details

property	value
status	complete
benchmark	Ex2_Luc02a_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)	0.022488 seconds
cpu usage	0.022923
user time	0.003519
system time	0.019404
max virtual memory	113188.0
max residence set size	5708.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S N:S X:S X1:S X2:S Y:S Z:S) (RULES activate(n__first(X1:S,X2:S)) -> first(X1:S,X2:S) activate(n__terms(X:S)) -> terms(X:S) activate(X:S) -> X:S add(0,X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) dbl(0) -> 0 dbl(s(X:S)) -> s(s(dbl(X:S))) first(0,X:S) -> nil first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S))) first(X1:S,X2:S) -> n__first(X1:S,X2:S) sqr(0) -> 0 sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) terms(N:S) -> cons(recip(sqr(N:S)),n__terms(s(N:S))) terms(X:S) -> n__terms(X:S) ) Problem 1: Dependency Pairs Processor: -> Pairs: ACTIVATE(n__first(X1:S,X2:S)) -> FIRST(X1:S,X2:S) ACTIVATE(n__terms(X:S)) -> TERMS(X:S) ADD(s(X:S),Y:S) -> ADD(X:S,Y:S) DBL(s(X:S)) -> DBL(X:S) FIRST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S) SQR(s(X:S)) -> ADD(sqr(X:S),dbl(X:S)) SQR(s(X:S)) -> DBL(X:S) SQR(s(X:S)) -> SQR(X:S) TERMS(N:S) -> SQR(N:S) -> Rules: activate(n__first(X1:S,X2:S)) -> first(X1:S,X2:S) activate(n__terms(X:S)) -> terms(X:S) activate(X:S) -> X:S add(0,X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) dbl(0) -> 0 dbl(s(X:S)) -> s(s(dbl(X:S))) first(0,X:S) -> nil first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S))) first(X1:S,X2:S) -> n__first(X1:S,X2:S) sqr(0) -> 0 sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) terms(N:S) -> cons(recip(sqr(N:S)),n__terms(s(N:S))) terms(X:S) -> n__terms(X:S) Problem 1: SCC Processor: -> Pairs: ACTIVATE(n__first(X1:S,X2:S)) -> FIRST(X1:S,X2:S) ACTIVATE(n__terms(X:S)) -> TERMS(X:S) ADD(s(X:S),Y:S) -> ADD(X:S,Y:S) DBL(s(X:S)) -> DBL(X:S) FIRST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S) SQR(s(X:S)) -> ADD(sqr(X:S),dbl(X:S)) SQR(s(X:S)) -> DBL(X:S) SQR(s(X:S)) -> SQR(X:S) TERMS(N:S) -> SQR(N:S) -> Rules: activate(n__first(X1:S,X2:S)) -> first(X1:S,X2:S) activate(n__terms(X:S)) -> terms(X:S) activate(X:S) -> X:S add(0,X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) dbl(0) -> 0 dbl(s(X:S)) -> s(s(dbl(X:S))) first(0,X:S) -> nil first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S))) first(X1:S,X2:S) -> n__first(X1:S,X2:S) sqr(0) -> 0 sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) terms(N:S) -> cons(recip(sqr(N:S)),n__terms(s(N:S))) terms(X:S) -> n__terms(X:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: DBL(s(X:S)) -> DBL(X:S) ->->-> Rules: activate(n__first(X1:S,X2:S)) -> first(X1:S,X2:S) activate(n__terms(X:S)) -> terms(X:S) activate(X:S) -> X:S add(0,X:S) -> X:S add(s(X:S),Y:S) -> s(add(X:S,Y:S)) dbl(0) -> 0 dbl(s(X:S)) -> s(s(dbl(X:S))) first(0,X:S) -> nil first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S))) first(X1:S,X2:S) -> n__first(X1:S,X2:S) sqr(0) -> 0 sqr(s(X:S)) -> s(add(sqr(X:S),dbl(X:S))) terms(N:S) -> cons(recip(sqr(N:S)),n__terms(s(N:S))) terms(X:S) -> n__terms(X:S) ->->Cycle: ->->-> Pairs: popout

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

job log

popout

actions

all output return to TRS Standard