SRS Standard pair #487083872

details

property	value
status	complete
benchmark	size-12-alpha-3-num-413.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	43.7671 seconds
cpu usage	171.064
user time	168.064
system time	2.99994
max virtual memory	1.1827616E7
max residence set size	132084.0

stage attributes

key	value
starexec-result	YES

output

YES

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

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

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