TRS Standard pair #487073902

details

property	value
status	complete
benchmark	matchbox2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n186.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.581522 seconds
cpu usage	1.20145
user time	0.749593
system time	0.451857
max virtual memory	1262988.0
max residence set size	65744.0

stage attributes

key	value
starexec-result	YES

output

YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(x,a()),y) -> f#(a(),x)
   f#(f(x,a()),y) -> f#(a(),y)
   f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x))
  TRS:
   f(f(x,a()),y) -> f(f(a(),y),f(a(),x))
  EDG Processor:
   DPs:
    f#(f(x,a()),y) -> f#(a(),x)
    f#(f(x,a()),y) -> f#(a(),y)
    f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x))
   TRS:
    f(f(x,a()),y) -> f(f(a(),y),f(a(),x))
   graph:
    f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x)) ->
    f#(f(x,a()),y) -> f#(a(),x)
    f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x)) ->
    f#(f(x,a()),y) -> f#(a(),y)
    f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x)) -> f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 3/9
    DPs:
     f#(f(x,a()),y) -> f#(f(a(),y),f(a(),x))
    TRS:
     f(f(x,a()),y) -> f(f(a(),y),f(a(),x))
    Bounds Processor:
     bound: 1
     enrichment: match
     automaton:
      final states: {6,1}
      transitions:
       f0(4,4) -> 6*
       f0(5,4) -> 6*
       f0(3,2) -> 5,4
       f0(3,3) -> 4*
       f0(3,4) -> 5*
       f1(9,4) -> 11*
       f1(11,10) -> 6*
       f1(9,3) -> 10*
       a0() -> 3*
       f{#,0}(5,4) -> 1*
       f30() -> 2*
       a1() -> 9*
     problem:
      DPs:
       
      TRS:
       f(f(x,a()),y) -> f(f(a(),y),f(a(),x))
     Qed

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