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TRS Standard pair #487069441
details
property
value
status
complete
benchmark
Ex2_Luc02a_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
NaTT v.1.6c
configuration
Default
runtime (wallclock)
0.284351 seconds
cpu usage
0.068668
user time
0.03936
system time
0.029308
max virtual memory
113188.0
max residence set size
6524.0
stage attributes
key
value
starexec-result
YES
output
YES Input TRS: 1: a__terms(N) -> cons(recip(a__sqr(mark(N))),terms(s(N))) 2: a__sqr(0()) -> 0() 3: a__sqr(s(X)) -> s(a__add(a__sqr(mark(X)),a__dbl(mark(X)))) 4: a__dbl(0()) -> 0() 5: a__dbl(s(X)) -> s(s(a__dbl(mark(X)))) 6: a__add(0(),X) -> mark(X) 7: a__add(s(X),Y) -> s(a__add(mark(X),mark(Y))) 8: a__first(0(),X) -> nil() 9: a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z)) 10: mark(terms(X)) -> a__terms(mark(X)) 11: mark(sqr(X)) -> a__sqr(mark(X)) 12: mark(add(X1,X2)) -> a__add(mark(X1),mark(X2)) 13: mark(dbl(X)) -> a__dbl(mark(X)) 14: mark(first(X1,X2)) -> a__first(mark(X1),mark(X2)) 15: mark(cons(X1,X2)) -> cons(mark(X1),X2) 16: mark(recip(X)) -> recip(mark(X)) 17: mark(s(X)) -> s(mark(X)) 18: mark(0()) -> 0() 19: mark(nil()) -> nil() 20: a__terms(X) -> terms(X) 21: a__sqr(X) -> sqr(X) 22: a__add(X1,X2) -> add(X1,X2) 23: a__dbl(X) -> dbl(X) 24: a__first(X1,X2) -> first(X1,X2) Number of strict rules: 24 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #a__add(0(),X) -> #mark(X) #2: #mark(dbl(X)) -> #a__dbl(mark(X)) #3: #mark(dbl(X)) -> #mark(X) #4: #a__first(s(X),cons(Y,Z)) -> #mark(Y) #5: #mark(sqr(X)) -> #a__sqr(mark(X)) #6: #mark(sqr(X)) -> #mark(X) #7: #mark(add(X1,X2)) -> #a__add(mark(X1),mark(X2)) #8: #mark(add(X1,X2)) -> #mark(X1) #9: #mark(add(X1,X2)) -> #mark(X2) #10: #mark(first(X1,X2)) -> #a__first(mark(X1),mark(X2)) #11: #mark(first(X1,X2)) -> #mark(X1) #12: #mark(first(X1,X2)) -> #mark(X2) #13: #a__add(s(X),Y) -> #a__add(mark(X),mark(Y)) #14: #a__add(s(X),Y) -> #mark(X) #15: #a__add(s(X),Y) -> #mark(Y) #16: #mark(terms(X)) -> #a__terms(mark(X)) #17: #mark(terms(X)) -> #mark(X) #18: #a__dbl(s(X)) -> #a__dbl(mark(X)) #19: #a__dbl(s(X)) -> #mark(X) #20: #mark(s(X)) -> #mark(X) #21: #mark(recip(X)) -> #mark(X) #22: #a__sqr(s(X)) -> #a__add(a__sqr(mark(X)),a__dbl(mark(X))) #23: #a__sqr(s(X)) -> #a__sqr(mark(X)) #24: #a__sqr(s(X)) -> #mark(X) #25: #a__sqr(s(X)) -> #a__dbl(mark(X)) #26: #a__sqr(s(X)) -> #mark(X) #27: #a__terms(N) -> #a__sqr(mark(N)) #28: #a__terms(N) -> #mark(N) #29: #mark(cons(X1,X2)) -> #mark(X1) Number of SCCs: 1, DPs: 29 SCC { #1..29 } POLO(Sum)... POLO(max)... succeeded. s w: x1 #a__first w: max(x2 + 19308) recip w: x1 + 1 dbl w: x1 + 32287 #a__add w: max(x1 + 19306, x2 + 19307) a__add w: max(x1, x2 + 11799) a__dbl w: x1 + 32287 a__sqr w: x1 + 44086 #a__terms w: x1 + 63393 #mark w: x1 + 19306 0 w: 8368 nil w: 4 #a__dbl w: x1 + 19307 mark w: x1 first w: max(x1 + 1, x2 + 3) a__first w: max(x1 + 1, x2 + 3) cons w: max(x1 + 4) add w: max(x1, x2 + 11799) sqr w: x1 + 44086 a__terms w: x1 + 44091 #a__sqr w: x1 + 63392 terms w: x1 + 44091 USABLE RULES: { 1..24 } Removed DPs: #1..4 #6 #9..12 #15..17 #19 #21 #24..29 Number of SCCs: 2, DPs: 9 SCC { #18 } POLO(Sum)... POLO(max)... QLPOS... succeeded. s s: [1] p: 0 #a__first s: [2,1] p: 0 recip s: [1] p: 0 dbl s: [1] p: 1 #a__add s: [1,2] p: 0 a__add s: [2,1] p: 1 a__dbl s: [1] p: 1 a__sqr s: [1] p: 2 #a__terms s: 1 #mark s: [] p: 0 0 s: [] p: 3
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