SRS Standard pair #487083578

details

property	value
status	complete
benchmark	size-12-alpha-3-num-437.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	46.0759 seconds
cpu usage	180.161
user time	176.424
system time	3.73716
max virtual memory	1.1640232E7
max residence set size	124304.0

stage attributes

key	value
starexec-result	YES

output

YES

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

Proof:
 String Reversal Processor:
  a(x1) -> b(c(b(b(x1))))
  b(b(c(x1))) -> c(a(x1))
  c(c(x1)) -> x1
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> b#(b(x1))
    a#(x1) -> c#(b(b(x1)))
    a#(x1) -> b#(c(b(b(x1))))
    b#(b(c(x1))) -> a#(x1)
    b#(b(c(x1))) -> c#(a(x1))
   TRS:
    a(x1) -> b(c(b(b(x1))))
    b(b(c(x1))) -> c(a(x1))
    c(c(x1)) -> x1
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1))
     a#(x1) -> c#(b(b(x1)))
     a#(x1) -> b#(c(b(b(x1))))
     b#(b(c(x1))) -> a#(x1)
     b#(b(c(x1))) -> c#(a(x1))
    TRS:
     a(x1) -> b(c(b(b(x1))))
     b(b(c(x1))) -> c(a(x1))
     c(c(x1)) -> x1
    graph:
     b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(c(b(b(x1))))
     b#(b(c(x1))) -> a#(x1) -> a#(x1) -> c#(b(b(x1)))
     b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(b(x1))
     b#(b(c(x1))) -> a#(x1) -> a#(x1) -> b#(x1)
     a#(x1) -> b#(c(b(b(x1)))) -> b#(b(c(x1))) -> c#(a(x1))
     a#(x1) -> b#(c(b(b(x1)))) -> b#(b(c(x1))) -> a#(x1)
     a#(x1) -> b#(b(x1)) -> b#(b(c(x1))) -> c#(a(x1))
     a#(x1) -> b#(b(x1)) -> b#(b(c(x1))) -> a#(x1)
     a#(x1) -> b#(x1) -> b#(b(c(x1))) -> c#(a(x1))
     a#(x1) -> b#(x1) -> b#(b(c(x1))) -> a#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 10/36
     DPs:
      b#(b(c(x1))) -> a#(x1)
      a#(x1) -> b#(x1)
      a#(x1) -> b#(b(x1))
      a#(x1) -> b#(c(b(b(x1))))
     TRS:
      a(x1) -> b(c(b(b(x1))))
      b(b(c(x1))) -> c(a(x1))
      c(c(x1)) -> x1
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> b(c(b(b(x1))))
       b(b(c(x1))) -> c(a(x1))
       c(c(x1)) -> x1
      interpretation:
       [b#](x0) = [1 0]x0 + [0],
       
                 [-& 0 ]     [1]
       [b](x0) = [0  -&]x0 + [1],
       
       [a#](x0) = [1 2]x0 + [3],
       
                 [0  2 ]     [3]
       [a](x0) = [-& 0 ]x0 + [1],
       
                 [-& 0 ]     [0]
       [c](x0) = [0  2 ]x0 + [3]
      orientation:
       b#(b(c(x1))) = [1 3]x1 + [4] >= [1 2]x1 + [3] = a#(x1)
       
       a#(x1) = [1 2]x1 + [3] >= [1 0]x1 + [0] = b#(x1)
       
       a#(x1) = [1 2]x1 + [3] >= [0 1]x1 + [2] = b#(b(x1))
       
       a#(x1) = [1 2]x1 + [3] >= [0 2]x1 + [3] = b#(c(b(b(x1))))
       
               [0  2 ]     [3]    [0  2 ]     [3]                 
       a(x1) = [-& 0 ]x1 + [1] >= [-& 0 ]x1 + [1] = b(c(b(b(x1))))
       
                     [-& 0 ]     [1]    [-& 0 ]     [1]           
       b(b(c(x1))) = [0  2 ]x1 + [3] >= [0  2 ]x1 + [3] = c(a(x1))
       
                  [0 2]     [3]           
       c(c(x1)) = [2 4]x1 + [5] >= x1 = x1
      problem:
       DPs:
        b#(b(c(x1))) -> a#(x1)
        a#(x1) -> b#(x1)

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