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


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YES

Problem:
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(le(),0()),y) -> true()
 app(app(le(),app(s(),x)),0()) -> false()
 app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
 app(app(maxlist(),x),app(app(cons(),y),ys)) ->
 app(app(if(),app(app(le(),x),y)),app(app(maxlist(),y),ys))
 app(app(maxlist(),x),nil()) -> x
 app(height(),app(app(node(),x),xs)) ->
 app(s(),app(app(maxlist(),0()),app(app(map(),height()),xs)))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   node ==> node0/0 node1/1 node2/2
   height ==> height0/0 height1/1
   if ==> if0/0 if1/1 if2/2
   maxlist ==> maxlist0/0 maxlist1/1 maxlist2/2
   false ==> false0/0
   s ==> s0/0 s1/1
   true ==> true0/0
   0 ==> 00/0
   le ==> le0/0 le1/1 le2/2
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   map ==> map0/0 map1/1 map2/2
   
  uncurry-rules:
   app(map1(x5),x6) -> map2(x5,x6)
   app(map0(),x5) -> map1(x5)
   app(cons1(x9),x10) -> cons2(x9,x10)
   app(cons0(),x9) -> cons1(x9)
   app(le1(x12),x13) -> le2(x12,x13)
   app(le0(),x12) -> le1(x12)
   app(s0(),x17) -> s1(x17)
   app(maxlist1(x20),x21) -> maxlist2(x20,x21)
   app(maxlist0(),x20) -> maxlist1(x20)
   app(if1(x23),x24) -> if2(x23,x24)
   app(if0(),x23) -> if1(x23)
   app(height0(),x26) -> height1(x26)
   app(node1(x28),x29) -> node2(x28,x29)
   app(node0(),x28) -> node1(x28)
  eta-rules:
   
