TRS Standard pair #487068422

details

property	value
status	complete
benchmark	z19.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n185.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	2.57987 seconds
cpu usage	8.97176
user time	7.16613
system time	1.80563
max virtual memory	5961668.0
max residence set size	78400.0

stage attributes

key	value
starexec-result	YES

output

YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(a(),a()),x) -> f#(a(),x)
   f#(f(a(),a()),x) -> f#(b(),f(a(),x))
   f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
   f#(x,f(y,z)) -> f#(x,y)
   f#(x,f(y,z)) -> f#(f(x,y),z)
  TRS:
   f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
   f(x,f(y,z)) -> f(f(x,y),z)
  EDG Processor:
   DPs:
    f#(f(a(),a()),x) -> f#(a(),x)
    f#(f(a(),a()),x) -> f#(b(),f(a(),x))
    f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
    f#(x,f(y,z)) -> f#(x,y)
    f#(x,f(y,z)) -> f#(f(x,y),z)
   TRS:
    f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
    f(x,f(y,z)) -> f(f(x,y),z)
   graph:
    f#(f(a(),a()),x) -> f#(b(),f(a(),x)) ->
    f#(x,f(y,z)) -> f#(x,y)
    f#(f(a(),a()),x) -> f#(b(),f(a(),x)) ->
    f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x))) ->
    f#(x,f(y,z)) -> f#(x,y)
    f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x))) ->
    f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(f(a(),a()),x) -> f#(a(),x) -> f#(x,f(y,z)) -> f#(x,y)
    f#(f(a(),a()),x) -> f#(a(),x) -> f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(x,f(y,z)) -> f#(f(x,y),z) -> f#(f(a(),a()),x) -> f#(a(),x)
    f#(x,f(y,z)) -> f#(f(x,y),z) ->
    f#(f(a(),a()),x) -> f#(b(),f(a(),x))
    f#(x,f(y,z)) -> f#(f(x,y),z) ->
    f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
    f#(x,f(y,z)) -> f#(f(x,y),z) -> f#(x,f(y,z)) -> f#(x,y)
    f#(x,f(y,z)) -> f#(f(x,y),z) -> f#(x,f(y,z)) -> f#(f(x,y),z)
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(a(),a()),x) -> f#(a(),x)
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(a(),a()),x) -> f#(b(),f(a(),x))
    f#(x,f(y,z)) -> f#(x,y) -> f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
    f#(x,f(y,z)) -> f#(x,y) -> f#(x,f(y,z)) -> f#(x,y)
    f#(x,f(y,z)) -> f#(x,y) -> f#(x,f(y,z)) -> f#(f(x,y),z)
   KBO Processor:
    argument filtering:
     pi(a) = []
     pi(f) = 0
     pi(b) = []
     pi(f#) = [0]
    usable rules:
     f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
     f(x,f(y,z)) -> f(f(x,y),z)
    weight function:
     w0 = 1
     w(f#) = w(b) = w(f) = w(a) = 1
    precedence:
     a > b > f > f#
    problem:
     DPs:
      f#(f(a(),a()),x) -> f#(a(),x)
      f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
      f#(x,f(y,z)) -> f#(x,y)
      f#(x,f(y,z)) -> f#(f(x,y),z)
     TRS:
      f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
      f(x,f(y,z)) -> f(f(x,y),z)
    Restore Modifier:
     DPs:
      f#(f(a(),a()),x) -> f#(a(),x)
      f#(f(a(),a()),x) -> f#(a(),f(b(),f(a(),x)))
      f#(x,f(y,z)) -> f#(x,y)
      f#(x,f(y,z)) -> f#(f(x,y),z)
     TRS:
      f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
      f(x,f(y,z)) -> f(f(x,y),z)
     Matrix Interpretation Processor: dim=1
      
      usable rules:
       f(f(a(),a()),x) -> f(a(),f(b(),f(a(),x)))
       f(x,f(y,z)) -> f(f(x,y),z)
      interpretation:
       [f](x0, x1) = x0 + x1,
       
       [f#](x0, x1) = x0 + x1,
       
       [a] = 4,
       
       [b] = 0
      orientation:
       f#(f(a(),a()),x) = x + 8 >= x + 4 = f#(a(),x)
       
       f#(f(a(),a()),x) = x + 8 >= x + 8 = f#(a(),f(b(),f(a(),x)))

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