/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:
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 quot(0(),s(y)) -> 0()
 quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
 app(nil(),y) -> y
 app(add(n,x),y) -> add(n,app(x,y))
 reverse(nil()) -> nil()
 reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
 shuffle(nil()) -> nil()
 shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
 concat(leaf(),y) -> y
 concat(cons(u,v),y) -> cons(u,concat(v,y))
 less_leaves(x,leaf()) -> false()
 less_leaves(leaf(),cons(w,z)) -> true()
 less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))

Proof:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> minus#(x,y)
   quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
   app#(add(n,x),y) -> app#(x,y)
   reverse#(add(n,x)) -> reverse#(x)
   reverse#(add(n,x)) -> app#(reverse(x),add(n,nil()))
   shuffle#(add(n,x)) -> reverse#(x)
   shuffle#(add(n,x)) -> shuffle#(reverse(x))
   concat#(cons(u,v),y) -> concat#(v,y)
   less_leaves#(cons(u,v),cons(w,z)) -> concat#(w,z)
   less_leaves#(cons(u,v),cons(w,z)) -> concat#(u,v)
   less_leaves#(cons(u,v),cons(w,z)) -> less_leaves#(concat(u,v),concat(w,z))
  TRS:
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   quot(0(),s(y)) -> 0()
   quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
   app(nil(),y) -> y
   app(add(n,x),y) -> add(n,app(x,y))
   reverse(nil()) -> nil()
   reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
   shuffle(nil()) -> nil()
   shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
   concat(leaf(),y) -> y
   concat(cons(u,v),y) -> cons(u,concat(v,y))
   less_leaves(x,leaf()) -> false()
   less_leaves(leaf(),cons(w,z)) -> true()
   less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
  TDG Processor:
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    app#(add(n,x),y) -> app#(x,y)
    reverse#(add(n,x)) -> reverse#(x)
    reverse#(add(n,x)) -> app#(reverse(x),add(n,nil()))
    shuffle#(add(n,x)) -> reverse#(x)
    shuffle#(add(n,x)) -> shuffle#(reverse(x))
    concat#(cons(u,v),y) -> concat#(v,y)
    less_leaves#(cons(u,v),cons(w,z)) -> concat#(w,z)
    less_leaves#(cons(u,v),cons(w,z)) -> concat#(u,v)
    less_leaves#(cons(u,v),cons(w,z)) -> less_leaves#(concat(u,v),concat(w,z))
   TRS:
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    quot(0(),s(y)) -> 0()
    quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
    app(nil(),y) -> y
    app(add(n,x),y) -> add(n,app(x,y))
    reverse(nil()) -> nil()
    reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
    shuffle(nil()) -> nil()
    shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
    concat(leaf(),y) -> y
    concat(cons(u,v),y) -> cons(u,concat(v,y))
    less_leaves(x,leaf()) -> false()
    less_leaves(leaf(),cons(w,z)) -> true()
    less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
   graph:
    less_leaves#(cons(u,v),cons(w,z)) -> less_leaves#(concat(u,v),concat(w,z)) ->
    less_leaves#(cons(u,v),cons(w,z)) -> less_leaves#(concat(u,v),concat(w,z))
    less_leaves#(cons(u,v),cons(w,z)) -> less_leaves#(concat(u,v),concat(w,z)) ->
    less_leaves#(cons(u,v),cons(w,z)) -> concat#(u,v)
    less_leaves#(cons(u,v),cons(w,z)) -> less_leaves#(concat(u,v),concat(w,z)) ->
    less_leaves#(cons(u,v),cons(w,z)) -> concat#(w,z)
    less_leaves#(cons(u,v),cons(w,z)) -> concat#(w,z) ->
    concat#(cons(u,v),y) -> concat#(v,y)
    less_leaves#(cons(u,v),cons(w,z)) -> concat#(u,v) ->
    concat#(cons(u,v),y) -> concat#(v,y)
    concat#(cons(u,v),y) -> concat#(v,y) ->
    concat#(cons(u,v),y) -> concat#(v,y)
    shuffle#(add(n,x)) -> shuffle#(reverse(x)) ->
    shuffle#(add(n,x)) -> shuffle#(reverse(x))
    shuffle#(add(n,x)) -> shuffle#(reverse(x)) ->
    shuffle#(add(n,x)) -> reverse#(x)
    shuffle#(add(n,x)) -> reverse#(x) ->
    reverse#(add(n,x)) -> app#(reverse(x),add(n,nil()))
    shuffle#(add(n,x)) -> reverse#(x) ->
    reverse#(add(n,x)) -> reverse#(x)
    reverse#(add(n,x)) -> reverse#(x) ->
    reverse#(add(n,x)) -> app#(reverse(x),add(n,nil()))
    reverse#(add(n,x)) -> reverse#(x) ->
    reverse#(add(n,x)) -> reverse#(x)
    reverse#(add(n,x)) -> app#(reverse(x),add(n,nil())) ->
    app#(add(n,x),y) -> app#(x,y)
    app#(add(n,x),y) -> app#(x,y) ->
    app#(add(n,x),y) -> app#(x,y)
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) ->
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    quot#(s(x),s(y)) -> quot#(minus(x,y),s(y)) ->
    quot#(s(x),s(y)) -> minus#(x,y)
    quot#(s(x),s(y)) -> minus#(x,y) ->
    minus#(s(x),s(y)) -> minus#(x,y)
    minus#(s(x),s(y)) -> minus#(x,y) -> minus#(s(x),s(y)) -> minus#(x,y)
   SCC Processor:
    #sccs: 7
    #rules: 7
    #arcs: 18/144
    DPs:
     quot#(s(x),s(y)) -> quot#(minus(x,y),s(y))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     app(nil(),y) -> y
     app(add(n,x),y) -> add(n,app(x,y))
     reverse(nil()) -> nil()
     reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
     shuffle(nil()) -> nil()
     shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
     concat(leaf(),y) -> y
     concat(cons(u,v),y) -> cons(u,concat(v,y))
     less_leaves(x,leaf()) -> false()
     less_leaves(leaf(),cons(w,z)) -> true()
     less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
    Subterm Criterion Processor:
     simple projection:
      pi(minus) = 0
      pi(quot#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       app(nil(),y) -> y
       app(add(n,x),y) -> add(n,app(x,y))
       reverse(nil()) -> nil()
       reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
       shuffle(nil()) -> nil()
       shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
       concat(leaf(),y) -> y
       concat(cons(u,v),y) -> cons(u,concat(v,y))
       less_leaves(x,leaf()) -> false()
       less_leaves(leaf(),cons(w,z)) -> true()
       less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
     Qed
    
