MAYBE

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)
  EDG 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) -> +#(x,minus(y)) -> minus#(x)
    +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,minus(y)) -> +#(minus(x),y)
    +#(x,+(y,z)) -> +#(+(x,y),z) ->
    +#(x,minus(y)) -> minus#(+(minus(x),y))
    +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(x,y)
    +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(x,+(y,z)) -> +#(+(x,y),z)
    +#(x,+(y,z)) -> +#(+(x,y),z) -> +#(minus(+(x,1())),1()) -> minus#(x)
    +#(x,+(y,z)) -> +#(x,y) -> +#(x,minus(y)) -> minus#(x)
    +#(x,+(y,z)) -> +#(x,y) -> +#(x,minus(y)) -> +#(minus(x),y)
    +#(x,+(y,z)) -> +#(x,y) -> +#(x,minus(y)) -> minus#(+(minus(x),y))
    +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(x,y)
    +#(x,+(y,z)) -> +#(x,y) -> +#(x,+(y,z)) -> +#(+(x,y),z)
    +#(x,+(y,z)) -> +#(x,y) -> +#(minus(+(x,1())),1()) -> minus#(x)
    +#(x,minus(y)) -> +#(minus(x),y) -> +#(x,minus(y)) -> minus#(x)
    +#(x,minus(y)) -> +#(minus(x),y) ->
    +#(x,minus(y)) -> +#(minus(x),y)
    +#(x,minus(y)) -> +#(minus(x),y) ->
    +#(x,minus(y)) -> minus#(+(minus(x),y))
    +#(x,minus(y)) -> +#(minus(x),y) -> +#(x,+(y,z)) -> +#(x,y)
    +#(x,minus(y)) -> +#(minus(x),y) ->
    +#(x,+(y,z)) -> +#(+(x,y),z)
    +#(x,minus(y)) -> +#(minus(x),y) -> +#(minus(+(x,1())),1()) -> minus#(x)
   Restore Modifier:
    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)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 18/36
     DPs:
      +#(x,+(y,z)) -> +#(+(x,y),z)
      +#(x,+(y,z)) -> +#(x,y)
      +#(x,minus(y)) -> +#(minus(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)
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [+#](x0, x1) = x1,
       
       [1] = 0,
       
       [+](x0, x1) = x0 + x1 + 1,
       
       [minus](x0) = x0,
       
       [0] = 1
      orientation:
       +#(x,+(y,z)) = y + z + 1 >= z = +#(+(x,y),z)
       
       +#(x,+(y,z)) = y + z + 1 >= y = +#(x,y)
       
       +#(x,minus(y)) = y >= y = +#(minus(x),y)
       
       minus(0()) = 1 >= 1 = 0()
       
       +(x,0()) = x + 2 >= x = x
       
       +(0(),y) = y + 2 >= y = y
       
       +(minus(1()),1()) = 1 >= 1 = 0()
       
       minus(minus(x)) = x >= x = x
       
       +(x,minus(y)) = x + y + 1 >= x + y + 1 = minus(+(minus(x),y))
       
       +(x,+(y,z)) = x + y + z + 2 >= x + y + z + 2 = +(+(x,y),z)
       
       +(minus(+(x,1())),1()) = x + 2 >= x = minus(x)
      problem:
       DPs:
        +#(x,minus(y)) -> +#(minus(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)
      Open