TRS Standard pair #487068107

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	n186.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.719392 seconds
cpu usage	1.8106
user time	1.4247
system time	0.385907
max virtual memory	1843328.0
max residence set size	68292.0

stage attributes

key	value
starexec-result	YES

output

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,
     
     [h2](x0, x1, x2) = x0 + x1 + x2 + 2,
     
     [k](x0) = 2x0 + 1
    orientation:
     f(j(x,y),y) = x + 2y + 4 >= x + 2y + 4 = g(f(x,k(y)))

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