SRS Standard pair #487513023

details

property	value
status	complete
benchmark	size-12-alpha-3-num-14.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n128.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	42.2640910149 seconds
cpu usage	167.602694823
max memory	1.322360832E9

stage attributes

key	value
output-size	4458
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(x1) -> b(x1)
 a(c(x1)) -> c(c(a(b(x1))))
 b(b(x1)) -> a(x1)

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

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