  problem:
   map2(f,nil0()) -> nil0()
   map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
   le2(00(),y) -> true0()
   le2(s1(x),00()) -> false0()
   le2(s1(x),s1(y)) -> le2(x,y)
   maxlist2(x,cons2(y,ys)) -> if2(le2(x,y),maxlist2(y,ys))
   maxlist2(x,nil0()) -> x
   height1(node2(x,xs)) -> s1(maxlist2(00(),map2(height0(),xs)))
   app(map1(x5),x6) -> map2(x5,x6)
   app(map0(),x5) -> map1(x5)
   app(cons1(x9),x10) -> cons2(x9,x10)
   app(cons0(),x9) -> cons1(x9)
   app(le1(x12),x13) -> le2(x12,x13)
   app(le0(),x12) -> le1(x12)
   app(s0(),x17) -> s1(x17)
   app(maxlist1(x20),x21) -> maxlist2(x20,x21)
   app(maxlist0(),x20) -> maxlist1(x20)
   app(if1(x23),x24) -> if2(x23,x24)
   app(if0(),x23) -> if1(x23)
   app(height0(),x26) -> height1(x26)
   app(node1(x28),x29) -> node2(x28,x29)
   app(node0(),x28) -> node1(x28)
  DP Processor:
   DPs:
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    le{2,#}(s1(x),s1(y)) -> le{2,#}(x,y)
    maxlist{2,#}(x,cons2(y,ys)) -> maxlist{2,#}(y,ys)
    maxlist{2,#}(x,cons2(y,ys)) -> le{2,#}(x,y)
    height{1,#}(node2(x,xs)) -> map{2,#}(height0(),xs)
    height{1,#}(node2(x,xs)) -> maxlist{2,#}(00(),map2(height0(),xs))
    app#(map1(x5),x6) -> map{2,#}(x5,x6)
    app#(le1(x12),x13) -> le{2,#}(x12,x13)
    app#(maxlist1(x20),x21) -> maxlist{2,#}(x20,x21)
    app#(height0(),x26) -> height{1,#}(x26)
   TRS:
    map2(f,nil0()) -> nil0()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    le2(00(),y) -> true0()
    le2(s1(x),00()) -> false0()
    le2(s1(x),s1(y)) -> le2(x,y)
    maxlist2(x,cons2(y,ys)) -> if2(le2(x,y),maxlist2(y,ys))
    maxlist2(x,nil0()) -> x
    height1(node2(x,xs)) -> s1(maxlist2(00(),map2(height0(),xs)))
    app(map1(x5),x6) -> map2(x5,x6)
    app(map0(),x5) -> map1(x5)
    app(cons1(x9),x10) -> cons2(x9,x10)
    app(cons0(),x9) -> cons1(x9)
    app(le1(x12),x13) -> le2(x12,x13)
    app(le0(),x12) -> le1(x12)
    app(s0(),x17) -> s1(x17)
    app(maxlist1(x20),x21) -> maxlist2(x20,x21)
    app(maxlist0(),x20) -> maxlist1(x20)
    app(if1(x23),x24) -> if2(x23,x24)
    app(if0(),x23) -> if1(x23)
    app(height0(),x26) -> height1(x26)
    app(node1(x28),x29) -> node2(x28,x29)
    app(node0(),x28) -> node1(x28)
   TDG Processor:
    DPs:
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     le{2,#}(s1(x),s1(y)) -> le{2,#}(x,y)
     maxlist{2,#}(x,cons2(y,ys)) -> maxlist{2,#}(y,ys)
     maxlist{2,#}(x,cons2(y,ys)) -> le{2,#}(x,y)
     height{1,#}(node2(x,xs)) -> map{2,#}(height0(),xs)
     height{1,#}(node2(x,xs)) -> maxlist{2,#}(00(),map2(height0(),xs))
     app#(map1(x5),x6) -> map{2,#}(x5,x6)
     app#(le1(x12),x13) -> le{2,#}(x12,x13)
     app#(maxlist1(x20),x21) -> maxlist{2,#}(x20,x21)
     app#(height0(),x26) -> height{1,#}(x26)
    TRS:
     map2(f,nil0()) -> nil0()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     le2(00(),y) -> true0()
     le2(s1(x),00()) -> false0()
     le2(s1(x),s1(y)) -> le2(x,y)
     maxlist2(x,cons2(y,ys)) -> if2(le2(x,y),maxlist2(y,ys))
     maxlist2(x,nil0()) -> x
     height1(node2(x,xs)) -> s1(maxlist2(00(),map2(height0(),xs)))
     app(map1(x5),x6) -> map2(x5,x6)
     app(map0(),x5) -> map1(x5)
     app(cons1(x9),x10) -> cons2(x9,x10)
     app(cons0(),x9) -> cons1(x9)
     app(le1(x12),x13) -> le2(x12,x13)
     app(le0(),x12) -> le1(x12)
     app(s0(),x17) -> s1(x17)
     app(maxlist1(x20),x21) -> maxlist2(x20,x21)
     app(maxlist0(),x20) -> maxlist1(x20)
     app(if1(x23),x24) -> if2(x23,x24)
     app(if0(),x23) -> if1(x23)
     app(height0(),x26) -> height1(x26)
     app(node1(x28),x29) -> node2(x28,x29)
     app(node0(),x28) -> node1(x28)
    graph:
     height{1,#}(node2(x,xs)) -> maxlist{2,#}(00(),map2(height0(),xs)) ->
     maxlist{2,#}(x,cons2(y,ys)) -> le{2,#}(x,y)
     height{1,#}(node2(x,xs)) -> maxlist{2,#}(00(),map2(height0(),xs)) ->
     maxlist{2,#}(x,cons2(y,ys)) -> maxlist{2,#}(y,ys)
     height{1,#}(node2(x,xs)) -> map{2,#}(height0(),xs) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     height{1,#}(node2(x,xs)) -> map{2,#}(height0(),xs) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     maxlist{2,#}(x,cons2(y,ys)) -> maxlist{2,#}(y,ys) ->
     maxlist{2,#}(x,cons2(y,ys)) -> le{2,#}(x,y)
     maxlist{2,#}(x,cons2(y,ys)) -> maxlist{2,#}(y,ys) ->
     maxlist{2,#}(x,cons2(y,ys)) -> maxlist{2,#}(y,ys)
     maxlist{2,#}(x,cons2(y,ys)) -> le{2,#}(x,y) ->
     le{2,#}(s1(x),s1(y)) -> le{2,#}(x,y)
     le{2,#}(s1(x),s1(y)) -> le{2,#}(x,y) ->
     le{2,#}(s1(x),s1(y)) -> le{2,#}(x,y)
     app#(height0(),x26) -> height{1,#}(x26) ->
     height{1,#}(node2(x,xs)) -> maxlist{2,#}(00(),map2(height0(),xs))
     app#(height0(),x26) -> height{1,#}(x26) ->
     height{1,#}(node2(x,xs)) -> map{2,#}(height0(),xs)
     app#(maxlist1(x20),x21) -> maxlist{2,#}(x20,x21) ->
     maxlist{2,#}(x,cons2(y,ys)) -> le{2,#}(x,y)
     app#(maxlist1(x20),x21) -> maxlist{2,#}(x20,x21) ->
     maxlist{2,#}(x,cons2(y,ys)) -> maxlist{2,#}(y,ys)
     app#(le1(x12),x13) -> le{2,#}(x12,x13) ->
     le{2,#}(s1(x),s1(y)) -> le{2,#}(x,y)
     app#(map1(x5),x6) -> map{2,#}(x5,x6) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x5),x6) -> map{2,#}(x5,x6) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(height0(),x26) -> height{1,#}(x26)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(maxlist1(x20),x21) -> maxlist{2,#}(x20,x21)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(le1(x12),x13) -> le{2,#}(x12,x13)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x5),x6) -> map{2,#}(x5,x6)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) -> map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    SCC Processor:
     #sccs: 3
     #rules: 7
     #arcs: 21/121
     DPs:
      height{1,#}(node2(x,xs)) -> map{2,#}(height0(),xs)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(map1(x5),x6) -> map{2,#}(x5,x6)
      app#(height0(),x26) -> height{1,#}(x26)
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      le2(00(),y) -> true0()
      le2(s1(x),00()) -> false0()
      le2(s1(x),s1(y)) -> le2(x,y)
      maxlist2(x,cons2(y,ys)) -> if2(le2(x,y),maxlist2(y,ys))
      maxlist2(x,nil0()) -> x
      height1(node2(x,xs)) -> s1(maxlist2(00(),map2(height0(),xs)))
      app(map1(x5),x6) -> map2(x5,x6)
      app(map0(),x5) -> map1(x5)
      app(cons1(x9),x10) -> cons2(x9,x10)
      app(cons0(),x9) -> cons1(x9)
      app(le1(x12),x13) -> le2(x12,x13)
      app(le0(),x12) -> le1(x12)
      app(s0(),x17) -> s1(x17)
      app(maxlist1(x20),x21) -> maxlist2(x20,x21)
      app(maxlist0(),x20) -> maxlist1(x20)
      app(if1(x23),x24) -> if2(x23,x24)
      app(if0(),x23) -> if1(x23)
      app(height0(),x26) -> height1(x26)
      app(node1(x28),x29) -> node2(x28,x29)
      app(node0(),x28) -> node1(x28)
     Subterm Criterion Processor:
      simple projection:
       pi(map{2,#}) = 1
       pi(app#) = 1
       pi(height{1,#}) = 0
      problem:
       DPs:
        app#(map1(x5),x6) -> map{2,#}(x5,x6)
        app#(height0(),x26) -> height{1,#}(x26)
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        le2(00(),y) -> true0()
        le2(s1(x),00()) -> false0()
        le2(s1(x),s1(y)) -> le2(x,y)
        maxlist2(x,cons2(y,ys)) -> if2(le2(x,y),maxlist2(y,ys))
        maxlist2(x,nil0()) -> x
        height1(node2(x,xs)) -> s1(maxlist2(00(),map2(height0(),xs)))
        app(map1(x5),x6) -> map2(x5,x6)
        app(map0(),x5) -> map1(x5)
        app(cons1(x9),x10) -> cons2(x9,x10)
        app(cons0(),x9) -> cons1(x9)
        app(le1(x12),x13) -> le2(x12,x13)
        app(le0(),x12) -> le1(x12)
        app(s0(),x17) -> s1(x17)
        app(maxlist1(x20),x21) -> maxlist2(x20,x21)
        app(maxlist0(),x20) -> maxlist1(x20)
        app(if1(x23),x24) -> if2(x23,x24)
        app(if0(),x23) -> if1(x23)
        app(height0(),x26) -> height1(x26)
        app(node1(x28),x29) -> node2(x28,x29)
        app(node0(),x28) -> node1(x28)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 9/4
       
