MAYBE

Problem:
 a__and(tt(),X) -> mark(X)
 a__plus(N,0()) -> mark(N)
 a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
 a__x(N,0()) -> 0()
 a__x(N,s(M)) -> a__plus(a__x(mark(N),mark(M)),mark(N))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
 mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
 mark(tt()) -> tt()
 mark(0()) -> 0()
 mark(s(X)) -> s(mark(X))
 a__and(X1,X2) -> and(X1,X2)
 a__plus(X1,X2) -> plus(X1,X2)
 a__x(X1,X2) -> x(X1,X2)

Proof:
 DP Processor:
  DPs:
   a__and#(tt(),X) -> mark#(X)
   a__plus#(N,0()) -> mark#(N)
   a__plus#(N,s(M)) -> mark#(M)
   a__plus#(N,s(M)) -> mark#(N)
   a__plus#(N,s(M)) -> a__plus#(mark(N),mark(M))
   a__x#(N,s(M)) -> mark#(M)
   a__x#(N,s(M)) -> mark#(N)
   a__x#(N,s(M)) -> a__x#(mark(N),mark(M))
   a__x#(N,s(M)) -> a__plus#(a__x(mark(N),mark(M)),mark(N))
   mark#(and(X1,X2)) -> mark#(X1)
   mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
   mark#(plus(X1,X2)) -> mark#(X2)
   mark#(plus(X1,X2)) -> mark#(X1)
   mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
   mark#(x(X1,X2)) -> mark#(X2)
   mark#(x(X1,X2)) -> mark#(X1)
   mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
   mark#(s(X)) -> mark#(X)
  TRS:
   a__and(tt(),X) -> mark(X)
   a__plus(N,0()) -> mark(N)
   a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
   a__x(N,0()) -> 0()
   a__x(N,s(M)) -> a__plus(a__x(mark(N),mark(M)),mark(N))
   mark(and(X1,X2)) -> a__and(mark(X1),X2)
   mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
   mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
   mark(tt()) -> tt()
   mark(0()) -> 0()
   mark(s(X)) -> s(mark(X))
   a__and(X1,X2) -> and(X1,X2)
   a__plus(X1,X2) -> plus(X1,X2)
   a__x(X1,X2) -> x(X1,X2)
  TDG Processor:
   DPs:
    a__and#(tt(),X) -> mark#(X)
    a__plus#(N,0()) -> mark#(N)
    a__plus#(N,s(M)) -> mark#(M)
    a__plus#(N,s(M)) -> mark#(N)
    a__plus#(N,s(M)) -> a__plus#(mark(N),mark(M))
    a__x#(N,s(M)) -> mark#(M)
    a__x#(N,s(M)) -> mark#(N)
    a__x#(N,s(M)) -> a__x#(mark(N),mark(M))
    a__x#(N,s(M)) -> a__plus#(a__x(mark(N),mark(M)),mark(N))
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(plus(X1,X2)) -> mark#(X2)
    mark#(plus(X1,X2)) -> mark#(X1)
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
    mark#(x(X1,X2)) -> mark#(X2)
    mark#(x(X1,X2)) -> mark#(X1)
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
    mark#(s(X)) -> mark#(X)
   TRS:
    a__and(tt(),X) -> mark(X)
    a__plus(N,0()) -> mark(N)
    a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
    a__x(N,0()) -> 0()
    a__x(N,s(M)) -> a__plus(a__x(mark(N),mark(M)),mark(N))
    mark(and(X1,X2)) -> a__and(mark(X1),X2)
    mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
    mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
    mark(tt()) -> tt()
    mark(0()) -> 0()
    mark(s(X)) -> s(mark(X))
    a__and(X1,X2) -> and(X1,X2)
    a__plus(X1,X2) -> plus(X1,X2)
    a__x(X1,X2) -> x(X1,X2)
   graph:
    a__x#(N,s(M)) -> a__x#(mark(N),mark(M)) ->
    a__x#(N,s(M)) -> a__plus#(a__x(mark(N),mark(M)),mark(N))
    a__x#(N,s(M)) -> a__x#(mark(N),mark(M)) ->
    a__x#(N,s(M)) -> a__x#(mark(N),mark(M))
    a__x#(N,s(M)) -> a__x#(mark(N),mark(M)) ->
    a__x#(N,s(M)) -> mark#(N)
    a__x#(N,s(M)) -> a__x#(mark(N),mark(M)) ->
    a__x#(N,s(M)) -> mark#(M)
    a__x#(N,s(M)) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) ->
    a__plus#(N,s(M)) -> a__plus#(mark(N),mark(M))
    a__x#(N,s(M)) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) ->
    a__plus#(N,s(M)) -> mark#(N)
    a__x#(N,s(M)) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) ->
    a__plus#(N,s(M)) -> mark#(M)
    a__x#(N,s(M)) -> a__plus#(a__x(mark(N),mark(M)),mark(N)) ->
