/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 Extended Uncurrying Processor:
  application symbol: f
  symbol table:
   a ==> a0/0 a1/1 a2/2
   
  uncurry-rules:
   f(a1(x1),x2) -> a2(x1,x2)
   f(a0(),x1) -> a1(x1)
  eta-rules:
   
  problem:
   a2(x,a0()) -> f(f(f(x,a0()),a1(a0())),a0())
   f(a1(x1),x2) -> a2(x1,x2)
   f(a0(),x1) -> a1(x1)
  DP Processor:
   DPs:
    a{2,#}(x,a0()) -> f#(x,a0())
    a{2,#}(x,a0()) -> f#(f(x,a0()),a1(a0()))
    a{2,#}(x,a0()) -> f#(f(f(x,a0()),a1(a0())),a0())
    f#(a1(x1),x2) -> a{2,#}(x1,x2)
   TRS:
    a2(x,a0()) -> f(f(f(x,a0()),a1(a0())),a0())
    f(a1(x1),x2) -> a2(x1,x2)
    f(a0(),x1) -> a1(x1)
   TDG Processor:
    DPs:
     a{2,#}(x,a0()) -> f#(x,a0())
     a{2,#}(x,a0()) -> f#(f(x,a0()),a1(a0()))
     a{2,#}(x,a0()) -> f#(f(f(x,a0()),a1(a0())),a0())
     f#(a1(x1),x2) -> a{2,#}(x1,x2)
    TRS:
     a2(x,a0()) -> f(f(f(x,a0()),a1(a0())),a0())
     f(a1(x1),x2) -> a2(x1,x2)
     f(a0(),x1) -> a1(x1)
    graph:
     f#(a1(x1),x2) -> a{2,#}(x1,x2) ->
     a{2,#}(x,a0()) -> f#(f(f(x,a0()),a1(a0())),a0())
     f#(a1(x1),x2) -> a{2,#}(x1,x2) ->
     a{2,#}(x,a0()) -> f#(f(x,a0()),a1(a0()))
     f#(a1(x1),x2) -> a{2,#}(x1,x2) ->
     a{2,#}(x,a0()) -> f#(x,a0())
     a{2,#}(x,a0()) -> f#(f(f(x,a0()),a1(a0())),a0()) ->
     f#(a1(x1),x2) -> a{2,#}(x1,x2)
     a{2,#}(x,a0()) -> f#(f(x,a0()),a1(a0())) ->
     f#(a1(x1),x2) -> a{2,#}(x1,x2)
     a{2,#}(x,a0()) -> f#(x,a0()) -> f#(a1(x1),x2) -> a{2,#}(x1,x2)
    Bounds Processor:
     bound: 0
     enrichment: match-dp
     automaton:
      final states: {9}
      transitions:
       a{0,0}() -> 10*
       f0(13,11) -> 14*
       f0(14,10) -> 13*
       f0(12,10) -> 13*
       a{1,0}(10) -> 11*
       a{2,0}(10,11) -> 14*
       a{2,0}(12,10) -> 13*
       f70() -> 12*
       f{#,0}(14,10) -> 9*
       11 -> 13*
     problem:
      DPs:
       a{2,#}(x,a0()) -> f#(x,a0())
       a{2,#}(x,a0()) -> f#(f(x,a0()),a1(a0()))
       f#(a1(x1),x2) -> a{2,#}(x1,x2)
      TRS:
       a2(x,a0()) -> f(f(f(x,a0()),a1(a0())),a0())
       f(a1(x1),x2) -> a2(x1,x2)
       f(a0(),x1) -> a1(x1)
     Bounds Processor:
      bound: 0
      enrichment: match-dp
      automaton:
       final states: {4}
       transitions:
        a{0,0}() -> 5*
        f0(7,5) -> 8*
        f0(8,6) -> 7*
        a{1,0}(5) -> 6*
        a{2,#,0}(5,6) -> 4*
        a{2,0}(7,5) -> 8*
        a{2,0}(5,6) -> 7*
        f180() -> 7*
        f{#,0}(8,6) -> 4*
        6 -> 8*
      problem:
       DPs:
        a{2,#}(x,a0()) -> f#(x,a0())
        f#(a1(x1),x2) -> a{2,#}(x1,x2)
       TRS:
        a2(x,a0()) -> f(f(f(x,a0()),a1(a0())),a0())
        f(a1(x1),x2) -> a2(x1,x2)
        f(a0(),x1) -> a1(x1)
      Bounds Processor:
       bound: 0
       enrichment: match-dp
       automaton:
        final states: {4}
        transitions:
         f{#,0}(5,6) -> 4*
         f200() -> 5*
         a{2,#,0}(5,5) -> 4*
         a{2,#,0}(5,6) -> 4*
         a{0,0}() -> 6*
       problem:
        DPs:
         a{2,#}(x,a0()) -> f#(x,a0())
        TRS:
         a2(x,a0()) -> f(f(f(x,a0()),a1(a0())),a0())
         f(a1(x1),x2) -> a2(x1,x2)
         f(a0(),x1) -> a1(x1)
       SCC Processor:
        #sccs: 0
        #rules: 0
        #arcs: 6/1