YES

Problem:
 minus(0()) -> 0()
 +(x,0()) -> x
 +(0(),y) -> y
 +(minus(1()),1()) -> 0()
 minus(minus(x)) -> x
 +(x,minus(y)) -> minus(+(minus(x),y))
 +(x,+(y,z)) -> +(+(x,y),z)
 +(minus(+(x,1())),1()) -> minus(x)

Proof:
 DP Processor:
  DPs:
   +#(x,minus(y)) -> minus#(x)
   +#(x,minus(y)) -> +#(minus(x),y)
   +#(x,minus(y)) -> minus#(+(minus(x),y))
   +#(x,+(y,z)) -> +#(x,y)
   +#(x,+(y,z)) -> +#(+(x,y),z)
   +#(minus(+(x,1())),1()) -> minus#(x)
  TRS:
   minus(0()) -> 0()
   +(x,0()) -> x
   +(0(),y) -> y
   +(minus(1()),1()) -> 0()
   minus(minus(x)) -> x
   +(x,minus(y)) -> minus(+(minus(x),y))
   +(x,+(y,z)) -> +(+(x,y),z)
   +(minus(+(x,1())),1()) -> minus(x)
  TDG Processor:
   DPs:
    +#(x,minus(y)) -> minus#(x)
    +#(x,minus(y)) -> +#(minus(x),y)
    +#(x,minus(y)) -> minus#(+(minus(x),y))
    +#(x,+(y,z)) -> +#(x,y)
    +#(x,+(y,z)) -> +#(+(x,y),z)
    +#(minus(+(x,1())),1()) -> minus#(x)
   TRS:
    minus(0()) -> 0()
    +(x,0()) -> x
    +(0(),y) -> y
    +(minus(1()),1()) -> 0()
    minus(minus(x)) -> x
    +(x,minus(y)) -> minus(+(minus(x),y))
    +(x,+(y,z)) -> +(+(x,y),z)
    +(minus(+(x,1())),1()) -> minus(x)
   graph:
    +#(x,+(y,z)) -> +#(+(x,y),z) ->
    +#(minus(+(x,1())),1()) -> minus#(x)
    +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z)
    +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(x,y)
    +#(x,+(y,z)) -> +#(+(x,y),z) ->
    +#(x,minus(y)) -> minus#(+(minus(x),y))
    +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,minus(y)) -> +#(minus(x),y)
    +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,minus(y)) -> minus#(x)
    +#(x,+(y,z)) -> +#(x,y) -> +#(minus(+(x,1())),1()) -> minus#(x)
    +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z)
    +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y)
    +#(x,+(y,z)) -> +#(x,y) -> +#(x,minus(y)) -> minus#(+(minus(x),y))
    +#(x,+(y,z)) -> +#(x,y) -> +#(x,minus(y)) -> +#(minus(x),y)
    +#(x,+(y,z)) -> +#(x,y) -> +#(x,minus(y)) -> minus#(x)
    +#(x,minus(y)) -> +#(minus(x),y) ->
    +#(minus(+(x,1())),1()) -> minus#(x)
    +#(x,minus(y)) -> +#(minus(x),y) ->
    +#(x,+(y,z)) -> +#(+(x,y),z)
    +#(x,minus(y)) -> +#(minus(x),y) -> +#(x,+(y,z)) -> +#(x,y)
    +#(x,minus(y)) -> +#(minus(x),y) ->
    +#(x,minus(y)) -> minus#(+(minus(x),y))
    +#(x,minus(y)) -> +#(minus(x),y) ->
    +#(x,minus(y)) -> +#(minus(x),y)
    +#(x,minus(y)) -> +#(minus(x),y) -> +#(x,minus(y)) -> minus#(x)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 18/36
    DPs:
     +#(x,+(y,z)) -> +#(+(x,y),z)
     +#(x,minus(y)) -> +#(minus(x),y)
     +#(x,+(y,z)) -> +#(x,y)
    TRS:
     minus(0()) -> 0()
     +(x,0()) -> x
     +(0(),y) -> y
     +(minus(1()),1()) -> 0()
     minus(minus(x)) -> x
     +(x,minus(y)) -> minus(+(minus(x),y))
     +(x,+(y,z)) -> +(+(x,y),z)
     +(minus(+(x,1())),1()) -> minus(x)
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 1
     problem:
      DPs:
       
      TRS:
       minus(0()) -> 0()
       +(x,0()) -> x
       +(0(),y) -> y
       +(minus(1()),1()) -> 0()
       minus(minus(x)) -> x
       +(x,minus(y)) -> minus(+(minus(x),y))
       +(x,+(y,z)) -> +(+(x,y),z)
       +(minus(+(x,1())),1()) -> minus(x)
     Qed