    a__plus#(N,0()) -> mark#(N)
    a__x#(N,s(M)) -> mark#(M) -> mark#(s(X)) -> mark#(X)
    a__x#(N,s(M)) -> mark#(M) ->
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
    a__x#(N,s(M)) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X1)
    a__x#(N,s(M)) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X2)
    a__x#(N,s(M)) -> mark#(M) ->
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
    a__x#(N,s(M)) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X1)
    a__x#(N,s(M)) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X2)
    a__x#(N,s(M)) -> mark#(M) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__x#(N,s(M)) -> mark#(M) -> mark#(and(X1,X2)) -> mark#(X1)
    a__x#(N,s(M)) -> mark#(N) -> mark#(s(X)) -> mark#(X)
    a__x#(N,s(M)) -> mark#(N) ->
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
    a__x#(N,s(M)) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1)
    a__x#(N,s(M)) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2)
    a__x#(N,s(M)) -> mark#(N) ->
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
    a__x#(N,s(M)) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1)
    a__x#(N,s(M)) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2)
    a__x#(N,s(M)) -> mark#(N) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__x#(N,s(M)) -> mark#(N) ->
    mark#(and(X1,X2)) -> mark#(X1)
    a__plus#(N,s(M)) -> a__plus#(mark(N),mark(M)) ->
    a__plus#(N,s(M)) -> a__plus#(mark(N),mark(M))
    a__plus#(N,s(M)) -> a__plus#(mark(N),mark(M)) ->
    a__plus#(N,s(M)) -> mark#(N)
    a__plus#(N,s(M)) -> a__plus#(mark(N),mark(M)) ->
    a__plus#(N,s(M)) -> mark#(M)
    a__plus#(N,s(M)) -> a__plus#(mark(N),mark(M)) ->
    a__plus#(N,0()) -> mark#(N)
    a__plus#(N,s(M)) -> mark#(M) -> mark#(s(X)) -> mark#(X)
    a__plus#(N,s(M)) -> mark#(M) ->
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
    a__plus#(N,s(M)) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X1)
    a__plus#(N,s(M)) -> mark#(M) -> mark#(x(X1,X2)) -> mark#(X2)
    a__plus#(N,s(M)) -> mark#(M) ->
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
    a__plus#(N,s(M)) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X1)
    a__plus#(N,s(M)) -> mark#(M) -> mark#(plus(X1,X2)) -> mark#(X2)
    a__plus#(N,s(M)) -> mark#(M) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__plus#(N,s(M)) -> mark#(M) -> mark#(and(X1,X2)) -> mark#(X1)
    a__plus#(N,s(M)) -> mark#(N) -> mark#(s(X)) -> mark#(X)
    a__plus#(N,s(M)) -> mark#(N) ->
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
    a__plus#(N,s(M)) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1)
    a__plus#(N,s(M)) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2)
    a__plus#(N,s(M)) -> mark#(N) ->
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
    a__plus#(N,s(M)) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1)
    a__plus#(N,s(M)) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2)
    a__plus#(N,s(M)) -> mark#(N) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__plus#(N,s(M)) -> mark#(N) -> mark#(and(X1,X2)) -> mark#(X1)
    a__plus#(N,0()) -> mark#(N) -> mark#(s(X)) -> mark#(X)
    a__plus#(N,0()) -> mark#(N) ->
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
    a__plus#(N,0()) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X1)
    a__plus#(N,0()) -> mark#(N) -> mark#(x(X1,X2)) -> mark#(X2)
    a__plus#(N,0()) -> mark#(N) ->
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
    a__plus#(N,0()) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X1)
    a__plus#(N,0()) -> mark#(N) -> mark#(plus(X1,X2)) -> mark#(X2)
    a__plus#(N,0()) -> mark#(N) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__plus#(N,0()) -> mark#(N) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) ->
