SRS Standard pair #487083662

details

property	value
status	complete
benchmark	size-12-alpha-3-num-288.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	45.3182 seconds
cpu usage	177.125
user time	173.092
system time	4.03313
max virtual memory	1.1071288E7
max residence set size	102156.0

stage attributes

key	value
starexec-result	YES

output

YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> b#(a(x1))
   a#(b(x1)) -> c#(b(a(x1)))
   a#(b(x1)) -> b#(c(b(a(x1))))
   a#(b(x1)) -> c#(b(c(b(a(x1)))))
   b#(x1) -> a#(x1)
  TRS:
   a(x1) -> x1
   a(b(x1)) -> c(b(c(b(a(x1)))))
   b(x1) -> a(x1)
   c(c(x1)) -> x1
  TDG Processor:
   DPs:
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(a(x1))
    a#(b(x1)) -> c#(b(a(x1)))
    a#(b(x1)) -> b#(c(b(a(x1))))
    a#(b(x1)) -> c#(b(c(b(a(x1)))))
    b#(x1) -> a#(x1)
   TRS:
    a(x1) -> x1
    a(b(x1)) -> c(b(c(b(a(x1)))))
    b(x1) -> a(x1)
    c(c(x1)) -> x1
   graph:
    b#(x1) -> a#(x1) -> a#(b(x1)) -> c#(b(c(b(a(x1)))))
    b#(x1) -> a#(x1) -> a#(b(x1)) -> b#(c(b(a(x1))))
    b#(x1) -> a#(x1) -> a#(b(x1)) -> c#(b(a(x1)))
    b#(x1) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
    b#(x1) -> a#(x1) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(c(b(a(x1)))) -> b#(x1) -> a#(x1)
    a#(b(x1)) -> b#(a(x1)) -> b#(x1) -> a#(x1)
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(b(c(b(a(x1)))))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(c(b(a(x1))))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(b(a(x1)))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 12/36
    DPs:
     b#(x1) -> a#(x1)
     a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> b#(a(x1))
     a#(b(x1)) -> b#(c(b(a(x1))))
    TRS:
     a(x1) -> x1
     a(b(x1)) -> c(b(c(b(a(x1)))))
     b(x1) -> a(x1)
     c(c(x1)) -> x1
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> x1
      a(b(x1)) -> c(b(c(b(a(x1)))))
      b(x1) -> a(x1)
      c(c(x1)) -> x1
     interpretation:
      [b#](x0) = [2 2]x0 + [0],
      
                [0 1]     [0]
      [b](x0) = [1 2]x0 + [3],
      
      [a#](x0) = [0 2]x0 + [0],
      
                [0  1 ]     [0]
      [a](x0) = [-& 0 ]x0 + [1],
      
                [0  0 ]     [0]
      [c](x0) = [0  -&]x0 + [0]
     orientation:
      b#(x1) = [2 2]x1 + [0] >= [0 2]x1 + [0] = a#(x1)
      
      a#(b(x1)) = [3 4]x1 + [5] >= [0 2]x1 + [0] = a#(x1)
      
      a#(b(x1)) = [3 4]x1 + [5] >= [2 3]x1 + [3] = b#(a(x1))
      
      a#(b(x1)) = [3 4]x1 + [5] >= [3 4]x1 + [5] = b#(c(b(a(x1))))
      
              [0  1 ]     [0]           
      a(x1) = [-& 0 ]x1 + [1] >= x1 = x1
      
                 [2 3]     [4]    [2 3]     [4]                    
      a(b(x1)) = [1 2]x1 + [3] >= [1 2]x1 + [3] = c(b(c(b(a(x1)))))
      
              [0 1]     [0]    [0  1 ]     [0]        
      b(x1) = [1 2]x1 + [3] >= [-& 0 ]x1 + [1] = a(x1)

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