TRS Standard pair #516965819

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	n053.star.cs.uiowa.edu
space	Hydras

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	23.0837318897 seconds
cpu usage	90.410323489
max memory	1.56923904E9

stage attributes

key	value
output-size	7878
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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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))

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