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TRS Standard pair #487070937
details
property
value
status
complete
benchmark
LengthOfFiniteLists_nokinds_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n190.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
2.83039 seconds
cpu usage
9.91974
user time
8.25602
system time
1.66371
max virtual memory
2003856.0
max residence set size
134592.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__isNatList(V1) a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(V) -> a__isNatList(V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) a__isNatIList(X) -> isNatIList(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [U11](x0, x1) = 2x0 + 2x1, [tt] = 0, [nil] = 0, [s](x0) = x0, [0] = 0, [cons](x0, x1) = x0 + 3x1, [isNatList](x0) = 2x0, [and](x0, x1) = x0 + x1, [isNat](x0) = x0, [a__U11](x0, x1) = 2x0 + 2x1, [a__isNat](x0) = x0, [a__zeros] = 0, [a__length](x0) = 2x0, [isNatIList](x0) = 2x0 + 4, [a__isNatList](x0) = 2x0, [length](x0) = 2x0, [a__and](x0, x1) = x0 + x1, [a__isNatIList](x0) = 2x0 + 4, [mark](x0) = x0, [zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),L) = 2L >= 2L = s(a__length(mark(L))) a__and(tt(),X) = X >= X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = 2V1 >= 2V1 = a__isNatList(V1) a__isNat(s(V1)) = V1 >= V1 = a__isNat(V1) a__isNatIList(V) = 2V + 4 >= 2V = a__isNatList(V) a__isNatIList(zeros()) = 4 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 2V1 + 6V2 + 4 >= V1 + 2V2 + 4 = a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(nil()) = 0 >= 0 = tt()
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