SRS Standard pair #487083758

details

property	value
status	complete
benchmark	size-12-alpha-3-num-91.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	Waldmann_07_size12

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	45.5501 seconds
cpu usage	178.347
user time	174.483
system time	3.86438
max virtual memory	1.125064E7
max residence set size	102032.0

stage attributes

key	value
starexec-result	YES

output

YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  a(a(x1)) -> c(b(b(x1)))
  c(x1) -> x1
  b(c(x1)) -> a(c(b(x1)))
  DP Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> b#(b(x1))
    a#(a(x1)) -> c#(b(b(x1)))
    b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> c#(b(x1))
    b#(c(x1)) -> a#(c(b(x1)))
   TRS:
    a(x1) -> x1
    a(a(x1)) -> c(b(b(x1)))
    c(x1) -> x1
    b(c(x1)) -> a(c(b(x1)))
   TDG Processor:
    DPs:
     a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> b#(b(x1))
     a#(a(x1)) -> c#(b(b(x1)))
     b#(c(x1)) -> b#(x1)
     b#(c(x1)) -> c#(b(x1))
     b#(c(x1)) -> a#(c(b(x1)))
    TRS:
     a(x1) -> x1
     a(a(x1)) -> c(b(b(x1)))
     c(x1) -> x1
     b(c(x1)) -> a(c(b(x1)))
    graph:
     b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> a#(c(b(x1)))
     b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> c#(b(x1))
     b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
     b#(c(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> c#(b(b(x1)))
     b#(c(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> b#(b(x1))
     b#(c(x1)) -> a#(c(b(x1))) -> a#(a(x1)) -> b#(x1)
     a#(a(x1)) -> b#(b(x1)) -> b#(c(x1)) -> a#(c(b(x1)))
     a#(a(x1)) -> b#(b(x1)) -> b#(c(x1)) -> c#(b(x1))
     a#(a(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1)
     a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> a#(c(b(x1)))
     a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> c#(b(x1))
     a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 12/36
     DPs:
      b#(c(x1)) -> b#(x1)
      b#(c(x1)) -> a#(c(b(x1)))
      a#(a(x1)) -> b#(x1)
      a#(a(x1)) -> b#(b(x1))
     TRS:
      a(x1) -> x1
      a(a(x1)) -> c(b(b(x1)))
      c(x1) -> x1
      b(c(x1)) -> a(c(b(x1)))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       a(a(x1)) -> c(b(b(x1)))
       c(x1) -> x1
       b(c(x1)) -> a(c(b(x1)))
      interpretation:
       [b#](x0) = [0 0]x0 + [2],
       
                 [0  -&]     [0]
       [c](x0) = [2  2 ]x0 + [3],
       
       [a#](x0) = [-& 0 ]x0 + [2],
       
                 [0 0]     [1]
       [a](x0) = [2 0]x0 + [0],
       
                 [-& 0 ]     [1]
       [b](x0) = [0  0 ]x0 + [0]
      orientation:
       b#(c(x1)) = [2 2]x1 + [3] >= [0 0]x1 + [2] = b#(x1)
       
       b#(c(x1)) = [2 2]x1 + [3] >= [2 2]x1 + [3] = a#(c(b(x1)))
       
       a#(a(x1)) = [2 0]x1 + [2] >= [0 0]x1 + [2] = b#(x1)
       
       a#(a(x1)) = [2 0]x1 + [2] >= [0 0]x1 + [2] = b#(b(x1))
       
               [0 0]     [1]           
       a(x1) = [2 0]x1 + [0] >= x1 = x1
       
                  [2 0]     [1]    [0 0]     [1]

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