SRS Standard pair #487085294

details

property	value
status	complete
benchmark	size-12-alpha-3-num-508.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	47.4387 seconds
cpu usage	185.779
user time	182.43
system time	3.34866
max virtual memory	1.1363672E7
max residence set size	116564.0

stage attributes

key	value
starexec-result	YES

output

YES

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

Proof:
 String Reversal Processor:
  a(a(x1)) -> c(b(x1))
  b(a(x1)) -> a(c(x1))
  c(c(x1)) -> b(a(x1))
  DP Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> c#(b(x1))
    b#(a(x1)) -> c#(x1)
    b#(a(x1)) -> a#(c(x1))
    c#(c(x1)) -> a#(x1)
    c#(c(x1)) -> b#(a(x1))
   TRS:
    a(a(x1)) -> c(b(x1))
    b(a(x1)) -> a(c(x1))
    c(c(x1)) -> b(a(x1))
   TDG Processor:
    DPs:
     a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> c#(x1)
     b#(a(x1)) -> a#(c(x1))
     c#(c(x1)) -> a#(x1)
     c#(c(x1)) -> b#(a(x1))
    TRS:
     a(a(x1)) -> c(b(x1))
     b(a(x1)) -> a(c(x1))
     c(c(x1)) -> b(a(x1))
    graph:
     c#(c(x1)) -> b#(a(x1)) -> b#(a(x1)) -> a#(c(x1))
     c#(c(x1)) -> b#(a(x1)) -> b#(a(x1)) -> c#(x1)
     c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> c#(b(x1))
     c#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1)
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(a(x1))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> a#(x1)
     b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(a(x1))
     a#(a(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(x1)
     a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(c(x1))
     a#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(x1)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      a(a(x1)) -> c(b(x1))
      b(a(x1)) -> a(c(x1))
      c(c(x1)) -> b(a(x1))
     interpretation:
      [b#](x0) = x0 + 0,
      
      [c](x0) = 3x0 + 0,
      
      [a#](x0) = x0 + 0,
      
      [c#](x0) = x0,
      
      [a](x0) = 3x0 + 0,
      
      [b](x0) = 3x0 + 0
     orientation:
      a#(a(x1)) = 3x1 + 0 >= x1 + 0 = b#(x1)
      
      a#(a(x1)) = 3x1 + 0 >= 3x1 + 0 = c#(b(x1))
      
      b#(a(x1)) = 3x1 + 0 >= x1 = c#(x1)
      
      b#(a(x1)) = 3x1 + 0 >= 3x1 + 0 = a#(c(x1))
      
      c#(c(x1)) = 3x1 + 0 >= x1 + 0 = a#(x1)
      
      c#(c(x1)) = 3x1 + 0 >= 3x1 + 0 = b#(a(x1))
      
      a(a(x1)) = 6x1 + 3 >= 6x1 + 3 = c(b(x1))
      
      b(a(x1)) = 6x1 + 3 >= 6x1 + 3 = a(c(x1))
      
      c(c(x1)) = 6x1 + 3 >= 6x1 + 3 = b(a(x1))
     problem:
      DPs:
       a#(a(x1)) -> b#(x1)
       a#(a(x1)) -> c#(b(x1))
       b#(a(x1)) -> a#(c(x1))
       c#(c(x1)) -> a#(x1)
       c#(c(x1)) -> b#(a(x1))
      TRS:
       a(a(x1)) -> c(b(x1))
       b(a(x1)) -> a(c(x1))
       c(c(x1)) -> b(a(x1))
     Restore Modifier:
      DPs:
       a#(a(x1)) -> b#(x1)
       a#(a(x1)) -> c#(b(x1))

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