TRS Standard pair #615305737

details

property	value
status	complete
benchmark	4.43.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n005.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.592365980148 seconds
cpu usage	1.269959042
max memory	2.08498688E8

stage attributes

key	value
output-size	3278
starexec-result	"YES"

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [g](x0) = 2x0 + 1,
   
   [+](x0, x1) = x0 + x1,
   
   [f](x0) = 2x0 + 1,
   
   [h](x0, x1) = 4x0 + x1,
   
   [0] = 0,
   
   [s](x0) = x0
  orientation:
   +(x,0()) = x >= x = x
   
   +(x,s(y)) = x + y >= x + y = s(+(x,y))
   
   +(0(),y) = y >= y = y
   
   +(s(x),y) = x + y >= x + y = s(+(x,y))
   
   +(x,+(y,z)) = x + y + z >= x + y + z = +(+(x,y),z)
   
   f(g(f(x))) = 8x + 7 >= 2x + 1 = f(h(s(0()),x))
   
   f(g(h(x,y))) = 16x + 4y + 3 >= 8x + 2y + 1 = f(h(s(x),y))
   
   f(h(x,h(y,z))) = 8x + 8y + 2z + 1 >= 8x + 8y + 2z + 1 = f(h(+(x,y),z))
  problem:
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   +(0(),y) -> y
   +(s(x),y) -> s(+(x,y))
   +(x,+(y,z)) -> +(+(x,y),z)
   f(h(x,h(y,z))) -> f(h(+(x,y),z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [+](x0, x1) = x0 + 4x1,
    
    [f](x0) = x0 + 6,
    
    [h](x0, x1) = 4x0 + 4x1 + 1,
    
    [0] = 3,
    
    [s](x0) = x0 + 2
   orientation:
    +(x,0()) = x + 12 >= x = x
    
    +(x,s(y)) = x + 4y + 8 >= x + 4y + 2 = s(+(x,y))
    
    +(0(),y) = 4y + 3 >= y = y
    
    +(s(x),y) = x + 4y + 2 >= x + 4y + 2 = s(+(x,y))
    
    +(x,+(y,z)) = x + 4y + 16z >= x + 4y + 4z = +(+(x,y),z)
    
    f(h(x,h(y,z))) = 4x + 16y + 16z + 11 >= 4x + 16y + 4z + 7 = f(h(+(x,y),z))
   problem:
    +(s(x),y) -> s(+(x,y))
    +(x,+(y,z)) -> +(+(x,y),z)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                        [1 0 1]     [0]
     [+](x0, x1) = x0 + [1 0 1]x1 + [1]
                        [0 0 1]     [1],
     
                 
     [s](x0) = x0
                 
    orientation:
                     [1 0 1]    [0]        [1 0 1]    [0]            
     +(s(x),y) = x + [1 0 1]y + [1] >= x + [1 0 1]y + [1] = s(+(x,y))
                     [0 0 1]    [1]        [0 0 1]    [1]            
     
                       [1 0 1]    [1 0 2]    [1]        [1 0 1]    [1 0 1]    [0]              
     +(x,+(y,z)) = x + [1 0 1]y + [1 0 2]z + [2] >= x + [1 0 1]y + [1 0 1]z + [2] = +(+(x,y),z)

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