TRS Standard pair #516966439

details

property	value
status	complete
benchmark	2.61.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)	0.731112957001 seconds
cpu usage	1.583155818
max memory	2.5307136E8

stage attributes

key	value
output-size	2890
starexec-result	YES

output

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


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YES

Problem:
 f(j(x,y),y) -> g(f(x,k(y)))
 f(x,h1(y,z)) -> h2(0(),x,h1(y,z))
 g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u))
 h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u))
 i(f(x,h(y))) -> y
 i(h2(s(x),y,h1(x,z))) -> z
 k(h(x)) -> h1(0(),x)
 k(h1(x,y)) -> h1(s(x),y)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [h1](x0, x1) = x0 + x1,
   
   [h](x0) = x0 + 3,
   
   [f](x0, x1) = x0 + x1 + 2,
   
   [g](x0) = 4x0,
   
   [0] = 0,
   
   [j](x0, x1) = 4x0 + 3x1 + 6,
   
   [s](x0) = x0,
   
   [i](x0) = x0 + 1,
   
   [h2](x0, x1, x2) = x0 + x1 + x2 + 2,
   
   [k](x0) = x0
  orientation:
   f(j(x,y),y) = 4x + 4y + 8 >= 4x + 4y + 8 = g(f(x,k(y)))
   
   f(x,h1(y,z)) = x + y + z + 2 >= x + y + z + 2 = h2(0(),x,h1(y,z))
   
   g(h2(x,y,h1(z,u))) = 4u + 4x + 4y + 4z + 8 >= u + x + y + z + 2 = h2(s(x),y,h1(z,u))
   
   h2(x,j(y,h1(z,u)),h1(z,u)) = 4u + x + 4y + 4z + 8 >= u + x + y + z + 2 = h2(s(x),y,h1(s(z),u))
   
   i(f(x,h(y))) = x + y + 6 >= y = y
   
   i(h2(s(x),y,h1(x,z))) = 2x + y + z + 3 >= z = z
   
   k(h(x)) = x + 3 >= x = h1(0(),x)
   
   k(h1(x,y)) = x + y >= x + y = h1(s(x),y)
  problem:
   f(j(x,y),y) -> g(f(x,k(y)))
   f(x,h1(y,z)) -> h2(0(),x,h1(y,z))
   k(h1(x,y)) -> h1(s(x),y)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [h1](x0, x1) = x0 + x1,
    
    [f](x0, x1) = 4x0 + 4x1 + 2,
    
    [g](x0) = 2x0 + 6,
    
    [0] = 0,
    
    [j](x0, x1) = 2x0 + x1 + 4,
    
    [s](x0) = x0,
    
    [h2](x0, x1, x2) = x0 + 4x1 + 4x2 + 2,
    
    [k](x0) = x0 + 1
   orientation:
    f(j(x,y),y) = 8x + 8y + 18 >= 8x + 8y + 18 = g(f(x,k(y)))
    
    f(x,h1(y,z)) = 4x + 4y + 4z + 2 >= 4x + 4y + 4z + 2 = h2(0(),x,h1(y,z))
    
    k(h1(x,y)) = x + y + 1 >= x + y = h1(s(x),y)
   problem:
    f(j(x,y),y) -> g(f(x,k(y)))
    f(x,h1(y,z)) -> h2(0(),x,h1(y,z))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [h1](x0, x1) = x0 + x1 + 4,
     
     [f](x0, x1) = x0 + x1 + 3,
     
     [g](x0) = x0,
     
     [0] = 0,
     
     [j](x0, x1) = x0 + x1 + 1,

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