TRS Standard pair #487066912

details

property	value
status	complete
benchmark	hydra_touzet.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n179.star.cs.uiowa.edu
space	Hydras

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	27.3078 seconds
cpu usage	105.962
user time	102.548
system time	3.41418
max virtual memory	5870704.0
max residence set size	235844.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 o(x) -> a(l(x))
 a(l(x)) -> l(a(a(x)))
 l(o(x)) -> o(l(x))
 a(x) -> x
 H(0(),x) -> o(x)
 a(H(H(0(),y),z)) -> c1(y,z)
 a(H(H(H(0(),x),y),z)) -> c2(x,y,z)
 c2(x,y,z) -> o(H(y,z))
 a(c1(x,y)) -> c1(x,H(x,y))
 a(c2(x,y,z)) -> c2(x,H(x,y),z)
 c1(y,z) -> o(z)

Proof:
 Embedding Processor:
  strict:
   o(x) -> a(l(x))
   a(l(x)) -> l(a(a(x)))
   l(o(x)) -> o(l(x))
   a(x) -> x
   H(0(),x) -> o(x)
   a(H(H(0(),y),z)) -> c1(y,z)
   a(H(H(H(0(),x),y),z)) -> c2(x,y,z)
   c2(x,y,z) -> o(H(y,z))
   a(c1(x,y)) -> c1(x,H(x,y))
   a(c2(x,y,z)) -> c2(x,H(x,y),z)
   c1(y,z) -> o(z)
  weak:
   o(x0) -> x0
   a(x0) -> x0
   l(x0) -> x0
   H(x0,x1) -> x0
   H(x0,x1) -> x1
   c1(x0,x1) -> x0
   c1(x0,x1) -> x1
   c2(x0,x1,x2) -> x0
   c2(x0,x1,x2) -> x1
   c2(x0,x1,x2) -> x2
  Higher Ordinal Interpretation Processor:
   degree: 3
   reverse arguments: false
   interpretation:
    o(x6) =  (+) x6
    a(x7) =  (+) x7
    l(x8) =  (+) x8
    H(x9,x10) = omega^( (+) x9) (+) x10 (+) 1
    0() = 0
    c1(x11,x12) = x12 + omega^( (+) x11 (+) 1)
    c2(x13,x14,x15) = omega^(x14 + omega^(x13 (+) 1) (+) 1) (+) x15
   problem:
    strict:
     o(x) -> a(l(x))
     a(l(x)) -> l(a(a(x)))
     l(o(x)) -> o(l(x))
     a(x) -> x
     a(c1(x,y)) -> c1(x,H(x,y))
     a(c2(x,y,z)) -> c2(x,H(x,y),z)
    weak:
     o(x0) -> x0
     a(x0) -> x0
     l(x0) -> x0
     f7(x11) -> c1(x11,x12)
     f8(x15) -> c2(x13,x14,x15)
   Matrix Interpretation Processor: dim=2
    
    interpretation:
                   [0]
     [H](x0, x1) = [0],
     
                [2 2]     [2]
     [f8](x0) = [2 2]x0 + [2],
     
               [1 0]  
     [l](x0) = [1 1]x0,
     
                    [2]
     [c1](x0, x1) = [2],
     
               [2 0]     [1]
     [o](x0) = [1 2]x0 + [0],
     
                [2 0]     [2]
     [f7](x0) = [0 2]x0 + [3],
     
                        [0 0]     [0]
     [c2](x0, x1, x2) = [1 1]x2 + [1],
     
                 
     [a](x0) = x0
    orientation:
            [2 0]    [1]    [1 0]           
     o(x) = [1 2]x + [0] >= [1 1]x = a(l(x))
     
               [1 0]     [1 0]              
     a(l(x)) = [1 1]x >= [1 1]x = l(a(a(x)))
     
               [2 0]    [1]    [2 0]    [1]          
     l(o(x)) = [3 2]x + [1] >= [3 2]x + [0] = o(l(x))

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