details

property	value
status	complete
benchmark	Ex1SimplyTyped.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n179.star.cs.uiowa.edu
space	AotoYamada_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.166177 seconds
cpu usage	0.15162
user time	0.101075
system time	0.050545
max virtual memory	113188.0
max residence set size	5760.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S f:S x:S xs:S y:S) (RULES app(app(add,app(s,x:S)),y:S) -> app(s,app(app(add,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),nil) -> nil app(add,0) -> id app(id,x:S) -> x:S ) Problem 1: Innermost Equivalent Processor: -> Rules: app(app(add,app(s,x:S)),y:S) -> app(s,app(app(add,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),nil) -> nil app(add,0) -> id app(id,x: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(add,app(s,x:S)),y:S) -> APP(app(add,x:S),y:S) APP(app(add,app(s,x:S)),y:S) -> APP(add,x:S) APP(app(add,app(s,x:S)),y:S) -> APP(s,app(app(add,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) -> Rules: app(app(add,app(s,x:S)),y:S) -> app(s,app(app(add,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),nil) -> nil app(add,0) -> id app(id,x:S) -> x:S Problem 1: SCC Processor: -> Pairs: APP(app(add,app(s,x:S)),y:S) -> APP(app(add,x:S),y:S) APP(app(add,app(s,x:S)),y:S) -> APP(add,x:S) APP(app(add,app(s,x:S)),y:S) -> APP(s,app(app(add,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) -> Rules: app(app(add,app(s,x:S)),y:S) -> app(s,app(app(add,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),nil) -> nil app(add,0) -> id app(id,x:S) -> x:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(add,app(s,x:S)),y:S) -> APP(app(add,x:S),y: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(add,app(s,x:S)),y:S) -> app(s,app(app(add,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),nil) -> nil app(add,0) -> id app(id,x:S) -> x:S Problem 1: Subterm Processor: -> Pairs: APP(app(add,app(s,x:S)),y:S) -> APP(app(add,x:S),y: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(add,app(s,x:S)),y:S) -> app(s,app(app(add,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),nil) -> nil app(add,0) -> id app(id,x:S) -> x:S ->Projection: pi(APP) = 2 Problem 1: SCC Processor: -> Pairs: APP(app(add,app(s,x:S)),y:S) -> APP(app(add,x:S),y:S) -> Rules: app(app(add,app(s,x:S)),y:S) -> app(s,app(app(add,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),nil) -> nil app(add,0) -> id app(id,x:S) -> x:S popout

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job log

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actions

all output return to TRS Standard