TRS Standard pair #487067402

details

property	value
status	complete
benchmark	#3.36.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n192.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.51553 seconds
cpu usage	1.01132
user time	0.774497
system time	0.236819
max virtual memory	96176.0
max residence set size	60848.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 f(0()) -> s(0())
 f(s(x)) -> minus(s(x),g(f(x)))
 g(0()) -> 0()
 g(s(x)) -> minus(s(x),f(g(x)))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = 4x0,
   
   [minus](x0, x1) = x0 + x1,
   
   [f](x0) = 4x0 + 4,
   
   [0] = 0,
   
   [s](x0) = 6x0 + 4
  orientation:
   minus(x,0()) = x >= x = x
   
   minus(s(x),s(y)) = 6x + 6y + 8 >= x + y = minus(x,y)
   
   f(0()) = 4 >= 4 = s(0())
   
   f(s(x)) = 24x + 20 >= 22x + 20 = minus(s(x),g(f(x)))
   
   g(0()) = 0 >= 0 = 0()
   
   g(s(x)) = 24x + 16 >= 22x + 8 = minus(s(x),f(g(x)))
  problem:
   minus(x,0()) -> x
   f(0()) -> s(0())
   f(s(x)) -> minus(s(x),g(f(x)))
   g(0()) -> 0()
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [g](x0) = x0,
    
    [minus](x0, x1) = x0 + x1,
    
    [f](x0) = 2x0,
    
    [0] = 1,
    
    [s](x0) = 2x0
   orientation:
    minus(x,0()) = x + 1 >= x = x
    
    f(0()) = 2 >= 2 = s(0())
    
    f(s(x)) = 4x >= 4x = minus(s(x),g(f(x)))
    
    g(0()) = 1 >= 1 = 0()
   problem:
    f(0()) -> s(0())
    f(s(x)) -> minus(s(x),g(f(x)))
    g(0()) -> 0()
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [g](x0) = x0,
     
     [minus](x0, x1) = x0 + 2x1 + 2,
     
     [f](x0) = 4x0 + 2,
     
     [0] = 1,
     
     [s](x0) = 4x0 + 2
    orientation:
     f(0()) = 6 >= 6 = s(0())
     
     f(s(x)) = 16x + 10 >= 12x + 8 = minus(s(x),g(f(x)))
     
     g(0()) = 1 >= 1 = 0()
    problem:
     f(0()) -> s(0())
     g(0()) -> 0()
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [1 0 0]     [1]
      [g](x0) = [0 0 0]x0 + [0]
                [0 0 0]     [0],
      
                [1 0 0]     [1]
      [f](x0) = [0 0 0]x0 + [0]
                [0 0 0]     [0],
      
            [0]
      [0] = [0]
            [0],

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