details

property	value
status	complete
benchmark	AC50.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	NaTT v.1.6c
configuration	Default
runtime (wallclock)	0.0606421 seconds
cpu usage	0.025455
user time	0.013706
system time	0.011749
max virtual memory	113188.0
max residence set size	5984.0

stage attributes

key	value
starexec-result	YES

output

YES Input TRS: AC symbols: plus 1: app(nil(),k) -> k 2: app(l,nil()) -> l 3: app(cons(x,l),k) -> cons(x,app(l,k)) 4: sum(cons(x,nil())) -> cons(x,nil()) 5: sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) 6: sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) 7: sum(cons(0(),cons(plus(x,y),l))) -> pred(sum(cons(s(x),cons(y,l)))) 8: plus(0(),y) -> y 9: plus(s(x),y) -> s(plus(x,y)) 10: pred(cons(s(x),nil())) -> cons(x,nil()) Number of strict rules: 10 Direct POLO(bPol) ... removes: 8 1 3 5 10 7 2 s w: x1 + 1 pred w: x1 sum w: x1 0 w: 14681 nil w: 26286 plus w: x1 + x2 + 1 cons w: 2 * x1 + x2 + 3000 app w: 2 * x1 + x2 + 2 Number of strict rules: 3 Direct POLO(bPol) ... failed. Uncurrying sum AC symbols: plus 4: sum^1_cons(x,nil()) -> cons(x,nil()) 6: sum^1_app(l,cons(x,cons(y,k))) -> sum^1_app(l,sum^1_cons(x,cons(y,k))) 9: plus(s(x),y) -> s(plus(x,y)) 11: sum(cons(_1,_2)) ->= sum^1_cons(_1,_2) 12: sum(app(_1,_2)) ->= sum^1_app(_1,_2) Number of strict rules: 3 Direct POLO(bPol) ... removes: 4 12 11 6 sum^1_app w: x1 + 2 * x2 s w: x1 sum^1_cons w: x1 + x2 + 8370 pred w: x1 sum w: 2 * x1 + 2 0 w: 0 nil w: 1 plus w: x1 + x2 cons w: x1 + 2 * x2 + 8368 app w: x1 + x2 + 1 Number of strict rules: 1 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) #2: #plus(x,plus(y,z)) ->= #plus(x,y) #3: #plus(s(x),y) -> #plus(x,y) Number of SCCs: 1, DPs: 3 SCC { #1..3 } POLO(Sum)... succeeded. sum^1_app w: 0 s w: x1 + 1 sum^1_cons w: 0 #plus w: x1 + x2 pred w: 0 sum w: 0 0 w: 0 nil w: 0 plus w: x1 + x2 + 39 cons w: 0 app w: 0 USABLE RULES: { 9 13 } Removed DPs: #2 #3 Number of SCCs: 1, DPs: 1 SCC { #1 } only weak rules. Number of SCCs: 0, DPs: 0 Next Dependency Pairs: #4: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) #5: #plus(x,plus(y,z)) ->= #plus(x,y) #6: #plus(plus(s(x),y),_1) -> #plus(s(plus(x,y)),_1) Number of SCCs: 1, DPs: 3 SCC { #4..6 } POLO(Sum)... succeeded. sum^1_app w: 0 s w: 23676 sum^1_cons w: 0 #plus w: x1 + x2 pred w: 0 sum w: 0 0 w: 0 nil w: 0 plus w: x1 + x2 + 1 cons w: 0 app w: 0 USABLE RULES: { 9 13 } Removed DPs: #5 #6 Number of SCCs: 1, DPs: 1 SCC { #4 } only weak rules. Number of SCCs: 0, DPs: 0 popout

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actions

all output return to TRS Equational