TRS Standard pair #487068792

details

property	value
status	complete
benchmark	z28.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)	2.87153 seconds
cpu usage	10.1129
user time	8.76031
system time	1.35264
max virtual memory	5639152.0
max residence set size	90232.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 f(f(0(),x),1()) -> f(g(f(x,x)),x)
 f(g(x),y) -> g(f(x,y))

Proof:
 DP Processor:
  DPs:
   f#(f(0(),x),1()) -> f#(x,x)
   f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
   f#(g(x),y) -> f#(x,y)
  TRS:
   f(f(0(),x),1()) -> f(g(f(x,x)),x)
   f(g(x),y) -> g(f(x,y))
  EDG Processor:
   DPs:
    f#(f(0(),x),1()) -> f#(x,x)
    f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
    f#(g(x),y) -> f#(x,y)
   TRS:
    f(f(0(),x),1()) -> f(g(f(x,x)),x)
    f(g(x),y) -> g(f(x,y))
   graph:
    f#(g(x),y) -> f#(x,y) -> f#(f(0(),x),1()) -> f#(x,x)
    f#(g(x),y) -> f#(x,y) -> f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
    f#(g(x),y) -> f#(x,y) -> f#(g(x),y) -> f#(x,y)
    f#(f(0(),x),1()) -> f#(g(f(x,x)),x) -> f#(g(x),y) -> f#(x,y)
    f#(f(0(),x),1()) -> f#(x,x) -> f#(g(x),y) -> f#(x,y)
   Arctic Interpretation Processor:
    dimension: 1
    usable rules:
     f(f(0(),x),1()) -> f(g(f(x,x)),x)
     f(g(x),y) -> g(f(x,y))
    interpretation:
     [f#](x0, x1) = 4x0 + 1x1 + 0,
     
     [f](x0, x1) = x0 + 1x1 + 0,
     
     [g](x0) = x0 + 1,
     
     [0] = 1,
     
     [1] = 4
    orientation:
     f#(f(0(),x),1()) = 5x + 5 >= 4x + 0 = f#(x,x)
     
     f#(f(0(),x),1()) = 5x + 5 >= 5x + 5 = f#(g(f(x,x)),x)
     
     f#(g(x),y) = 4x + 1y + 5 >= 4x + 1y + 0 = f#(x,y)
     
     f(f(0(),x),1()) = 1x + 5 >= 1x + 1 = f(g(f(x,x)),x)
     
     f(g(x),y) = x + 1y + 1 >= x + 1y + 1 = g(f(x,y))
    problem:
     DPs:
      f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
      f#(g(x),y) -> f#(x,y)
     TRS:
      f(f(0(),x),1()) -> f(g(f(x,x)),x)
      f(g(x),y) -> g(f(x,y))
    Restore Modifier:
     DPs:
      f#(f(0(),x),1()) -> f#(g(f(x,x)),x)
      f#(g(x),y) -> f#(x,y)
     TRS:
      f(f(0(),x),1()) -> f(g(f(x,x)),x)
      f(g(x),y) -> g(f(x,y))
     Bounds Processor:
      bound: 1
      enrichment: top-dp
      automaton:
       final states: {17,7}
       transitions:
        f0(1,4) -> 10*
        f0(2,6) -> 8*
        f0(6,16) -> 8*
        f0(1,12) -> 10*
        f0(5,12) -> 10*
        f0(16,11) -> 15*
        f0(16,13) -> 15*
        f0(3,12) -> 10*
        f0(14,11) -> 15*
        f0(1,1) -> 10*
        f0(3,5) -> 10*
        f0(4,2) -> 10*
        f0(10,16) -> 15*
        f0(6,6) -> 8*
        f0(11,6) -> 8*
        f0(16,12) -> 15*
        f0(16,3) -> 10*
        f0(4,17) -> 10*
        f0(6,12) -> 8*
        f0(17,6) -> 8*
        f0(5,11) -> 10*
        f0(16,16) -> 15*
        f0(2,16) -> 10*
        f0(1,16) -> 10*
        f0(15,10) -> 15*
        f0(5,16) -> 10*

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