SRS Standard pair #516975392

details

property	value
status	complete
benchmark	size-12-alpha-3-num-300.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n063.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	47.1042170525 seconds
cpu usage	186.933725111
max memory	1.790656512E9

stage attributes

key	value
output-size	6556
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(b(a(x1))) -> c(b(b(b(x1))))
  b(c(x1)) -> a(a(x1))
  DP Processor:
   DPs:
    b#(b(a(x1))) -> b#(x1)
    b#(b(a(x1))) -> b#(b(x1))
    b#(b(a(x1))) -> b#(b(b(x1)))
    b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> a#(a(x1))
   TRS:
    a(x1) -> x1
    b(b(a(x1))) -> c(b(b(b(x1))))
    b(c(x1)) -> a(a(x1))
   TDG Processor:
    DPs:
     b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(b(b(x1)))
     b#(c(x1)) -> a#(x1)
     b#(c(x1)) -> a#(a(x1))
    TRS:
     a(x1) -> x1
     b(b(a(x1))) -> c(b(b(b(x1))))
     b(c(x1)) -> a(a(x1))
    graph:
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(c(x1)) -> a#(a(x1))
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(c(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> b#(b(b(x1)))
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(b(x1)) -> b#(c(x1)) -> a#(a(x1))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(c(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(b(x1)))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(x1) -> b#(c(x1)) -> a#(a(x1))
     b#(b(a(x1))) -> b#(x1) -> b#(c(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(b(x1)))
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 15/25
     DPs:
      b#(b(a(x1))) -> b#(b(b(x1)))
      b#(b(a(x1))) -> b#(x1)
      b#(b(a(x1))) -> b#(b(x1))
     TRS:
      a(x1) -> x1
      b(b(a(x1))) -> c(b(b(b(x1))))
      b(c(x1)) -> a(a(x1))
     Arctic Interpretation Processor:
      dimension: 3
      usable rules:
       a(x1) -> x1
       b(b(a(x1))) -> c(b(b(b(x1))))
       b(c(x1)) -> a(a(x1))
      interpretation:
       [b#](x0) = [-& 0  -&]x0 + [0],
       
                 [-& 0  -&]     [0 ]
       [b](x0) = [-& -& 0 ]x0 + [-&]
                 [0  -& -&]     [0 ],
       
                 [0  -& -&]     [-&]
       [a](x0) = [0  0  -&]x0 + [-&]
                 [1  0  0 ]     [1 ],
       
                 [1  0  0 ]     [1]
       [c](x0) = [0  -& -&]x0 + [0]
                 [0  0  -&]     [0]
      orientation:
       b#(b(a(x1))) = [1 0 0]x1 + [1] >= [0  -& -&]x1 + [0] = b#(b(b(x1)))
       
       b#(b(a(x1))) = [1 0 0]x1 + [1] >= [-& 0  -&]x1 + [0] = b#(x1)
       
       b#(b(a(x1))) = [1 0 0]x1 + [1] >= [-& -& 0 ]x1 + [0] = b#(b(x1))
       
               [0  -& -&]     [-&]           
       a(x1) = [0  0  -&]x1 + [-&] >= x1 = x1
               [1  0  0 ]     [1 ]           
       
                     [1  0  0 ]     [1]    [1  0  0 ]     [1]

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