    a__x#(N,s(M)) -> a__plus#(a__x(mark(N),mark(M)),mark(N))
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) ->
    a__x#(N,s(M)) -> a__x#(mark(N),mark(M))
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) ->
    a__x#(N,s(M)) -> mark#(N)
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2)) ->
    a__x#(N,s(M)) -> mark#(M)
    mark#(x(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X)
    mark#(x(X1,X2)) -> mark#(X2) ->
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
    mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X1)
    mark#(x(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X2)
    mark#(x(X1,X2)) -> mark#(X2) ->
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
    mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X1)
    mark#(x(X1,X2)) -> mark#(X2) -> mark#(plus(X1,X2)) -> mark#(X2)
    mark#(x(X1,X2)) -> mark#(X2) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(x(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1)
    mark#(x(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(x(X1,X2)) -> mark#(X1) ->
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
    mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1)
    mark#(x(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2)
    mark#(x(X1,X2)) -> mark#(X1) ->
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
    mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1)
    mark#(x(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2)
    mark#(x(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(x(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) ->
    a__plus#(N,s(M)) -> a__plus#(mark(N),mark(M))
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) ->
    a__plus#(N,s(M)) -> mark#(N)
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) ->
    a__plus#(N,s(M)) -> mark#(M)
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2)) ->
    a__plus#(N,0()) -> mark#(N)
    mark#(plus(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X)
    mark#(plus(X1,X2)) -> mark#(X2) ->
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
    mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X1)
    mark#(plus(X1,X2)) -> mark#(X2) -> mark#(x(X1,X2)) -> mark#(X2)
    mark#(plus(X1,X2)) -> mark#(X2) ->
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
    mark#(plus(X1,X2)) -> mark#(X2) ->
    mark#(plus(X1,X2)) -> mark#(X1)
    mark#(plus(X1,X2)) -> mark#(X2) ->
    mark#(plus(X1,X2)) -> mark#(X2)
    mark#(plus(X1,X2)) -> mark#(X2) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(plus(X1,X2)) -> mark#(X2) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(plus(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(plus(X1,X2)) -> mark#(X1) ->
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
    mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1)
    mark#(plus(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2)
    mark#(plus(X1,X2)) -> mark#(X1) ->
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
    mark#(plus(X1,X2)) -> mark#(X1) ->
    mark#(plus(X1,X2)) -> mark#(X1)
    mark#(plus(X1,X2)) -> mark#(X1) ->
    mark#(plus(X1,X2)) -> mark#(X2)
    mark#(plus(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(plus(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(x(X1,X2)) -> mark#(X2)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> mark#(X1) -> mark#(plus(X1,X2)) -> mark#(X2)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(and(X1,X2)) -> mark#(X1) ->
    mark#(and(X1,X2)) -> mark#(X1)
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2) -> a__and#(tt(),X) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
    mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X2)
    mark#(s(X)) -> mark#(X) ->
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
    mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X2)
    mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
    a__and#(tt(),X) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    a__and#(tt(),X) -> mark#(X) ->
    mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
    a__and#(tt(),X) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X1)
    a__and#(tt(),X) -> mark#(X) -> mark#(x(X1,X2)) -> mark#(X2)
    a__and#(tt(),X) -> mark#(X) ->
    mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
    a__and#(tt(),X) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X1)
    a__and#(tt(),X) -> mark#(X) -> mark#(plus(X1,X2)) -> mark#(X2)
    a__and#(tt(),X) -> mark#(X) ->
    mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
    a__and#(tt(),X) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
   Restore Modifier:
    DPs:
     a__and#(tt(),X) -> mark#(X)
     a__plus#(N,0()) -> mark#(N)
     a__plus#(N,s(M)) -> mark#(M)
     a__plus#(N,s(M)) -> mark#(N)
     a__plus#(N,s(M)) -> a__plus#(mark(N),mark(M))
     a__x#(N,s(M)) -> mark#(M)
     a__x#(N,s(M)) -> mark#(N)
     a__x#(N,s(M)) -> a__x#(mark(N),mark(M))
     a__x#(N,s(M)) -> a__plus#(a__x(mark(N),mark(M)),mark(N))
     mark#(and(X1,X2)) -> mark#(X1)
     mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
     mark#(plus(X1,X2)) -> mark#(X2)
     mark#(plus(X1,X2)) -> mark#(X1)
     mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
     mark#(x(X1,X2)) -> mark#(X2)
     mark#(x(X1,X2)) -> mark#(X1)
     mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
     mark#(s(X)) -> mark#(X)
    TRS:
     a__and(tt(),X) -> mark(X)
     a__plus(N,0()) -> mark(N)
     a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
     a__x(N,0()) -> 0()
     a__x(N,s(M)) -> a__plus(a__x(mark(N),mark(M)),mark(N))
     mark(and(X1,X2)) -> a__and(mark(X1),X2)
     mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
     mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
     mark(tt()) -> tt()
     mark(0()) -> 0()
     mark(s(X)) -> s(mark(X))
     a__and(X1,X2) -> and(X1,X2)
     a__plus(X1,X2) -> plus(X1,X2)
     a__x(X1,X2) -> x(X1,X2)
    SCC Processor:
     #sccs: 1
     #rules: 18
     #arcs: 129/324
     DPs:
      a__x#(N,s(M)) -> a__x#(mark(N),mark(M))
      a__x#(N,s(M)) -> mark#(M)
      mark#(and(X1,X2)) -> mark#(X1)
      mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
      a__and#(tt(),X) -> mark#(X)
      mark#(plus(X1,X2)) -> mark#(X2)
      mark#(plus(X1,X2)) -> mark#(X1)
      mark#(plus(X1,X2)) -> a__plus#(mark(X1),mark(X2))
      a__plus#(N,0()) -> mark#(N)
      mark#(x(X1,X2)) -> mark#(X2)
      mark#(x(X1,X2)) -> mark#(X1)
      mark#(x(X1,X2)) -> a__x#(mark(X1),mark(X2))
      a__x#(N,s(M)) -> mark#(N)
      mark#(s(X)) -> mark#(X)
      a__x#(N,s(M)) -> a__plus#(a__x(mark(N),mark(M)),mark(N))
      a__plus#(N,s(M)) -> mark#(M)
      a__plus#(N,s(M)) -> mark#(N)
      a__plus#(N,s(M)) -> a__plus#(mark(N),mark(M))
     TRS:
      a__and(tt(),X) -> mark(X)
      a__plus(N,0()) -> mark(N)
      a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
      a__x(N,0()) -> 0()
      a__x(N,s(M)) -> a__plus(a__x(mark(N),mark(M)),mark(N))
      mark(and(X1,X2)) -> a__and(mark(X1),X2)
      mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
      mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
      mark(tt()) -> tt()
      mark(0()) -> 0()
      mark(s(X)) -> s(mark(X))
      a__and(X1,X2) -> and(X1,X2)
      a__plus(X1,X2) -> plus(X1,X2)
      a__x(X1,X2) -> x(X1,X2)
     Open