SRS Stand 10685 pair #381721695

details

property	value
status	complete
benchmark	size-12-alpha-3-num-470.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n100.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	ttt2-1.17+nonreach
configuration	ttt2-1.17+nonreach
runtime (wallclock)	30.847892046 seconds
cpu usage	122.040610709
max memory	1.651429376E9

stage attributes

key	value
output-size	3914
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 DP Processor:
  DPs:
   b#(b(x1)) -> c#(x1)
   b#(b(x1)) -> b#(c(x1))
   b#(b(x1)) -> a#(b(c(x1)))
   c#(c(x1)) -> b#(x1)
   c#(c(x1)) -> b#(b(x1))
   c#(c(x1)) -> b#(b(b(x1)))
  TRS:
   a(a(x1)) -> x1
   b(b(x1)) -> a(b(c(x1)))
   c(c(x1)) -> b(b(b(x1)))
  TDG Processor:
   DPs:
    b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> b#(c(x1))
    b#(b(x1)) -> a#(b(c(x1)))
    c#(c(x1)) -> b#(x1)
    c#(c(x1)) -> b#(b(x1))
    c#(c(x1)) -> b#(b(b(x1)))
   TRS:
    a(a(x1)) -> x1
    b(b(x1)) -> a(b(c(x1)))
    c(c(x1)) -> b(b(b(x1)))
   graph:
    c#(c(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> a#(b(c(x1)))
    c#(c(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> b#(c(x1))
    c#(c(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(x1)
    c#(c(x1)) -> b#(b(x1)) -> b#(b(x1)) -> a#(b(c(x1)))
    c#(c(x1)) -> b#(b(x1)) -> b#(b(x1)) -> b#(c(x1))
    c#(c(x1)) -> b#(b(x1)) -> b#(b(x1)) -> c#(x1)
    c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> a#(b(c(x1)))
    c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> b#(c(x1))
    c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> b#(b(b(x1)))
    b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> b#(b(x1))
    b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> b#(x1)
    b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> a#(b(c(x1)))
    b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> b#(c(x1))
    b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 5
    #arcs: 15/36
    DPs:
     c#(c(x1)) -> b#(b(b(x1)))
     b#(b(x1)) -> c#(x1)
     c#(c(x1)) -> b#(x1)
     b#(b(x1)) -> b#(c(x1))
     c#(c(x1)) -> b#(b(x1))
    TRS:
     a(a(x1)) -> x1
     b(b(x1)) -> a(b(c(x1)))
     c(c(x1)) -> b(b(b(x1)))
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(a(x1)) -> x1
      b(b(x1)) -> a(b(c(x1)))
      c(c(x1)) -> b(b(b(x1)))
     interpretation:
      [c#](x0) = [-& 0 ]x0 + [0],
      
      [b#](x0) = [0  -&]x0 + [-4],
      
                [-4 0 ]     [0]
      [c](x0) = [0  1 ]x0 + [1],
      
                [0  1 ]     [1 ]
      [b](x0) = [-1 -2]x0 + [-4],
      
                [-& 2 ]     [0]
      [a](x0) = [-2 0 ]x0 + [0]
     orientation:
      c#(c(x1)) = [0 1]x1 + [1] >= [0 1]x1 + [1] = b#(b(b(x1)))
      
      b#(b(x1)) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = c#(x1)
      
      c#(c(x1)) = [0 1]x1 + [1] >= [0  -&]x1 + [-4] = b#(x1)
      
      b#(b(x1)) = [0 1]x1 + [1] >= [-4 0 ]x1 + [0] = b#(c(x1))
      
      c#(c(x1)) = [0 1]x1 + [1] >= [0 1]x1 + [1] = b#(b(x1))
      
                 [0  2 ]     [2]           
      a(a(x1)) = [-2 0 ]x1 + [0] >= x1 = x1

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