details

property	value
status	complete
benchmark	011.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	AotoYamada_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.680416 seconds
cpu usage	0.520017
user time	0.30515
system time	0.214867
max virtual memory	452896.0
max residence set size	6484.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S f:S g:S x:S xs:S y:S) (RULES app(app(app(curry,g:S),x:S),y:S) -> app(app(g:S,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(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S inc -> app(map,app(app(curry,plus),app(s,0))) ) Problem 1: Innermost Equivalent Processor: -> Rules: app(app(app(curry,g:S),x:S),y:S) -> app(app(g:S,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(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S inc -> app(map,app(app(curry,plus),app(s,0))) -> 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(curry,g:S),x:S),y:S) -> APP(app(g:S,x:S),y:S) APP(app(app(curry,g:S),x:S),y: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) APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) APP(app(plus,app(s,x:S)),y:S) -> APP(s,app(app(plus,x:S),y:S)) -> Rules: app(app(app(curry,g:S),x:S),y:S) -> app(app(g:S,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(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S inc -> app(map,app(app(curry,plus),app(s,0))) Problem 1: SCC Processor: -> Pairs: APP(app(app(curry,g:S),x:S),y:S) -> APP(app(g:S,x:S),y:S) APP(app(app(curry,g:S),x:S),y: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) APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) APP(app(plus,app(s,x:S)),y:S) -> APP(s,app(app(plus,x:S),y:S)) -> Rules: app(app(app(curry,g:S),x:S),y:S) -> app(app(g:S,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(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S inc -> app(map,app(app(curry,plus),app(s,0))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) ->->-> Rules: app(app(app(curry,g:S),x:S),y:S) -> app(app(g:S,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(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S inc -> app(map,app(app(curry,plus),app(s,0))) ->->Cycle: ->->-> Pairs: APP(app(app(curry,g:S),x:S),y:S) -> APP(app(g:S,x:S),y:S) APP(app(app(curry,g:S),x:S),y: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(curry,g:S),x:S),y:S) -> app(app(g:S,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(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S inc -> app(map,app(app(curry,plus),app(s,0))) The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pairs Processor: -> Pairs: APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) -> Rules: popout

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

job log

popout

actions

all output return to TRS Standard