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


--------------------------------------------------------------------------------


YES

Problem:
 f(f(a(),a()),x) -> f(f(x,a()),f(a(),f(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,a0()),a1(a1(a0())))
   f(a1(x1),x2) -> a2(x1,x2)
   f(a0(),x1) -> a1(x1)
  DP Processor:
   DPs:
    a{2,#}(a0(),x) -> f#(x,a0())
    a{2,#}(a0(),x) -> f#(f(x,a0()),a1(a1(a0())))
    f#(a1(x1),x2) -> a{2,#}(x1,x2)
   TRS:
    a2(a0(),x) -> f(f(x,a0()),a1(a1(a0())))
    f(a1(x1),x2) -> a2(x1,x2)
    f(a0(),x1) -> a1(x1)
   TDG Processor:
    DPs:
     a{2,#}(a0(),x) -> f#(x,a0())
     a{2,#}(a0(),x) -> f#(f(x,a0()),a1(a1(a0())))
     f#(a1(x1),x2) -> a{2,#}(x1,x2)
    TRS:
     a2(a0(),x) -> f(f(x,a0()),a1(a1(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,a0()),a1(a1(a0())))
     f#(a1(x1),x2) -> a{2,#}(x1,x2) ->
     a{2,#}(a0(),x) -> f#(x,a0())
     a{2,#}(a0(),x) -> f#(f(x,a0()),a1(a1(a0()))) ->
     f#(a1(x1),x2) -> a{2,#}(x1,x2)
     a{2,#}(a0(),x) -> f#(x,a0()) -> f#(a1(x1),x2) -> a{2,#}(x1,x2)
    Bounds Processor:
     bound: 1
     enrichment: match-dp
     automaton:
      final states: {8,4,1}
      transitions:
       a{2,0}(3,2) -> 7*
       a{2,0}(5,2) -> 7*
       a{2,0}(2,6) -> 7*
       a{2,#,1}(5,9) -> 4,1
       a{2,#,1}(5,2) -> 4,1
       a{2,#,1}(2,6) -> 4,1
       f{#,1}(14,13) -> 4*
       f{#,1}(6,9) -> 4*
       f1(6,9) -> 14*
       a{0,1}() -> 9*
       a{1,1}(12) -> 13*
       a{1,1}(9) -> 12*
       a{2,1}(5,9) -> 14*
       f70() -> 3*
       f{#,0}(6,2) -> 4*
       f{#,0}(3,2) -> 1*
       f{#,0}(2,2) -> 8*
       f{#,0}(7,6) -> 4*
       a{0,0}() -> 2*
       f0(6,2) -> 7*
       f0(3,2) -> 7*
       f0(2,2) -> 7*
       f0(7,6) -> 7*
       a{1,0}(5) -> 6*
       a{1,0}(2) -> 5*
       a{2,#,0}(3,3) -> 8*
       a{2,#,0}(3,2) -> 1*
       a{2,#,0}(5,2) -> 4,8
       a{2,#,0}(2,6) -> 4,8
       1 -> 8*
       4 -> 8*
       5 -> 7*
       8 -> 1*
     problem:
      DPs:
       
      TRS:
       a2(a0(),x) -> f(f(x,a0()),a1(a1(a0())))
       f(a1(x1),x2) -> a2(x1,x2)
       f(a0(),x1) -> a1(x1)
     Qed