SRS Standard pair #487511823

details

property	value
status	complete
benchmark	size-12-alpha-3-num-72.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n186.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	42.0700159073 seconds
cpu usage	166.991113605
max memory	1.268723712E9

stage attributes

key	value
output-size	4410
starexec-result	YES

output

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


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YES

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

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

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