     
     DPs:
      maxlist{2,#}(x,cons2(y,ys)) -> maxlist{2,#}(y,ys)
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      le2(00(),y) -> true0()
      le2(s1(x),00()) -> false0()
      le2(s1(x),s1(y)) -> le2(x,y)
      maxlist2(x,cons2(y,ys)) -> if2(le2(x,y),maxlist2(y,ys))
      maxlist2(x,nil0()) -> x
      height1(node2(x,xs)) -> s1(maxlist2(00(),map2(height0(),xs)))
      app(map1(x5),x6) -> map2(x5,x6)
      app(map0(),x5) -> map1(x5)
      app(cons1(x9),x10) -> cons2(x9,x10)
      app(cons0(),x9) -> cons1(x9)
      app(le1(x12),x13) -> le2(x12,x13)
      app(le0(),x12) -> le1(x12)
      app(s0(),x17) -> s1(x17)
      app(maxlist1(x20),x21) -> maxlist2(x20,x21)
      app(maxlist0(),x20) -> maxlist1(x20)
      app(if1(x23),x24) -> if2(x23,x24)
      app(if0(),x23) -> if1(x23)
      app(height0(),x26) -> height1(x26)
      app(node1(x28),x29) -> node2(x28,x29)
      app(node0(),x28) -> node1(x28)
     Subterm Criterion Processor:
      simple projection:
       pi(maxlist{2,#}) = 1
      problem:
       DPs:
        
