app(app(map,app(treemap,f:S)),xs: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) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S) APP(app(treemap,f:S),app(app(node,x:S),xs:S)) -> APP(app(map,app(treemap,f:S)),xs:S) APP(app(treemap,f:S),app(app(node,x:S),xs:S)) -> APP(f:S,x:S) ->->-> Rules: 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(treemap,f:S),app(app(node,x:S),xs:S)) -> app(app(node,app(f:S,x:S)),app(app(map,app(treemap,f:S)),xs:S)) Problem 1: Subterm Processor: -> Pairs: 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) APP(app(treemap,f:S),app(app(node,x:S),xs:S)) -> APP(app(map,app(treemap,f:S)),xs:S) APP(app(treemap,f:S),app(app(node,x:S),xs:S)) -> APP(f:S,x:S) -> Rules: 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(treemap,f:S),app(app(node,x:S),xs:S)) -> app(app(node,app(f:S,x:S)),app(app(map,app(treemap,f:S)),xs:S)) ->Projection: pi(APP) = 2 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: 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(treemap,f:S),app(app(node,x:S),xs:S)) -> app(app(node,app(f:S,x:S)),app(app(map,app(treemap,f:S)),xs:S)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. popout

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