MAYBE

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

Proof:
 DP Processor:
  DPs:
   minus#(x,y) -> min#(x,y)
   minus#(x,y) -> equal#(min(x,y),y)
   minus#(x,y) -> cond#(equal(min(x,y),y),x,y)
   cond#(true(),x,y) -> minus#(x,s(y))
   min#(s(u),s(v)) -> min#(u,v)
   equal#(s(x),s(y)) -> equal#(x,y)
  TRS:
   minus(x,y) -> cond(equal(min(x,y),y),x,y)
   cond(true(),x,y) -> s(minus(x,s(y)))
   min(0(),v) -> 0()
   min(u,0()) -> 0()
   min(s(u),s(v)) -> s(min(u,v))
   equal(0(),0()) -> true()
   equal(s(x),0()) -> false()
   equal(0(),s(y)) -> false()
   equal(s(x),s(y)) -> equal(x,y)
  TDG Processor:
   DPs:
    minus#(x,y) -> min#(x,y)
    minus#(x,y) -> equal#(min(x,y),y)
    minus#(x,y) -> cond#(equal(min(x,y),y),x,y)
    cond#(true(),x,y) -> minus#(x,s(y))
    min#(s(u),s(v)) -> min#(u,v)
    equal#(s(x),s(y)) -> equal#(x,y)
   TRS:
    minus(x,y) -> cond(equal(min(x,y),y),x,y)
    cond(true(),x,y) -> s(minus(x,s(y)))
    min(0(),v) -> 0()
    min(u,0()) -> 0()
    min(s(u),s(v)) -> s(min(u,v))
    equal(0(),0()) -> true()
    equal(s(x),0()) -> false()
    equal(0(),s(y)) -> false()
    equal(s(x),s(y)) -> equal(x,y)
   graph:
    cond#(true(),x,y) -> minus#(x,s(y)) ->
    minus#(x,y) -> cond#(equal(min(x,y),y),x,y)
    cond#(true(),x,y) -> minus#(x,s(y)) ->
    minus#(x,y) -> equal#(min(x,y),y)
    cond#(true(),x,y) -> minus#(x,s(y)) -> minus#(x,y) -> min#(x,y)
    equal#(s(x),s(y)) -> equal#(x,y) ->
    equal#(s(x),s(y)) -> equal#(x,y)
    min#(s(u),s(v)) -> min#(u,v) ->
    min#(s(u),s(v)) -> min#(u,v)
    minus#(x,y) -> cond#(equal(min(x,y),y),x,y) ->
    cond#(true(),x,y) -> minus#(x,s(y))
    minus#(x,y) -> equal#(min(x,y),y) -> equal#(s(x),s(y)) -> equal#(x,y)
    minus#(x,y) -> min#(x,y) -> min#(s(u),s(v)) -> min#(u,v)
   SCC Processor:
    #sccs: 3
    #rules: 4
    #arcs: 8/36
    DPs:
     cond#(true(),x,y) -> minus#(x,s(y))
     minus#(x,y) -> cond#(equal(min(x,y),y),x,y)
    TRS:
     minus(x,y) -> cond(equal(min(x,y),y),x,y)
     cond(true(),x,y) -> s(minus(x,s(y)))
     min(0(),v) -> 0()
     min(u,0()) -> 0()
     min(s(u),s(v)) -> s(min(u,v))
     equal(0(),0()) -> true()
     equal(s(x),0()) -> false()
     equal(0(),s(y)) -> false()
     equal(s(x),s(y)) -> equal(x,y)
    Open
    
    DPs:
     equal#(s(x),s(y)) -> equal#(x,y)
    TRS:
     minus(x,y) -> cond(equal(min(x,y),y),x,y)
     cond(true(),x,y) -> s(minus(x,s(y)))
     min(0(),v) -> 0()
     min(u,0()) -> 0()
     min(s(u),s(v)) -> s(min(u,v))
     equal(0(),0()) -> true()
     equal(s(x),0()) -> false()
     equal(0(),s(y)) -> false()
     equal(s(x),s(y)) -> equal(x,y)
    Subterm Criterion Processor:
     simple projection:
      pi(equal#) = 1
     problem:
      DPs:
       
      TRS:
       minus(x,y) -> cond(equal(min(x,y),y),x,y)
       cond(true(),x,y) -> s(minus(x,s(y)))
       min(0(),v) -> 0()
       min(u,0()) -> 0()
       min(s(u),s(v)) -> s(min(u,v))
       equal(0(),0()) -> true()
       equal(s(x),0()) -> false()
       equal(0(),s(y)) -> false()
       equal(s(x),s(y)) -> equal(x,y)
     Qed
    
    DPs:
     min#(s(u),s(v)) -> min#(u,v)
    TRS:
     minus(x,y) -> cond(equal(min(x,y),y),x,y)
     cond(true(),x,y) -> s(minus(x,s(y)))
     min(0(),v) -> 0()
     min(u,0()) -> 0()
     min(s(u),s(v)) -> s(min(u,v))
     equal(0(),0()) -> true()
     equal(s(x),0()) -> false()
     equal(0(),s(y)) -> false()
     equal(s(x),s(y)) -> equal(x,y)
    Subterm Criterion Processor:
     simple projection:
      pi(min#) = 1
     problem:
      DPs:
       
      TRS:
       minus(x,y) -> cond(equal(min(x,y),y),x,y)
       cond(true(),x,y) -> s(minus(x,s(y)))
       min(0(),v) -> 0()
       min(u,0()) -> 0()
       min(s(u),s(v)) -> s(min(u,v))
       equal(0(),0()) -> true()
       equal(s(x),0()) -> false()
       equal(0(),s(y)) -> false()
       equal(s(x),s(y)) -> equal(x,y)
     Qed