details

property	value
status	complete
benchmark	08.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n073.star.cs.uiowa.edu
space	Applicative_first_order_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.044958 seconds
cpu usage	0.045543
user time	0.030943
system time	0.0146
max virtual memory	113188.0
max residence set size	8328.0

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,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,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) -> 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,constant) -> 0 app(D,t) -> 1 Problem 1: SCC 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))) popout

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actions

all output return to TRS Standard