TRS Standard pair #615298247

details

property	value
status	complete
benchmark	t013.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n153.star.cs.uiowa.edu
space	HirokawaMiddeldorp_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.53719496727 seconds
cpu usage	1.069393435
max memory	1.880064E8

stage attributes

key	value
output-size	2835
starexec-result	"YES"

output

/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = 4x0 + 1,
   
   [-](x0, x1) = x0 + x1,
   
   [f](x0) = 4x0,
   
   [0] = 0,
   
   [s](x0) = 6x0 + 1
  orientation:
   -(x,0()) = x >= x = x
   
   -(0(),s(y)) = 6y + 1 >= 0 = 0()
   
   -(s(x),s(y)) = 6x + 6y + 2 >= x + y = -(x,y)
   
   f(0()) = 0 >= 0 = 0()
   
   f(s(x)) = 24x + 4 >= 22x + 2 = -(s(x),g(f(x)))
   
   g(0()) = 1 >= 1 = s(0())
   
   g(s(x)) = 24x + 5 >= 22x + 5 = -(s(x),f(g(x)))
  problem:
   -(x,0()) -> x
   f(0()) -> 0()
   g(0()) -> s(0())
   g(s(x)) -> -(s(x),f(g(x)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 1]  
    [g](x0) = [0 0 0]x0
              [0 1 1]  ,
    
                       [1 0 1]  
    [-](x0, x1) = x0 + [0 0 0]x1
                       [0 0 0]  ,
    
              [1 1 0]     [1]
    [f](x0) = [0 0 0]x0 + [1]
              [0 1 0]     [0],
    
          [0]
    [0] = [1]
          [1],
    
              [1 0 1]     [0]
    [s](x0) = [0 0 0]x0 + [0]
              [1 0 1]     [1]
   orientation:
                   [1]         
    -(x,0()) = x + [0] >= x = x
                   [0]         
    
             [2]    [0]      
    f(0()) = [1] >= [1] = 0()
             [1]    [1]      
    
             [1]    [1]         
    g(0()) = [0] >= [0] = s(0())
             [2]    [2]         
    
              [2 0 2]    [1]    [2 0 2]    [1]                  
    g(s(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = -(s(x),f(g(x)))
              [1 0 1]    [1]    [1 0 1]    [1]                  
   problem:
    g(0()) -> s(0())
    g(s(x)) -> -(s(x),f(g(x)))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [g](x0) = 6x0 + 2,
     
     [-](x0, x1) = x0 + 2x1,
     
     [f](x0) = x0,
     
     [0] = 0,

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