SRS Standard pair #487084010

details

property	value
status	complete
benchmark	size-12-alpha-3-num-350.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	44.1999 seconds
cpu usage	172.632
user time	169.14
system time	3.49172
max virtual memory	1.0871872E7
max residence set size	102068.0

stage attributes

key	value
starexec-result	YES

output

YES

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

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

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