SRS Stand 10685 pair #381719307

details

property	value
status	complete
benchmark	size-12-alpha-3-num-479.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n020.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	ttt2-1.17+nonreach
configuration	ttt2-1.17+nonreach
runtime (wallclock)	27.5253949165 seconds
cpu usage	108.511480436
max memory	1.582665728E9

stage attributes

key	value
output-size	5611
starexec-result	YES

output

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


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YES

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

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

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