    DPs:
     minus#(s(x),s(y)) -> minus#(x,y)
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     app(nil(),y) -> y
     app(add(n,x),y) -> add(n,app(x,y))
     reverse(nil()) -> nil()
     reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
     shuffle(nil()) -> nil()
     shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
     concat(leaf(),y) -> y
     concat(cons(u,v),y) -> cons(u,concat(v,y))
     less_leaves(x,leaf()) -> false()
     less_leaves(leaf(),cons(w,z)) -> true()
     less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
    Subterm Criterion Processor:
     simple projection:
      pi(minus#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       app(nil(),y) -> y
       app(add(n,x),y) -> add(n,app(x,y))
       reverse(nil()) -> nil()
       reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
       shuffle(nil()) -> nil()
       shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
       concat(leaf(),y) -> y
       concat(cons(u,v),y) -> cons(u,concat(v,y))
       less_leaves(x,leaf()) -> false()
       less_leaves(leaf(),cons(w,z)) -> true()
       less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
     Qed
    
    DPs:
     shuffle#(add(n,x)) -> shuffle#(reverse(x))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     app(nil(),y) -> y
     app(add(n,x),y) -> add(n,app(x,y))
     reverse(nil()) -> nil()
     reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
     shuffle(nil()) -> nil()
     shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
     concat(leaf(),y) -> y
     concat(cons(u,v),y) -> cons(u,concat(v,y))
     less_leaves(x,leaf()) -> false()
     less_leaves(leaf(),cons(w,z)) -> true()
     less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
    Usable Rule Processor:
     DPs:
      shuffle#(add(n,x)) -> shuffle#(reverse(x))
     TRS:
      reverse(nil()) -> nil()
      reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
      app(nil(),y) -> y
      app(add(n,x),y) -> add(n,app(x,y))
     Semantic Labeling Processor:
      dimension: 1
      usable rules:
       
      interpretation:
       [reverse](x0) = x0,
       
       [add](x0, x1) = x1 + 1,
       
       [app](x0, x1) = x0 + x1,
       
       [nil] = 0
       labeled:
        shuffle#
        add
        reverse
       usable (for model):
        shuffle#
        add
        reverse
        nil
        app
       argument filtering:
        pi(nil) = []
        pi(app) = 1
        pi(add) = 1
        pi(reverse) = 0
        pi(shuffle#) = []
      precedence:
       shuffle# ~ reverse ~ add ~ app ~ nil
      problem:
       DPs:
        
