TRS Standard pair #487067582

details

property	value
status	complete
benchmark	#3.56.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.550709 seconds
cpu usage	1.15005
user time	0.851127
system time	0.298919
max virtual memory	673752.0
max residence set size	60772.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 g(c(x,s(y))) -> g(c(s(x),y))
 f(c(s(x),y)) -> f(c(x,s(y)))
 f(f(x)) -> f(d(f(x)))
 f(x) -> x

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

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