SRS Standard pair #487085648

details

property	value
status	complete
benchmark	05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	Bouchare_06

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	45.7479 seconds
cpu usage	179.153
user time	175.144
system time	4.00882
max virtual memory	1.0930392E7
max residence set size	123164.0

stage attributes

key	value
starexec-result	YES

output

YES

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

Proof:
 String Reversal Processor:
  b(b(a(x1))) -> a(x1)
  a(a(x1)) -> b(b(b(x1)))
  a(b(b(x1))) -> a(b(a(x1)))
  DP Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> b#(b(x1))
    a#(a(x1)) -> b#(b(b(x1)))
    a#(b(b(x1))) -> a#(x1)
    a#(b(b(x1))) -> b#(a(x1))
    a#(b(b(x1))) -> a#(b(a(x1)))
   TRS:
    b(b(a(x1))) -> a(x1)
    a(a(x1)) -> b(b(b(x1)))
    a(b(b(x1))) -> a(b(a(x1)))
   TDG Processor:
    DPs:
     a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> b#(b(x1))
     a#(a(x1)) -> b#(b(b(x1)))
     a#(b(b(x1))) -> a#(x1)
     a#(b(b(x1))) -> b#(a(x1))
     a#(b(b(x1))) -> a#(b(a(x1)))
    TRS:
     b(b(a(x1))) -> a(x1)
     a(a(x1)) -> b(b(b(x1)))
     a(b(b(x1))) -> a(b(a(x1)))
    graph:
     a#(b(b(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) -> a#(b(a(x1)))
     a#(b(b(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) -> b#(a(x1))
     a#(b(b(x1))) -> a#(b(a(x1))) -> a#(b(b(x1))) -> a#(x1)
     a#(b(b(x1))) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(b(b(x1)))
     a#(b(b(x1))) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(b(x1))
     a#(b(b(x1))) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(x1)
     a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(b(a(x1)))
     a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> b#(a(x1))
     a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(x1)
     a#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(b(b(x1)))
     a#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(b(x1))
     a#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 12/36
     DPs:
      a#(b(b(x1))) -> a#(b(a(x1)))
      a#(b(b(x1))) -> a#(x1)
     TRS:
      b(b(a(x1))) -> a(x1)
      a(a(x1)) -> b(b(b(x1)))
      a(b(b(x1))) -> a(b(a(x1)))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       b(b(a(x1))) -> a(x1)
       a(a(x1)) -> b(b(b(x1)))
       a(b(b(x1))) -> a(b(a(x1)))
      interpretation:
                 [0 0]     [0]
       [a](x0) = [2 2]x0 + [2],
       
       [a#](x0) = [0 0]x0,
       
                 [0 0]     [0]
       [b](x0) = [2 0]x0 + [2]
      orientation:
       a#(b(b(x1))) = [2 2]x1 + [2] >= [2 2]x1 + [2] = a#(b(a(x1)))
       
       a#(b(b(x1))) = [2 2]x1 + [2] >= [0 0]x1 = a#(x1)
       
                     [2 2]     [2]    [0 0]     [0]        
       b(b(a(x1))) = [4 4]x1 + [4] >= [2 2]x1 + [2] = a(x1)
       
                  [2 2]     [2]    [2 2]     [2]              
       a(a(x1)) = [4 4]x1 + [4] >= [4 2]x1 + [4] = b(b(b(x1)))
       
                     [2 2]     [2]    [2 2]     [2]              
       a(b(b(x1))) = [4 4]x1 + [4] >= [4 4]x1 + [4] = a(b(a(x1)))
      problem:
       DPs:
        a#(b(b(x1))) -> a#(b(a(x1)))
       TRS:
        b(b(a(x1))) -> a(x1)
        a(a(x1)) -> b(b(b(x1)))
        a(b(b(x1))) -> a(b(a(x1)))
      Restore Modifier:
       DPs:
        a#(b(b(x1))) -> a#(b(a(x1)))
       TRS:
        b(b(a(x1))) -> a(x1)
        a(a(x1)) -> b(b(b(x1)))

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