TRS Standard pair #487068462

details

property	value
status	complete
benchmark	z25.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.563885 seconds
cpu usage	1.17297
user time	0.838973
system time	0.333994
max virtual memory	96176.0
max residence set size	67604.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 f(a(),f(b(),x)) -> f(b(),f(a(),x))
 f(b(),f(c(),x)) -> f(c(),f(b(),x))
 f(c(),f(a(),x)) -> f(a(),f(c(),x))

Proof:
 Extended Uncurrying Processor:
  application symbol: f
  symbol table:
   c ==> c0/0 c1/1
   b ==> b0/0 b1/1
   a ==> a0/0 a1/1
   
  uncurry-rules:
   f(a0(),x1) -> a1(x1)
   f(b0(),x3) -> b1(x3)
   f(c0(),x5) -> c1(x5)
  eta-rules:
   
  problem:
   a1(b1(x)) -> b1(a1(x))
   b1(c1(x)) -> c1(b1(x))
   c1(a1(x)) -> a1(c1(x))
   f(a0(),x1) -> a1(x1)
   f(b0(),x3) -> b1(x3)
   f(c0(),x5) -> c1(x5)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [a0] = 1,
    
    [c0] = 2,
    
    [a1](x0) = 2x0 + 2,
    
    [b1](x0) = 2x0 + 2,
    
    [c1](x0) = 2x0 + 2,
    
    [b0] = 1,
    
    [f](x0, x1) = x0 + 2x1 + 1
   orientation:
    a1(b1(x)) = 4x + 6 >= 4x + 6 = b1(a1(x))
    
    b1(c1(x)) = 4x + 6 >= 4x + 6 = c1(b1(x))
    
    c1(a1(x)) = 4x + 6 >= 4x + 6 = a1(c1(x))
    
    f(a0(),x1) = 2x1 + 2 >= 2x1 + 2 = a1(x1)
    
    f(b0(),x3) = 2x3 + 2 >= 2x3 + 2 = b1(x3)
    
    f(c0(),x5) = 2x5 + 3 >= 2x5 + 2 = c1(x5)
   problem:
    a1(b1(x)) -> b1(a1(x))
    b1(c1(x)) -> c1(b1(x))
    c1(a1(x)) -> a1(c1(x))
    f(a0(),x1) -> a1(x1)
    f(b0(),x3) -> b1(x3)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
            [0]
     [a0] = [0]
            [1],
     
                [1 0 1]     [0]
     [a1](x0) = [0 0 0]x0 + [1]
                [0 1 0]     [0],
     
                [1 0 1]     [0]
     [b1](x0) = [0 0 0]x0 + [1]
                [0 1 0]     [0],
     
                [1 1 1]     [0]
     [c1](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [1],
     
            [0]
     [b0] = [0]
            [0],
     
                   [1 0 1]     [1 0 1]     [0]
     [f](x0, x1) = [0 0 0]x0 + [1 0 0]x1 + [1]
                   [0 0 0]     [1 1 0]     [0]
    orientation:
                 [1 1 1]    [0]    [1 1 1]    [0]            
     a1(b1(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = b1(a1(x))
                 [0 0 0]    [1]    [0 0 0]    [1]            
     
                 [1 1 1]    [1]    [1 1 1]    [1]            
     b1(c1(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = c1(b1(x))
                 [0 0 0]    [1]    [0 0 0]    [1]            
     
                 [1 1 1]    [1]    [1 1 1]    [1]            
     c1(a1(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = a1(c1(x))
                 [0 0 0]    [1]    [0 0 0]    [1]

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