TRS Standard pair #487069902

details

property	value
status	complete
benchmark	LengthOfFiniteLists_nosorts_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	4.66187 seconds
cpu usage	14.8829
user time	12.5402
system time	2.34276
max virtual memory	6479032.0
max residence set size	172764.0

stage attributes

key	value
starexec-result	NO

output

NO

Problem:
 active(zeros()) -> mark(cons(0(),zeros()))
 active(and(tt(),X)) -> mark(X)
 active(length(nil())) -> mark(0())
 active(length(cons(N,L))) -> mark(s(length(L)))
 mark(zeros()) -> active(zeros())
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(0()) -> active(0())
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(tt()) -> active(tt())
 mark(length(X)) -> active(length(mark(X)))
 mark(nil()) -> active(nil())
 mark(s(X)) -> active(s(mark(X)))
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons(active(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 and(active(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 length(mark(X)) -> length(X)
 length(active(X)) -> length(X)
 s(mark(X)) -> s(X)
 s(active(X)) -> s(X)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [mark](x0) = 4x0,
   
   [length](x0) = x0,
   
   [active](x0) = x0,
   
   [cons](x0, x1) = 4x0 + 4x1,
   
   [tt] = 1,
   
   [zeros] = 0,
   
   [nil] = 0,
   
   [s](x0) = x0,
   
   [and](x0, x1) = 6x0 + 6x1 + 4,
   
   [0] = 0
  orientation:
   active(zeros()) = 0 >= 0 = mark(cons(0(),zeros()))
   
   active(and(tt(),X)) = 6X + 10 >= 4X = mark(X)
   
   active(length(nil())) = 0 >= 0 = mark(0())
   
   active(length(cons(N,L))) = 4L + 4N >= 4L = mark(s(length(L)))
   
   mark(zeros()) = 0 >= 0 = active(zeros())
   
   mark(cons(X1,X2)) = 16X1 + 16X2 >= 16X1 + 4X2 = active(cons(mark(X1),X2))
   
   mark(0()) = 0 >= 0 = active(0())
   
   mark(and(X1,X2)) = 24X1 + 24X2 + 16 >= 24X1 + 6X2 + 4 = active(and(mark(X1),X2))
   
   mark(tt()) = 4 >= 1 = active(tt())
   
   mark(length(X)) = 4X >= 4X = active(length(mark(X)))
   
   mark(nil()) = 0 >= 0 = active(nil())
   
   mark(s(X)) = 4X >= 4X = active(s(mark(X)))
   
   cons(mark(X1),X2) = 16X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2)
   
   cons(X1,mark(X2)) = 4X1 + 16X2 >= 4X1 + 4X2 = cons(X1,X2)
   
   cons(active(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2)
   
   cons(X1,active(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2)
   
   and(mark(X1),X2) = 24X1 + 6X2 + 4 >= 6X1 + 6X2 + 4 = and(X1,X2)
   
   and(X1,mark(X2)) = 6X1 + 24X2 + 4 >= 6X1 + 6X2 + 4 = and(X1,X2)
   
   and(active(X1),X2) = 6X1 + 6X2 + 4 >= 6X1 + 6X2 + 4 = and(X1,X2)
   
   and(X1,active(X2)) = 6X1 + 6X2 + 4 >= 6X1 + 6X2 + 4 = and(X1,X2)
   
   length(mark(X)) = 4X >= X = length(X)
   
   length(active(X)) = X >= X = length(X)
   
   s(mark(X)) = 4X >= X = s(X)
   
   s(active(X)) = X >= X = s(X)
  problem:

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