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        le2(00(),y) -> true0()
        le2(s1(x),00()) -> false0()
        le2(s1(x),s1(y)) -> le2(x,y)
        maxlist2(x,cons2(y,ys)) -> if2(le2(x,y),maxlist2(y,ys))
        maxlist2(x,nil0()) -> x
        height1(node2(x,xs)) -> s1(maxlist2(00(),map2(height0(),xs)))
        app(map1(x5),x6) -> map2(x5,x6)
        app(map0(),x5) -> map1(x5)
        app(cons1(x9),x10) -> cons2(x9,x10)
        app(cons0(),x9) -> cons1(x9)
        app(le1(x12),x13) -> le2(x12,x13)
        app(le0(),x12) -> le1(x12)
        app(s0(),x17) -> s1(x17)
        app(maxlist1(x20),x21) -> maxlist2(x20,x21)
        app(maxlist0(),x20) -> maxlist1(x20)
        app(if1(x23),x24) -> if2(x23,x24)
        app(if0(),x23) -> if1(x23)
        app(height0(),x26) -> height1(x26)
        app(node1(x28),x29) -> node2(x28,x29)
        app(node0(),x28) -> node1(x28)
      Qed
     
     DPs:
      le{2,#}(s1(x),s1(y)) -> le{2,#}(x,y)
     TRS:
      map2(f,nil0()) -> nil0()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      le2(00(),y) -> true0()
      le2(s1(x),00()) -> false0()
      le2(s1(x),s1(y)) -> le2(x,y)
      maxlist2(x,cons2(y,ys)) -> if2(le2(x,y),maxlist2(y,ys))
      maxlist2(x,nil0()) -> x
      height1(node2(x,xs)) -> s1(maxlist2(00(),map2(height0(),xs)))
      app(map1(x5),x6) -> map2(x5,x6)
      app(map0(),x5) -> map1(x5)
      app(cons1(x9),x10) -> cons2(x9,x10)
      app(cons0(),x9) -> cons1(x9)
      app(le1(x12),x13) -> le2(x12,x13)
      app(le0(),x12) -> le1(x12)
      app(s0(),x17) -> s1(x17)
      app(maxlist1(x20),x21) -> maxlist2(x20,x21)
      app(maxlist0(),x20) -> maxlist1(x20)
      app(if1(x23),x24) -> if2(x23,x24)
      app(if0(),x23) -> if1(x23)
      app(height0(),x26) -> height1(x26)
      app(node1(x28),x29) -> node2(x28,x29)
      app(node0(),x28) -> node1(x28)
     Subterm Criterion Processor:
      simple projection:
       pi(le{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        map2(f,nil0()) -> nil0()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        le2(00(),y) -> true0()
        le2(s1(x),00()) -> false0()
        le2(s1(x),s1(y)) -> le2(x,y)
        maxlist2(x,cons2(y,ys)) -> if2(le2(x,y),maxlist2(y,ys))
        maxlist2(x,nil0()) -> x
        height1(node2(x,xs)) -> s1(maxlist2(00(),map2(height0(),xs)))
        app(map1(x5),x6) -> map2(x5,x6)
        app(map0(),x5) -> map1(x5)
        app(cons1(x9),x10) -> cons2(x9,x10)
        app(cons0(),x9) -> cons1(x9)
        app(le1(x12),x13) -> le2(x12,x13)
        app(le0(),x12) -> le1(x12)
        app(s0(),x17) -> s1(x17)
        app(maxlist1(x20),x21) -> maxlist2(x20,x21)
        app(maxlist0(),x20) -> maxlist1(x20)
        app(if1(x23),x24) -> if2(x23,x24)
        app(if0(),x23) -> if1(x23)
        app(height0(),x26) -> height1(x26)
        app(node1(x28),x29) -> node2(x28,x29)
        app(node0(),x28) -> node1(x28)
      Qed