TRS Standard pair #516965609

details

property	value
status	complete
benchmark	z06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n183.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.859791040421 seconds
cpu usage	2.024997739
max memory	3.66170112E8

stage attributes

key	value
output-size	6377
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 f(a(),f(b(),x)) -> f(a(),f(a(),f(a(),x)))
 f(b(),f(a(),x)) -> f(b(),f(b(),f(b(),x)))

Proof:
 Extended Uncurrying Processor:
  application symbol: f
  symbol table:
   b ==> b0/0 b1/1
   a ==> a0/0 a1/1
   
  uncurry-rules:
   f(a0(),x1) -> a1(x1)
   f(b0(),x3) -> b1(x3)
  eta-rules:
   
  problem:
   a1(b1(x)) -> a1(a1(a1(x)))
   b1(a1(x)) -> b1(b1(b1(x)))
   f(a0(),x1) -> a1(x1)
   f(b0(),x3) -> b1(x3)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
               [1 0 0]  
    [a1](x0) = [0 0 0]x0
               [0 0 0]  ,
    
           [0]
    [a0] = [0]
           [0],
    
           [0]
    [b0] = [1]
           [0],
    
               [1 0 0]  
    [b1](x0) = [0 0 0]x0
               [0 0 0]  ,
    
                  [1 0 0]     [1 0 0]     [1]
    [f](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [0]
                  [0 0 0]     [0 0 0]     [0]
   orientation:
                [1 0 0]     [1 0 0]                 
    a1(b1(x)) = [0 0 0]x >= [0 0 0]x = a1(a1(a1(x)))
                [0 0 0]     [0 0 0]                 
    
                [1 0 0]     [1 0 0]                 
    b1(a1(x)) = [0 0 0]x >= [0 0 0]x = b1(b1(b1(x)))
                [0 0 0]     [0 0 0]                 
    
                 [1 0 0]     [1]    [1 0 0]           
    f(a0(),x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 = a1(x1)
                 [0 0 0]     [0]    [0 0 0]           
    
                 [1 0 0]     [1]    [1 0 0]           
    f(b0(),x3) = [0 0 0]x3 + [1] >= [0 0 0]x3 = b1(x3)
                 [0 0 0]     [0]    [0 0 0]           
   problem:
    a1(b1(x)) -> a1(a1(a1(x)))
    b1(a1(x)) -> b1(b1(b1(x)))
   DP Processor:
    DPs:
     a{1,#}(b1(x)) -> a{1,#}(x)
     a{1,#}(b1(x)) -> a{1,#}(a1(x))
     a{1,#}(b1(x)) -> a{1,#}(a1(a1(x)))
     b{1,#}(a1(x)) -> b{1,#}(x)
     b{1,#}(a1(x)) -> b{1,#}(b1(x))
     b{1,#}(a1(x)) -> b{1,#}(b1(b1(x)))
    TRS:
     a1(b1(x)) -> a1(a1(a1(x)))
     b1(a1(x)) -> b1(b1(b1(x)))
    TDG Processor:
     DPs:
      a{1,#}(b1(x)) -> a{1,#}(x)
      a{1,#}(b1(x)) -> a{1,#}(a1(x))
      a{1,#}(b1(x)) -> a{1,#}(a1(a1(x)))
      b{1,#}(a1(x)) -> b{1,#}(x)
      b{1,#}(a1(x)) -> b{1,#}(b1(x))
      b{1,#}(a1(x)) -> b{1,#}(b1(b1(x)))
     TRS:
      a1(b1(x)) -> a1(a1(a1(x)))
      b1(a1(x)) -> b1(b1(b1(x)))
     graph:
      b{1,#}(a1(x)) -> b{1,#}(b1(b1(x))) ->
      b{1,#}(a1(x)) -> b{1,#}(b1(b1(x)))
      b{1,#}(a1(x)) -> b{1,#}(b1(b1(x))) ->
      b{1,#}(a1(x)) -> b{1,#}(b1(x))
      b{1,#}(a1(x)) -> b{1,#}(b1(b1(x))) ->
      b{1,#}(a1(x)) -> b{1,#}(x)
      b{1,#}(a1(x)) -> b{1,#}(b1(x)) ->

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