SRS Standard pair #487085654

details

property	value
status	complete
benchmark	14.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	Bouchare_06

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	43.6038 seconds
cpu usage	170.831
user time	167.356
system time	3.47509
max virtual memory	1.1440516E7
max residence set size	117420.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 a(a(a(x1))) -> b(x1)
 b(b(x1)) -> b(a(b(x1)))
 b(b(x1)) -> a(a(x1))

Proof:
 DP Processor:
  DPs:
   a#(a(a(x1))) -> b#(x1)
   b#(b(x1)) -> a#(b(x1))
   b#(b(x1)) -> b#(a(b(x1)))
   b#(b(x1)) -> a#(x1)
   b#(b(x1)) -> a#(a(x1))
  TRS:
   a(a(a(x1))) -> b(x1)
   b(b(x1)) -> b(a(b(x1)))
   b(b(x1)) -> a(a(x1))
  TDG Processor:
   DPs:
    a#(a(a(x1))) -> b#(x1)
    b#(b(x1)) -> a#(b(x1))
    b#(b(x1)) -> b#(a(b(x1)))
    b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> a#(a(x1))
   TRS:
    a(a(a(x1))) -> b(x1)
    b(b(x1)) -> b(a(b(x1)))
    b(b(x1)) -> a(a(x1))
   graph:
    b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(a(x1))
    b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> b#(a(b(x1)))
    b#(b(x1)) -> b#(a(b(x1))) -> b#(b(x1)) -> a#(b(x1))
    b#(b(x1)) -> a#(b(x1)) -> a#(a(a(x1))) -> b#(x1)
    b#(b(x1)) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(x1)
    b#(b(x1)) -> a#(x1) -> a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(a(x1))
    a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> b#(a(b(x1)))
    a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(b(x1))
   Arctic Interpretation Processor:
    dimension: 2
    usable rules:
     a(a(a(x1))) -> b(x1)
     b(b(x1)) -> b(a(b(x1)))
     b(b(x1)) -> a(a(x1))
    interpretation:
               [0 1]     [0]
     [b](x0) = [0 1]x0 + [0],
     
     [b#](x0) = [-& 0 ]x0 + [0],
     
               [0  1 ]     [0]
     [a](x0) = [0  -&]x0 + [0],
     
     [a#](x0) = [0 0]x0 + [0]
    orientation:
     a#(a(a(x1))) = [1 1]x1 + [1] >= [-& 0 ]x1 + [0] = b#(x1)
     
     b#(b(x1)) = [0 1]x1 + [0] >= [0 1]x1 + [0] = a#(b(x1))
     
     b#(b(x1)) = [0 1]x1 + [0] >= [0 1]x1 + [0] = b#(a(b(x1)))
     
     b#(b(x1)) = [0 1]x1 + [0] >= [0 0]x1 + [0] = a#(x1)
     
     b#(b(x1)) = [0 1]x1 + [0] >= [0 1]x1 + [0] = a#(a(x1))
     
                   [1 2]     [1]    [0 1]     [0]        
     a(a(a(x1))) = [1 1]x1 + [1] >= [0 1]x1 + [0] = b(x1)
     
                [1 2]     [1]    [1 2]     [1]              
     b(b(x1)) = [1 2]x1 + [1] >= [1 2]x1 + [1] = b(a(b(x1)))
     
                [1 2]     [1]    [1 1]     [1]           
     b(b(x1)) = [1 2]x1 + [1] >= [0 1]x1 + [0] = a(a(x1))
    problem:
     DPs:
      b#(b(x1)) -> a#(b(x1))
      b#(b(x1)) -> b#(a(b(x1)))
      b#(b(x1)) -> a#(x1)
      b#(b(x1)) -> a#(a(x1))
     TRS:
      a(a(a(x1))) -> b(x1)
      b(b(x1)) -> b(a(b(x1)))
      b(b(x1)) -> a(a(x1))
    Restore Modifier:
     DPs:
      b#(b(x1)) -> a#(b(x1))
      b#(b(x1)) -> b#(a(b(x1)))
      b#(b(x1)) -> a#(x1)
      b#(b(x1)) -> a#(a(x1))
     TRS:
      a(a(a(x1))) -> b(x1)
      b(b(x1)) -> b(a(b(x1)))
      b(b(x1)) -> a(a(x1))
     EDG Processor:
      DPs:
       b#(b(x1)) -> a#(b(x1))

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