       TRS:
        reverse(nil()) -> nil()
        reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
        app(nil(),y) -> y
        app(add(n,x),y) -> add(n,app(x,y))
      Qed
    
    DPs:
     reverse#(add(n,x)) -> reverse#(x)
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     app(nil(),y) -> y
     app(add(n,x),y) -> add(n,app(x,y))
     reverse(nil()) -> nil()
     reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
     shuffle(nil()) -> nil()
     shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
     concat(leaf(),y) -> y
     concat(cons(u,v),y) -> cons(u,concat(v,y))
     less_leaves(x,leaf()) -> false()
     less_leaves(leaf(),cons(w,z)) -> true()
     less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
    Subterm Criterion Processor:
     simple projection:
      pi(reverse#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       app(nil(),y) -> y
       app(add(n,x),y) -> add(n,app(x,y))
       reverse(nil()) -> nil()
       reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
       shuffle(nil()) -> nil()
       shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
       concat(leaf(),y) -> y
       concat(cons(u,v),y) -> cons(u,concat(v,y))
       less_leaves(x,leaf()) -> false()
       less_leaves(leaf(),cons(w,z)) -> true()
       less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
     Qed
    
    DPs:
     app#(add(n,x),y) -> app#(x,y)
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     app(nil(),y) -> y
     app(add(n,x),y) -> add(n,app(x,y))
     reverse(nil()) -> nil()
     reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
     shuffle(nil()) -> nil()
     shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
     concat(leaf(),y) -> y
     concat(cons(u,v),y) -> cons(u,concat(v,y))
     less_leaves(x,leaf()) -> false()
     less_leaves(leaf(),cons(w,z)) -> true()
     less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
    Subterm Criterion Processor:
     simple projection:
      pi(app#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       app(nil(),y) -> y
       app(add(n,x),y) -> add(n,app(x,y))
       reverse(nil()) -> nil()
       reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
       shuffle(nil()) -> nil()
       shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
       concat(leaf(),y) -> y
       concat(cons(u,v),y) -> cons(u,concat(v,y))
       less_leaves(x,leaf()) -> false()
       less_leaves(leaf(),cons(w,z)) -> true()
       less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
     Qed
    
    DPs:
     less_leaves#(cons(u,v),cons(w,z)) -> less_leaves#(concat(u,v),concat(w,z))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     app(nil(),y) -> y
     app(add(n,x),y) -> add(n,app(x,y))
     reverse(nil()) -> nil()
     reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
     shuffle(nil()) -> nil()
     shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
     concat(leaf(),y) -> y
     concat(cons(u,v),y) -> cons(u,concat(v,y))
     less_leaves(x,leaf()) -> false()
     less_leaves(leaf(),cons(w,z)) -> true()
     less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
    Subterm Criterion Processor:
     simple projection:
      pi(s) = [0,0,0]
      pi(add) = [1,1,1]
      pi(concat) = [0,0,1]
      pi(cons) = [0,0,0,1]
      pi(less_leaves#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       app(nil(),y) -> y
       app(add(n,x),y) -> add(n,app(x,y))
       reverse(nil()) -> nil()
       reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
       shuffle(nil()) -> nil()
       shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
       concat(leaf(),y) -> y
       concat(cons(u,v),y) -> cons(u,concat(v,y))
       less_leaves(x,leaf()) -> false()
       less_leaves(leaf(),cons(w,z)) -> true()
       less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
     Qed
    
    DPs:
     concat#(cons(u,v),y) -> concat#(v,y)
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     quot(0(),s(y)) -> 0()
     quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
     app(nil(),y) -> y
     app(add(n,x),y) -> add(n,app(x,y))
     reverse(nil()) -> nil()
     reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
     shuffle(nil()) -> nil()
     shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
     concat(leaf(),y) -> y
     concat(cons(u,v),y) -> cons(u,concat(v,y))
     less_leaves(x,leaf()) -> false()
     less_leaves(leaf(),cons(w,z)) -> true()
     less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
    Subterm Criterion Processor:
     simple projection:
      pi(concat#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       quot(0(),s(y)) -> 0()
       quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
       app(nil(),y) -> y
       app(add(n,x),y) -> add(n,app(x,y))
       reverse(nil()) -> nil()
       reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
       shuffle(nil()) -> nil()
       shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
       concat(leaf(),y) -> y
       concat(cons(u,v),y) -> cons(u,concat(v,y))
       less_leaves(x,leaf()) -> false()
       less_leaves(leaf(),cons(w,z)) -> true()
       less_leaves(cons(u,v),cons(w,z)) -> less_leaves(concat(u,v),concat(w,z))
     Qed