SRS Standard pair #487084244

details

property	value
status	complete
benchmark	size-12-alpha-3-num-436.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	44.56 seconds
cpu usage	175.501
user time	172.719
system time	2.78201
max virtual memory	1.1253096E7
max residence set size	116480.0

stage attributes

key	value
starexec-result	YES

output

YES

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

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

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