details

property	value
status	complete
benchmark	11.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n190.star.cs.uiowa.edu
space	Applicative_first_order_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0937241 seconds
cpu usage	0.094361
user time	0.082847
system time	0.011514
max virtual memory	113188.0
max residence set size	9060.0

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(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S) app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S)) app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S) app(app(filter,f:S),nil) -> nil 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(D,app(app(*,x:S),y:S)) -> app(app(+,app(app(*,y:S),app(D,x:S))),app(app(*,x:S),app(D,y:S))) app(D,app(app(+,x:S),y:S)) -> app(app(+,app(D,x:S)),app(D,y:S)) app(D,app(app(-,x:S),y:S)) -> app(app(-,app(D,x:S)),app(D,y:S)) app(D,app(app(div,x:S),y:S)) -> app(app(-,app(app(div,app(D,x:S)),y:S)),app(app(div,app(app(*,x:S),app(D,y:S))),app(app(pow,y:S),2))) app(D,app(app(pow,x:S),y:S)) -> app(app(+,app(app(*,app(app(*,y:S),app(app(pow,x:S),app(app(-,y:S),1)))),app(D,x:S))),app(app(*,app(app(*,app(app(pow,x:S),y:S)),app(ln,x:S))),app(D,y:S))) app(D,app(ln,x:S)) -> app(app(div,app(D,x:S)),x:S) app(D,app(minus,x:S)) -> app(minus,app(D,x:S)) app(D,constant) -> 0 app(D,t) -> 1 ) Problem 1: Innermost Equivalent Processor: -> Rules: app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S) app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S)) app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S) app(app(filter,f:S),nil) -> nil 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(D,app(app(*,x:S),y:S)) -> app(app(+,app(app(*,y:S),app(D,x:S))),app(app(*,x:S),app(D,y:S))) app(D,app(app(+,x:S),y:S)) -> app(app(+,app(D,x:S)),app(D,y:S)) app(D,app(app(-,x:S),y:S)) -> app(app(-,app(D,x:S)),app(D,y:S)) app(D,app(app(div,x:S),y:S)) -> app(app(-,app(app(div,app(D,x:S)),y:S)),app(app(div,app(app(*,x:S),app(D,y:S))),app(app(pow,y:S),2))) app(D,app(app(pow,x:S),y:S)) -> app(app(+,app(app(*,app(app(*,y:S),app(app(pow,x:S),app(app(-,y:S),1)))),app(D,x:S))),app(app(*,app(app(*,app(app(pow,x:S),y:S)),app(ln,x:S))),app(D,y:S))) app(D,app(ln,x:S)) -> app(app(div,app(D,x:S)),x:S) app(D,app(minus,x:S)) -> app(minus,app(D,x:S)) app(D,constant) -> 0 app(D,t) -> 1 -> 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(app(filter2,ffalse),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S) APP(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> APP(app(cons,x:S),app(app(filter,f:S),xs:S)) APP(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> APP(app(filter,f:S),xs:S) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(app(filter2,app(f:S,x:S)),f:S),x:S) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(app(filter2,app(f:S,x:S)),f:S) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(filter2,app(f:S,x:S)) APP(app(filter,f:S),app(app(cons,x:S),xs:S)) -> APP(f: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(D,app(app(*,x:S),y:S)) -> APP(app(*,x:S),app(D,y:S)) APP(D,app(app(*,x:S),y:S)) -> APP(app(*,y:S),app(D,x:S)) APP(D,app(app(*,x:S),y:S)) -> APP(app(+,app(app(*,y:S),app(D,x:S))),app(app(*,x:S),app(D,y:S))) APP(D,app(app(*,x:S),y:S)) -> APP(+,app(app(*,y:S),app(D,x:S))) APP(D,app(app(*,x:S),y:S)) -> APP(D,x:S) APP(D,app(app(*,x:S),y:S)) -> APP(D,y:S) APP(D,app(app(+,x:S),y:S)) -> APP(app(+,app(D,x:S)),app(D,y:S)) APP(D,app(app(+,x:S),y:S)) -> APP(+,app(D,x:S)) APP(D,app(app(+,x:S),y:S)) -> APP(D,x:S) APP(D,app(app(+,x:S),y:S)) -> APP(D,y:S) APP(D,app(app(-,x:S),y:S)) -> APP(app(-,app(D,x:S)),app(D,y:S)) APP(D,app(app(-,x:S),y:S)) -> APP(-,app(D,x:S)) APP(D,app(app(-,x:S),y:S)) -> APP(D,x:S) APP(D,app(app(-,x:S),y:S)) -> APP(D,y:S) APP(D,app(app(div,x:S),y:S)) -> APP(app(*,x:S),app(D,y:S)) APP(D,app(app(div,x:S),y:S)) -> APP(app(-,app(app(div,app(D,x:S)),y:S)),app(app(div,app(app(*,x:S),app(D,y:S))),app(app(pow,y:S),2))) APP(D,app(app(div,x:S),y:S)) -> APP(app(div,app(app(*,x:S),app(D,y:S))),app(app(pow,y:S),2)) APP(D,app(app(div,x:S),y:S)) -> APP(app(div,app(D,x:S)),y:S) APP(D,app(app(div,x:S),y:S)) -> APP(-,app(app(div,app(D,x:S)),y:S)) APP(D,app(app(div,x:S),y:S)) -> APP(D,x:S) APP(D,app(app(div,x:S),y:S)) -> APP(D,y:S) APP(D,app(app(div,x:S),y:S)) -> APP(div,app(app(*,x:S),app(D,y:S))) APP(D,app(app(div,x:S),y:S)) -> APP(div,app(D,x:S)) APP(D,app(app(pow,x:S),y:S)) -> APP(app(*,app(app(*,app(app(pow,x:S),y:S)),app(ln,x:S))),app(D,y:S)) APP(D,app(app(pow,x:S),y:S)) -> APP(app(*,app(app(*,y:S),app(app(pow,x:S),app(app(-,y:S),1)))),app(D,x:S)) APP(D,app(app(pow,x:S),y:S)) -> APP(app(+,app(app(*,app(app(*,y:S),app(app(pow,x:S),app(app(-,y:S),1)))),app(D,x:S))),app(app(*,app(app(*,app(app(pow,x:S),y:S)),app(ln,x:S))),app(D,y:S))) APP(D,app(app(pow,x:S),y:S)) -> APP(+,app(app(*,app(app(*,y:S),app(app(pow,x:S),app(app(-,y:S),1)))),app(D,x:S))) APP(D,app(app(pow,x:S),y:S)) -> APP(D,x:S) APP(D,app(app(pow,x:S),y:S)) -> APP(D,y:S) APP(D,app(ln,x:S)) -> APP(app(div,app(D,x:S)),x:S) APP(D,app(ln,x:S)) -> APP(D,x:S) APP(D,app(ln,x:S)) -> APP(div,app(D,x:S)) APP(D,app(minus,x:S)) -> APP(D,x:S) APP(D,app(minus,x:S)) -> APP(minus,app(D,x:S)) -> Rules: app(app(app(app(filter2,ffalse),f:S),x:S),xs:S) -> app(app(filter,f:S),xs:S) app(app(app(app(filter2,ttrue),f:S),x:S),xs:S) -> app(app(cons,x:S),app(app(filter,f:S),xs:S)) app(app(filter,f:S),app(app(cons,x:S),xs:S)) -> app(app(app(app(filter2,app(f:S,x:S)),f:S),x:S),xs:S) app(app(filter,f:S),nil) -> nil popout

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all output return to TRS Standard