/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(),a()),x) -> f(f(x,f(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(a0(),x) -> f(f(x,a1(a1(a0()))),a0())
   f(a1(x1),x2) -> a2(x1,x2)
   f(a0(),x1) -> a1(x1)
  DP Processor:
   DPs:
    a{2,#}(a0(),x) -> f#(x,a1(a1(a0())))
    a{2,#}(a0(),x) -> f#(f(x,a1(a1(a0()))),a0())
    f#(a1(x1),x2) -> a{2,#}(x1,x2)
   TRS:
    a2(a0(),x) -> f(f(x,a1(a1(a0()))),a0())
    f(a1(x1),x2) -> a2(x1,x2)
    f(a0(),x1) -> a1(x1)
   TDG Processor:
    DPs:
     a{2,#}(a0(),x) -> f#(x,a1(a1(a0())))
     a{2,#}(a0(),x) -> f#(f(x,a1(a1(a0()))),a0())
     f#(a1(x1),x2) -> a{2,#}(x1,x2)
    TRS:
     a2(a0(),x) -> f(f(x,a1(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,#}(a0(),x) -> f#(f(x,a1(a1(a0()))),a0())
     f#(a1(x1),x2) -> a{2,#}(x1,x2) ->
     a{2,#}(a0(),x) -> f#(x,a1(a1(a0())))
     a{2,#}(a0(),x) -> f#(f(x,a1(a1(a0()))),a0()) ->
     f#(a1(x1),x2) -> a{2,#}(x1,x2)
     a{2,#}(a0(),x) -> f#(x,a1(a1(a0()))) -> f#(a1(x1),x2) -> a{2,#}(x1,x2)
    Bounds Processor:
     bound: 0
     enrichment: match-dp
     automaton:
      final states: {1}
      transitions:
       f70() -> 5*
       f{#,0}(19,2) -> 1*
       f{#,0}(4,4) -> 1*
       f{#,0}(5,4) -> 1*
       a{1,0}(2) -> 3*
       a{1,0}(3) -> 4*
       a{0,0}() -> 2*
       f0(4,4) -> 19*
       a{2,#,0}(3,4) -> 1*
       a{2,#,0}(5,4) -> 1*
       a{2,0}(3,4) -> 19*
     problem:
      DPs:
       a{2,#}(a0(),x) -> f#(f(x,a1(a1(a0()))),a0())
       f#(a1(x1),x2) -> a{2,#}(x1,x2)
      TRS:
       a2(a0(),x) -> f(f(x,a1(a1(a0()))),a0())
       f(a1(x1),x2) -> a2(x1,x2)
       f(a0(),x1) -> a1(x1)
     Bounds Processor:
      bound: 1
      enrichment: match
      automaton:
       final states: {10,9,8,7,1}
       transitions:
        a{2,0}(4,2) -> 8,9
        a{2,0}(5,5) -> 9*
        a{2,0}(3,4) -> 12*
        a{2,0}(5,4) -> 6*
        a{2,#,1}(4,2) -> 1,7
        f160() -> 5*
        a{2,1}(4,2) -> 8*
        a{2,1}(3,4) -> 12*
        f{#,0}(6,2) -> 1*
        a{1,0}(5) -> 10*
        a{1,0}(2) -> 3*
        a{1,0}(4) -> 6*
        a{1,0}(3) -> 4*
        a{0,0}() -> 2*
        f0(4,4) -> 12*
        f0(6,2) -> 8*
        f0(5,4) -> 6*
        f0(12,2) -> 6*
        a{2,#,0}(4,2) -> 1,7
        a{2,#,0}(5,5) -> 7*
        1 -> 7*
        8 -> 9*
      problem:
       DPs:
        
       TRS:
        a2(a0(),x) -> f(f(x,a1(a1(a0()))),a0())
        f(a1(x1),x2) -> a2(x1,x2)
        f(a0(),x1) -> a1(x1)
      Qed