SRS Standard pair #487083656

details

property	value
status	complete
benchmark	size-12-alpha-3-num-348.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	44.5003 seconds
cpu usage	173.983
user time	171.037
system time	2.94547
max virtual memory	1.14406E7
max residence set size	132316.0

stage attributes

key	value
starexec-result	YES

output

YES

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

Proof:
 DP Processor:
  DPs:
   c#(c(b(x1))) -> c#(x1)
   c#(c(b(x1))) -> c#(c(x1))
   c#(c(b(x1))) -> a#(c(c(x1)))
   c#(c(b(x1))) -> c#(a(c(c(x1))))
  TRS:
   a(x1) -> b(x1)
   a(b(x1)) -> x1
   c(c(b(x1))) -> b(c(a(c(c(x1)))))
  TDG Processor:
   DPs:
    c#(c(b(x1))) -> c#(x1)
    c#(c(b(x1))) -> c#(c(x1))
    c#(c(b(x1))) -> a#(c(c(x1)))
    c#(c(b(x1))) -> c#(a(c(c(x1))))
   TRS:
    a(x1) -> b(x1)
    a(b(x1)) -> x1
    c(c(b(x1))) -> b(c(a(c(c(x1)))))
   graph:
    c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(a(c(c(x1))))
    c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> a#(c(c(x1)))
    c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(c(x1))
    c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(x1)
    c#(c(b(x1))) -> c#(a(c(c(x1)))) ->
    c#(c(b(x1))) -> c#(a(c(c(x1))))
    c#(c(b(x1))) -> c#(a(c(c(x1)))) -> c#(c(b(x1))) -> a#(c(c(x1)))
    c#(c(b(x1))) -> c#(a(c(c(x1)))) -> c#(c(b(x1))) -> c#(c(x1))
    c#(c(b(x1))) -> c#(a(c(c(x1)))) -> c#(c(b(x1))) -> c#(x1)
    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(a(c(c(x1))))
    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(c(x1)))
    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(c(x1))
    c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 12/16
    DPs:
     c#(c(b(x1))) -> c#(c(x1))
     c#(c(b(x1))) -> c#(x1)
     c#(c(b(x1))) -> c#(a(c(c(x1))))
    TRS:
     a(x1) -> b(x1)
     a(b(x1)) -> x1
     c(c(b(x1))) -> b(c(a(c(c(x1)))))
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> b(x1)
      a(b(x1)) -> x1
      c(c(b(x1))) -> b(c(a(c(c(x1)))))
     interpretation:
      [c#](x0) = [0  -&]x0 + [1],
      
                [-& 0 ]     [0]
      [b](x0) = [0  1 ]x0 + [2],
      
                [-& 0 ]     [0]
      [a](x0) = [0  1 ]x0 + [2],
      
                [-& 0 ]     [0]
      [c](x0) = [0  -&]x0 + [0]
     orientation:
      c#(c(b(x1))) = [0 1]x1 + [2] >= [-& 0 ]x1 + [1] = c#(c(x1))
      
      c#(c(b(x1))) = [0 1]x1 + [2] >= [0  -&]x1 + [1] = c#(x1)
      
      c#(c(b(x1))) = [0 1]x1 + [2] >= [-& 0 ]x1 + [1] = c#(a(c(c(x1))))
      
              [-& 0 ]     [0]    [-& 0 ]     [0]        
      a(x1) = [0  1 ]x1 + [2] >= [0  1 ]x1 + [2] = b(x1)
      
                 [0 1]     [2]           
      a(b(x1)) = [1 2]x1 + [3] >= x1 = x1
      
                    [-& 0 ]     [0]    [-& 0 ]     [0]                    
      c(c(b(x1))) = [0  1 ]x1 + [2] >= [0  1 ]x1 + [2] = b(c(a(c(c(x1)))))
     problem:
      DPs:
       c#(c(b(x1))) -> c#(x1)
      TRS:
       a(x1) -> b(x1)
       a(b(x1)) -> x1
       c(c(b(x1))) -> b(c(a(c(c(x1)))))
     Restore Modifier:
      DPs:
       c#(c(b(x1))) -> c#(x1)
      TRS:
       a(x1) -> b(x1)
       a(b(x1)) -> x1
       c(c(b(x1))) -> b(c(a(c(c(x1)))))

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