SRS Standard pair #487513971

details

property	value
status	complete
benchmark	11.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n027.star.cs.uiowa.edu
space	Bouchare_06

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	47.2808990479 seconds
cpu usage	187.552310592
max memory	1.652645888E9

stage attributes

key	value
output-size	6802
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(a(a(x1))) -> b(x1)
 b(b(x1)) -> a(a(x1))
 a(a(x1)) -> a(b(a(x1)))

Proof:
 DP Processor:
  DPs:
   a#(a(a(x1))) -> b#(x1)
   b#(b(x1)) -> a#(x1)
   b#(b(x1)) -> a#(a(x1))
   a#(a(x1)) -> b#(a(x1))
   a#(a(x1)) -> a#(b(a(x1)))
  TRS:
   a(a(a(x1))) -> b(x1)
   b(b(x1)) -> a(a(x1))
   a(a(x1)) -> a(b(a(x1)))
  TDG Processor:
   DPs:
    a#(a(a(x1))) -> b#(x1)
    b#(b(x1)) -> a#(x1)
    b#(b(x1)) -> a#(a(x1))
    a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> a#(b(a(x1)))
   TRS:
    a(a(a(x1))) -> b(x1)
    b(b(x1)) -> a(a(x1))
    a(a(x1)) -> a(b(a(x1)))
   graph:
    b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> a#(b(a(x1)))
    b#(b(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(x1))
    b#(b(x1)) -> a#(a(x1)) -> a#(a(a(x1))) -> b#(x1)
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1)))
    b#(b(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
    b#(b(x1)) -> a#(x1) -> a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(a(x1))
    a#(a(a(x1))) -> b#(x1) -> b#(b(x1)) -> a#(x1)
    a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(a(x1))
    a#(a(x1)) -> b#(a(x1)) -> b#(b(x1)) -> a#(x1)
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1)))
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1))
    a#(a(x1)) -> a#(b(a(x1))) -> a#(a(a(x1))) -> b#(x1)
   Arctic Interpretation Processor:
    dimension: 2
    usable rules:
     a(a(a(x1))) -> b(x1)
     b(b(x1)) -> a(a(x1))
     a(a(x1)) -> a(b(a(x1)))
    interpretation:
               [2 2]     [3]
     [b](x0) = [2 0]x0 + [3],
     
     [b#](x0) = [0 0]x0 + [0],
     
               [-& 0 ]     [0]
     [a](x0) = [0  2 ]x0 + [3],
     
     [a#](x0) = [-& 0 ]x0 + [0]
    orientation:
     a#(a(a(x1))) = [2 4]x1 + [5] >= [0 0]x1 + [0] = b#(x1)
     
     b#(b(x1)) = [2 2]x1 + [3] >= [-& 0 ]x1 + [0] = a#(x1)
     
     b#(b(x1)) = [2 2]x1 + [3] >= [0 2]x1 + [3] = a#(a(x1))
     
     a#(a(x1)) = [0 2]x1 + [3] >= [0 2]x1 + [3] = b#(a(x1))
     
     a#(a(x1)) = [0 2]x1 + [3] >= [0 2]x1 + [3] = a#(b(a(x1)))
     
                   [2 4]     [5]    [2 2]     [3]        
     a(a(a(x1))) = [4 6]x1 + [7] >= [2 0]x1 + [3] = b(x1)
     
                [4 4]     [5]    [0 2]     [3]           
     b(b(x1)) = [4 4]x1 + [5] >= [2 4]x1 + [5] = a(a(x1))
     
                [0 2]     [3]    [0 2]     [3]              
     a(a(x1)) = [2 4]x1 + [5] >= [2 4]x1 + [5] = a(b(a(x1)))
    problem:
     DPs:
      b#(b(x1)) -> a#(a(x1))
      a#(a(x1)) -> b#(a(x1))
      a#(a(x1)) -> a#(b(a(x1)))
     TRS:
      a(a(a(x1))) -> b(x1)
      b(b(x1)) -> a(a(x1))
      a(a(x1)) -> a(b(a(x1)))
    Restore Modifier:
     DPs:
      b#(b(x1)) -> a#(a(x1))
      a#(a(x1)) -> b#(a(x1))
      a#(a(x1)) -> a#(b(a(x1)))
     TRS:

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