MAYBE

Problem:
 minus(x,y) -> cond(ge(x,s(y)),x,y)
 cond(false(),x,y) -> 0()
 cond(true(),x,y) -> s(minus(x,s(y)))
 ge(u,0()) -> true()
 ge(0(),s(v)) -> false()
 ge(s(u),s(v)) -> ge(u,v)

Proof:
 DP Processor:
  DPs:
   minus#(x,y) -> ge#(x,s(y))
   minus#(x,y) -> cond#(ge(x,s(y)),x,y)
   cond#(true(),x,y) -> minus#(x,s(y))
   ge#(s(u),s(v)) -> ge#(u,v)
  TRS:
   minus(x,y) -> cond(ge(x,s(y)),x,y)
   cond(false(),x,y) -> 0()
   cond(true(),x,y) -> s(minus(x,s(y)))
   ge(u,0()) -> true()
   ge(0(),s(v)) -> false()
   ge(s(u),s(v)) -> ge(u,v)
  TDG Processor:
   DPs:
    minus#(x,y) -> ge#(x,s(y))
    minus#(x,y) -> cond#(ge(x,s(y)),x,y)
    cond#(true(),x,y) -> minus#(x,s(y))
    ge#(s(u),s(v)) -> ge#(u,v)
   TRS:
    minus(x,y) -> cond(ge(x,s(y)),x,y)
    cond(false(),x,y) -> 0()
    cond(true(),x,y) -> s(minus(x,s(y)))
    ge(u,0()) -> true()
    ge(0(),s(v)) -> false()
    ge(s(u),s(v)) -> ge(u,v)
   graph:
    cond#(true(),x,y) -> minus#(x,s(y)) ->
    minus#(x,y) -> cond#(ge(x,s(y)),x,y)
    cond#(true(),x,y) -> minus#(x,s(y)) -> minus#(x,y) -> ge#(x,s(y))
    ge#(s(u),s(v)) -> ge#(u,v) -> ge#(s(u),s(v)) -> ge#(u,v)
    minus#(x,y) -> cond#(ge(x,s(y)),x,y) ->
    cond#(true(),x,y) -> minus#(x,s(y))
    minus#(x,y) -> ge#(x,s(y)) -> ge#(s(u),s(v)) -> ge#(u,v)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 5/16
    DPs:
     cond#(true(),x,y) -> minus#(x,s(y))
     minus#(x,y) -> cond#(ge(x,s(y)),x,y)
    TRS:
     minus(x,y) -> cond(ge(x,s(y)),x,y)
     cond(false(),x,y) -> 0()
     cond(true(),x,y) -> s(minus(x,s(y)))
     ge(u,0()) -> true()
     ge(0(),s(v)) -> false()
     ge(s(u),s(v)) -> ge(u,v)
    Open
    
    DPs:
     ge#(s(u),s(v)) -> ge#(u,v)
    TRS:
     minus(x,y) -> cond(ge(x,s(y)),x,y)
     cond(false(),x,y) -> 0()
     cond(true(),x,y) -> s(minus(x,s(y)))
     ge(u,0()) -> true()
     ge(0(),s(v)) -> false()
     ge(s(u),s(v)) -> ge(u,v)
    Subterm Criterion Processor:
     simple projection:
      pi(ge#) = 1
     problem:
      DPs:
       
      TRS:
       minus(x,y) -> cond(ge(x,s(y)),x,y)
       cond(false(),x,y) -> 0()
       cond(true(),x,y) -> s(minus(x,s(y)))
       ge(u,0()) -> true()
       ge(0(),s(v)) -> false()
       ge(s(u),s(v)) -> ge(u,v)
     Qed