TRS Standard pair #487066832

details

property	value
status	complete
benchmark	goodstein.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	Hydras

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	22.5631 seconds
cpu usage	87.1638
user time	83.6407
system time	3.52308
max virtual memory	6123100.0
max residence set size	210640.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 l(o(x)) -> o(l(x))
 a(l(x)) -> l(a(a(x)))
 o(x) -> a(l(x))
 C(0(),x) -> o(x)
 a(C(C(x,y),z)) -> a(f(C(x,y),z))
 a(f(0(),x)) -> x
 a(f(C(x,y),z)) -> h(a(f(x,y)),a(a(f(f(x,y),z))))
 a(h(x,y)) -> h(a(x),a(a(C(x,y))))
 h(x,y) -> o(y)
 a(f(x,y)) -> f(a(x),y)
 a(C(x,y)) -> C(a(x),a(y))
 a(x) -> x
 o(x) -> x

Proof:
 Embedding Processor:
  strict:
   l(o(x)) -> o(l(x))
   a(l(x)) -> l(a(a(x)))
   o(x) -> a(l(x))
   C(0(),x) -> o(x)
   a(C(C(x,y),z)) -> a(f(C(x,y),z))
   a(f(0(),x)) -> x
   a(f(C(x,y),z)) -> h(a(f(x,y)),a(a(f(f(x,y),z))))
   a(h(x,y)) -> h(a(x),a(a(C(x,y))))
   h(x,y) -> o(y)
   a(f(x,y)) -> f(a(x),y)
   a(C(x,y)) -> C(a(x),a(y))
   a(x) -> x
   o(x) -> x
  weak:
   l(x0) -> x0
   o(x0) -> x0
   a(x0) -> x0
   C(x0,x1) -> x0
   C(x0,x1) -> x1
   f(x0,x1) -> x0
   f(x0,x1) -> x1
   h(x0,x1) -> x0
   h(x0,x1) -> x1
  Higher Ordinal Interpretation Processor:
   degree: 2
   reverse arguments: false
   interpretation:
    l(x5) =  (+) x5 (+) 1
    o(x6) =  (+) x6 (+) 1
    a(x7) =  (+) x7
    C(x8,x9) = omega^( (+) x8) (+) x9 (+) 1
    0() =  (+) 1
    f(x10,x11) = omega^( (+) x10) (+) x11
    h(x12,x13) = x13 + omega^( (+) x12 (+) 1)
   problem:
    strict:
     l(o(x)) -> o(l(x))
     a(l(x)) -> l(a(a(x)))
     o(x) -> a(l(x))
     a(f(C(x,y),z)) -> h(a(f(x,y)),a(a(f(f(x,y),z))))
     a(h(x,y)) -> h(a(x),a(a(C(x,y))))
     a(f(x,y)) -> f(a(x),y)
     a(C(x,y)) -> C(a(x),a(y))
     a(x) -> x
    weak:
     a(x0) -> x0
     f7(x12) -> h(x12,x13)
   Matrix Interpretation Processor: dim=2
    
    interpretation:
                   [0 0]     [0 0]  
     [C](x0, x1) = [2 2]x0 + [0 2]x1,
     
               [1 1]     [0]
     [l](x0) = [1 0]x0 + [2],
     
                   [0 1]     [2 0]     [2]
     [f](x0, x1) = [1 0]x0 + [2 2]x1 + [0],
     
               [1 1]     [0]
     [o](x0) = [1 0]x0 + [2],
     
                [0 0]     [2]
     [f7](x0) = [1 0]x0 + [2],
     
                   [0]
     [h](x0, x1) = [0],
     
                 
     [a](x0) = x0
    orientation:
               [2 1]    [2]    [2 1]    [2]          
     l(o(x)) = [1 1]x + [2] >= [1 1]x + [2] = o(l(x))
     
               [1 1]    [0]    [1 1]    [0]             
     a(l(x)) = [1 0]x + [2] >= [1 0]x + [2] = l(a(a(x)))
     
            [1 1]    [0]    [1 1]    [0]          
     o(x) = [1 0]x + [2] >= [1 0]x + [2] = a(l(x))

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