TRS Relative pair #487081718

details

property	value
status	complete
benchmark	#3.56_rand.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	INVY_15

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	2.95711 seconds
cpu usage	10.6088
user time	8.22104
system time	2.38776
max virtual memory	6721104.0
max residence set size	68360.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 strict:
  g(c(x,s(y))) -> g(c(s(x),y))
  f(c(s(x),y)) -> f(c(x,s(y)))
  f(f(x)) -> f(d(f(x)))
  f(x) -> x
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
             [1 0]  
   [d](x0) = [0 0]x0,
   
                 [1 1]     [1 0]     [1]
   [c](x0, x1) = [2 2]x0 + [1 0]x1 + [2],
   
               
   [f](x0) = x0,
   
                [2 0]     [2]
   [rand](x0) = [0 1]x0 + [0],
   
               
   [s](x0) = x0,
   
             [2 0]     [1]
   [g](x0) = [1 1]x0 + [0]
  orientation:
                  [2 2]    [2 0]    [3]    [2 2]    [2 0]    [3]               
   g(c(x,s(y))) = [3 3]x + [2 0]y + [3] >= [3 3]x + [2 0]y + [3] = g(c(s(x),y))
   
                  [1 1]    [1 0]    [1]    [1 1]    [1 0]    [1]               
   f(c(s(x),y)) = [2 2]x + [1 0]y + [2] >= [2 2]x + [1 0]y + [2] = f(c(x,s(y)))
   
                  [1 0]              
   f(f(x)) = x >= [0 0]x = f(d(f(x)))
   
                    
   f(x) = x >= x = x
   
             [2 0]    [2]         
   rand(x) = [0 1]x + [0] >= x = x
   
             [2 0]    [2]    [2 0]    [2]             
   rand(x) = [0 1]x + [0] >= [0 1]x + [0] = rand(s(x))
  problem:
   strict:
    g(c(x,s(y))) -> g(c(s(x),y))
    f(c(s(x),y)) -> f(c(x,s(y)))
    f(f(x)) -> f(d(f(x)))
    f(x) -> x
   weak:
    rand(x) -> rand(s(x))
  Bounds Processor:
   bound: 1
   enrichment: match-rt
   automaton:
    final states: {7}
    transitions:
     g0(7) -> 7*
     s1(14) -> 14*
     s1(7) -> 14*
     d1(7) -> 15*
     s0(7) -> 7*
     c0(7,7) -> 7*
     c1(14,14) -> 45*
     c1(14,7) -> 45*
     c1(7,14) -> 15*
     g1(45) -> 7*
     f0(7) -> 7*
     rand0(7) -> 7*
     d0(7) -> 7*
     rand1(14) -> 7*
     f1(7) -> 7*
     f1(15) -> 7*
     15 -> 7*
   problem:
    strict:
     g(c(x,s(y))) -> g(c(s(x),y))
     f(f(x)) -> f(d(f(x)))
     f(x) -> x
    weak:
     rand(x) -> rand(s(x))
   Bounds Processor:
    bound: 1
    enrichment: match-rt
    automaton:
     final states: {7}
     transitions:
      g0(7) -> 7*
      s1(10) -> 10*
      s1(45) -> 46*
      s1(7) -> 10*
      d1(25) -> 26*

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