details

property	value
status	complete
benchmark	Ex26_Luc03b_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n187.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	3.87897 seconds
cpu usage	13.6607
user time	11.8629
system time	1.79783
max virtual memory	6055152.0
max residence set size	109528.0

stage attributes

key	value
starexec-result	YES

output

YES Problem: a__terms(N) -> cons(recip(a__sqr(mark(N))),terms(s(N))) a__sqr(0()) -> 0() a__sqr(s(X)) -> s(add(sqr(X),dbl(X))) a__dbl(0()) -> 0() a__dbl(s(X)) -> s(s(dbl(X))) a__add(0(),X) -> mark(X) a__add(s(X),Y) -> s(add(X,Y)) a__first(0(),X) -> nil() a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z)) mark(terms(X)) -> a__terms(mark(X)) mark(sqr(X)) -> a__sqr(mark(X)) mark(add(X1,X2)) -> a__add(mark(X1),mark(X2)) mark(dbl(X)) -> a__dbl(mark(X)) mark(first(X1,X2)) -> a__first(mark(X1),mark(X2)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(recip(X)) -> recip(mark(X)) mark(s(X)) -> s(X) mark(0()) -> 0() mark(nil()) -> nil() a__terms(X) -> terms(X) a__sqr(X) -> sqr(X) a__add(X1,X2) -> add(X1,X2) a__dbl(X) -> dbl(X) a__first(X1,X2) -> first(X1,X2) Proof: WPO Processor: algebra: Max weight function: w0 = 0 w(0) = w(cons) = 3 w(add) = w(recip) = w(a__terms) = 1 w(first) = w(nil) = w(a__first) = w(a__add) = w(a__dbl) = w(dbl) = w( sqr) = w(terms) = w(s) = w(a__sqr) = w(mark) = 0 status function: st(first) = st(a__add) = st(add) = [1, 0] st(nil) = [] st(a__first) = [0, 1] st(a__dbl) = st(dbl) = st(sqr) = [0] st(0) = [] st(cons) = [0, 1] st(terms) = st(s) = st(recip) = st(a__sqr) = st(mark) = st(a__terms) = [0] subterm penalty function: sp(terms, 0) = sp(a__terms, 0) = 4 sp(cons, 0) = 2 sp(a__add, 1) = sp(add, 1) = sp(sqr, 0) = sp(recip, 0) = sp(a__sqr, 0) = 1 sp(first, 1) = sp(first, 0) = sp(a__first, 1) = sp(a__first, 0) = sp( a__add, 0) = sp(a__dbl, 0) = sp(add, 0) = sp(dbl, 0) = sp(cons, 1) = sp( s, 0) = sp(mark, 0) = 0 precedence: mark > a__first > a__add ~ a__dbl ~ a__sqr ~ a__terms > first ~ nil ~ add ~ dbl ~ sqr ~ 0 ~ cons ~ terms ~ s ~ recip problem: Qed popout

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