/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /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: 1
     enrichment: match
     automaton:
      final states: {12,11,10,9,7,4,1}
      transitions:
       f{#,1}(3,14) -> 1,9
       a{2,0}(2,5) -> 8*
       a{2,0}(3,3) -> 11*
       a{2,0}(3,2) -> 6*
       f1(3,14) -> 6,3
       f70() -> 3*
       a{2,#,0}(3,3) -> 9*
       a{2,#,0}(2,5) -> 4,1
       a{2,#,0}(3,2) -> 1*
       a{1,0}(2) -> 5*
       a{1,0}(3) -> 12*
       f{#,0}(8,2) -> 1,7
       f{#,0}(3,2) -> 1*
       f{#,0}(6,5) -> 1,4
       f0(6,5) -> 8*
       f0(3,2) -> 6*
       f0(8,2) -> 6,10
       a{0,0}() -> 2*
       a{0,1}() -> 14*
       a{2,#,1}(2,5) -> 4,1
       a{1,1}(14) -> 14*
       a{2,1}(2,5) -> 8*
       7 -> 9*
       4 -> 9*
       1 -> 9*
       5 -> 6*
       10 -> 11*
     problem:
      DPs:
       
      TRS:
       a2(x,a0()) -> f(f(f(x,a0()),a1(a0())),a0())
       f(a1(x1),x2) -> a2(x1,x2)
       f(a0(),x1) -> a1(x1)
     Qed