TRS Standard pair #487068102

details

property	value
status	complete
benchmark	2.13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n189.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.440799 seconds
cpu usage	0.722859
user time	0.530712
system time	0.192147
max virtual memory	96176.0
max residence set size	59416.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 double(0()) -> 0()
 double(s(x)) -> s(s(double(x)))
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 +(s(x),y) -> s(+(x,y))
 double(x) -> +(x,x)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [double](x0) = 6x0,
   
   [+](x0, x1) = 4x0 + x1,
   
   [0] = 0,
   
   [s](x0) = x0 + 4
  orientation:
   double(0()) = 0 >= 0 = 0()
   
   double(s(x)) = 6x + 24 >= 6x + 8 = s(s(double(x)))
   
   +(x,0()) = 4x >= x = x
   
   +(x,s(y)) = 4x + y + 4 >= 4x + y + 4 = s(+(x,y))
   
   +(s(x),y) = 4x + y + 16 >= 4x + y + 4 = s(+(x,y))
   
   double(x) = 6x >= 5x = +(x,x)
  problem:
   double(0()) -> 0()
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   double(x) -> +(x,x)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [double](x0) = 4x0,
    
    [+](x0, x1) = 2x0 + 2x1,
    
    [0] = 0,
    
    [s](x0) = x0 + 6
   orientation:
    double(0()) = 0 >= 0 = 0()
    
    +(x,0()) = 2x >= x = x
    
    +(x,s(y)) = 2x + 2y + 12 >= 2x + 2y + 6 = s(+(x,y))
    
    double(x) = 4x >= 4x = +(x,x)
   problem:
    double(0()) -> 0()
    +(x,0()) -> x
    double(x) -> +(x,x)
   Matrix Interpretation Processor: dim=2
    
    interpretation:
                    [2 2]     [1]
     [double](x0) = [1 1]x0 + [2],
     
                   [1 2]     [1 0]  
     [+](x0, x1) = [0 1]x0 + [0 0]x1,
     
           [0]
     [0] = [1]
    orientation:
                   [3]    [0]      
     double(0()) = [3] >= [1] = 0()
     
                [1 2]          
     +(x,0()) = [0 1]x >= x = x
     
                 [2 2]    [1]    [2 2]          
     double(x) = [1 1]x + [2] >= [0 1]x = +(x,x)
    problem:
     +(x,0()) -> x
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                         [1 0 0]     [1]
      [+](x0, x1) = x0 + [0 1 0]x1 + [0]
                         [0 0 0]     [0],
      
            [0]
      [0] = [1]
            [0]
     orientation:
                     [1]         
      +(x,0()) = x + [1] >= x = x
                     [0]         
     problem:
      
     Qed

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Standard