details

property	value
status	complete
benchmark	ExAppendixB_AEL03_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n186.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0254529 seconds
cpu usage	0.026039
user time	0.013488
system time	0.012551
max virtual memory	113188.0
max residence set size	8008.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S N:S X:S Y:S Z:S) (RULES 2ndsneg(0,Z:S) -> rnil 2ndsneg(s(N:S),cons(X:S,Z:S)) -> 2ndsneg(s(N:S),cons2(X:S,activate(Z:S))) 2ndsneg(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> rcons(negrecip(Y:S),2ndspos(N:S,activate(Z:S))) 2ndspos(0,Z:S) -> rnil 2ndspos(s(N:S),cons(X:S,Z:S)) -> 2ndspos(s(N:S),cons2(X:S,activate(Z:S))) 2ndspos(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> rcons(posrecip(Y:S),2ndsneg(N:S,activate(Z:S))) activate(n__from(X:S)) -> from(X:S) activate(X:S) -> X:S from(X:S) -> cons(X:S,n__from(s(X:S))) from(X:S) -> n__from(X:S) pi(X:S) -> 2ndspos(X:S,from(0)) plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) square(X:S) -> times(X:S,X:S) times(0,Y:S) -> 0 times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y:S)) ) Problem 1: Dependency Pairs Processor: -> Pairs: 2NDSNEG(s(N:S),cons(X:S,Z:S)) -> 2NDSNEG(s(N:S),cons2(X:S,activate(Z:S))) 2NDSNEG(s(N:S),cons(X:S,Z:S)) -> ACTIVATE(Z:S) 2NDSNEG(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> 2NDSPOS(N:S,activate(Z:S)) 2NDSNEG(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> ACTIVATE(Z:S) 2NDSPOS(s(N:S),cons(X:S,Z:S)) -> 2NDSPOS(s(N:S),cons2(X:S,activate(Z:S))) 2NDSPOS(s(N:S),cons(X:S,Z:S)) -> ACTIVATE(Z:S) 2NDSPOS(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> 2NDSNEG(N:S,activate(Z:S)) 2NDSPOS(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> ACTIVATE(Z:S) ACTIVATE(n__from(X:S)) -> FROM(X:S) PI(X:S) -> 2NDSPOS(X:S,from(0)) PI(X:S) -> FROM(0) PLUS(s(X:S),Y:S) -> PLUS(X:S,Y:S) SQUARE(X:S) -> TIMES(X:S,X:S) TIMES(s(X:S),Y:S) -> PLUS(Y:S,times(X:S,Y:S)) TIMES(s(X:S),Y:S) -> TIMES(X:S,Y:S) -> Rules: 2ndsneg(0,Z:S) -> rnil 2ndsneg(s(N:S),cons(X:S,Z:S)) -> 2ndsneg(s(N:S),cons2(X:S,activate(Z:S))) 2ndsneg(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> rcons(negrecip(Y:S),2ndspos(N:S,activate(Z:S))) 2ndspos(0,Z:S) -> rnil 2ndspos(s(N:S),cons(X:S,Z:S)) -> 2ndspos(s(N:S),cons2(X:S,activate(Z:S))) 2ndspos(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> rcons(posrecip(Y:S),2ndsneg(N:S,activate(Z:S))) activate(n__from(X:S)) -> from(X:S) activate(X:S) -> X:S from(X:S) -> cons(X:S,n__from(s(X:S))) from(X:S) -> n__from(X:S) pi(X:S) -> 2ndspos(X:S,from(0)) plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) square(X:S) -> times(X:S,X:S) times(0,Y:S) -> 0 times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y:S)) Problem 1: SCC Processor: -> Pairs: 2NDSNEG(s(N:S),cons(X:S,Z:S)) -> 2NDSNEG(s(N:S),cons2(X:S,activate(Z:S))) 2NDSNEG(s(N:S),cons(X:S,Z:S)) -> ACTIVATE(Z:S) 2NDSNEG(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> 2NDSPOS(N:S,activate(Z:S)) 2NDSNEG(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> ACTIVATE(Z:S) 2NDSPOS(s(N:S),cons(X:S,Z:S)) -> 2NDSPOS(s(N:S),cons2(X:S,activate(Z:S))) 2NDSPOS(s(N:S),cons(X:S,Z:S)) -> ACTIVATE(Z:S) 2NDSPOS(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> 2NDSNEG(N:S,activate(Z:S)) 2NDSPOS(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> ACTIVATE(Z:S) ACTIVATE(n__from(X:S)) -> FROM(X:S) PI(X:S) -> 2NDSPOS(X:S,from(0)) PI(X:S) -> FROM(0) PLUS(s(X:S),Y:S) -> PLUS(X:S,Y:S) SQUARE(X:S) -> TIMES(X:S,X:S) TIMES(s(X:S),Y:S) -> PLUS(Y:S,times(X:S,Y:S)) TIMES(s(X:S),Y:S) -> TIMES(X:S,Y:S) -> Rules: 2ndsneg(0,Z:S) -> rnil 2ndsneg(s(N:S),cons(X:S,Z:S)) -> 2ndsneg(s(N:S),cons2(X:S,activate(Z:S))) 2ndsneg(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> rcons(negrecip(Y:S),2ndspos(N:S,activate(Z:S))) 2ndspos(0,Z:S) -> rnil 2ndspos(s(N:S),cons(X:S,Z:S)) -> 2ndspos(s(N:S),cons2(X:S,activate(Z:S))) 2ndspos(s(N:S),cons2(X:S,cons(Y:S,Z:S))) -> rcons(posrecip(Y:S),2ndsneg(N:S,activate(Z:S))) activate(n__from(X:S)) -> from(X:S) activate(X:S) -> X:S from(X:S) -> cons(X:S,n__from(s(X:S))) from(X:S) -> n__from(X:S) pi(X:S) -> 2ndspos(X:S,from(0)) plus(0,Y:S) -> Y:S plus(s(X:S),Y:S) -> s(plus(X:S,Y:S)) square(X:S) -> times(X:S,X:S) times(0,Y:S) -> 0 times(s(X:S),Y:S) -> plus(Y:S,times(X:S,Y:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: popout

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

job log

popout

actions

all output return to TRS Standard