TRS Standard pair #487073447

details

property	value
status	complete
benchmark	jwtpa2.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	Waldmann_06

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	1.31985 seconds
cpu usage	4.1564
user time	3.10379
system time	1.0526
max virtual memory	5447336.0
max residence set size	73532.0

stage attributes

key	value
starexec-result	YES

output

YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),y)) -> f#(a(),x)
   f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
   f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
   f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
  TRS:
   f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
  EDG Processor:
   DPs:
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
   TRS:
    f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
   graph:
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y) ->
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y) ->
    f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y) ->
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y) ->
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y)) ->
    f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y)) ->
    f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y)) ->
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y)) ->
    f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),x)
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(f(a(),x),h(a()))
    f#(x,f(a(),y)) -> f#(a(),x) ->
    f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
    f#(x,f(a(),y)) -> f#(a(),x) -> f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 12/16
    DPs:
     f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
     f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
     f#(x,f(a(),y)) -> f#(a(),x)
    TRS:
     f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
    Bounds Processor:
     bound: 1
     enrichment: match-dp
     automaton:
      final states: {14}
      transitions:
       f{#,0}(16,15) -> 14*
       a0() -> 16*
       f0(16,16) -> 20*
       f0(20,19) -> 16*
       f0(16,15) -> 15*
       f40() -> 15*
       h0(16) -> 19*
       a1() -> 30*
       f{#,1}(30,16) -> 14*
     problem:
      DPs:
       f#(x,f(a(),y)) -> f#(f(f(a(),x),h(a())),y)
       f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
      TRS:
       f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
     Subterm Criterion Processor:
      simple projection:
       pi(f) = [1,1]
       pi(f#) = [1,1]
      problem:
       DPs:
        f#(x,f(a(),y)) -> f#(a(),f(f(f(a(),x),h(a())),y))
       TRS:
        f(x,f(a(),y)) -> f(a(),f(f(f(a(),x),h(a())),y))
      Semantic Labeling Processor:
       dimension: 2
       usable rules:
        
       interpretation:
                      [0 1]     [1 1]  
        [f](x0, x1) = [0 0]x0 + [1 0]x1,
        
              [1]
        [a] = [1],
        
                  [0 0]     [0]
        [h](x0) = [1 1]x0 + [1]
        labeled:
         f#
        usable (for model):

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