MAYBE

Problem:
 f(true(),x,y) -> f(gt(x,y),x,round(s(y)))
 round(0()) -> 0()
 round(s(0())) -> s(s(0()))
 round(s(s(x))) -> s(s(round(x)))
 gt(0(),v) -> false()
 gt(s(u),0()) -> true()
 gt(s(u),s(v)) -> gt(u,v)

Proof:
 DP Processor:
  DPs:
   f#(true(),x,y) -> round#(s(y))
   f#(true(),x,y) -> gt#(x,y)
   f#(true(),x,y) -> f#(gt(x,y),x,round(s(y)))
   round#(s(s(x))) -> round#(x)
   gt#(s(u),s(v)) -> gt#(u,v)
  TRS:
   f(true(),x,y) -> f(gt(x,y),x,round(s(y)))
   round(0()) -> 0()
   round(s(0())) -> s(s(0()))
   round(s(s(x))) -> s(s(round(x)))
   gt(0(),v) -> false()
   gt(s(u),0()) -> true()
   gt(s(u),s(v)) -> gt(u,v)
  TDG Processor:
   DPs:
    f#(true(),x,y) -> round#(s(y))
    f#(true(),x,y) -> gt#(x,y)
    f#(true(),x,y) -> f#(gt(x,y),x,round(s(y)))
    round#(s(s(x))) -> round#(x)
    gt#(s(u),s(v)) -> gt#(u,v)
   TRS:
    f(true(),x,y) -> f(gt(x,y),x,round(s(y)))
    round(0()) -> 0()
    round(s(0())) -> s(s(0()))
    round(s(s(x))) -> s(s(round(x)))
    gt(0(),v) -> false()
    gt(s(u),0()) -> true()
    gt(s(u),s(v)) -> gt(u,v)
   graph:
    gt#(s(u),s(v)) -> gt#(u,v) -> gt#(s(u),s(v)) -> gt#(u,v)
    round#(s(s(x))) -> round#(x) -> round#(s(s(x))) -> round#(x)
    f#(true(),x,y) -> gt#(x,y) -> gt#(s(u),s(v)) -> gt#(u,v)
    f#(true(),x,y) -> round#(s(y)) ->
    round#(s(s(x))) -> round#(x)
    f#(true(),x,y) -> f#(gt(x,y),x,round(s(y))) ->
    f#(true(),x,y) -> f#(gt(x,y),x,round(s(y)))
    f#(true(),x,y) -> f#(gt(x,y),x,round(s(y))) ->
    f#(true(),x,y) -> gt#(x,y)
    f#(true(),x,y) -> f#(gt(x,y),x,round(s(y))) -> f#(true(),x,y) -> round#(s(y))
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 7/25
    DPs:
     f#(true(),x,y) -> f#(gt(x,y),x,round(s(y)))
    TRS:
     f(true(),x,y) -> f(gt(x,y),x,round(s(y)))
     round(0()) -> 0()
     round(s(0())) -> s(s(0()))
     round(s(s(x))) -> s(s(round(x)))
     gt(0(),v) -> false()
     gt(s(u),0()) -> true()
     gt(s(u),s(v)) -> gt(u,v)
    Open
    
    DPs:
     round#(s(s(x))) -> round#(x)
    TRS:
     f(true(),x,y) -> f(gt(x,y),x,round(s(y)))
     round(0()) -> 0()
     round(s(0())) -> s(s(0()))
     round(s(s(x))) -> s(s(round(x)))
     gt(0(),v) -> false()
     gt(s(u),0()) -> true()
     gt(s(u),s(v)) -> gt(u,v)
    Subterm Criterion Processor:
     simple projection:
      pi(round#) = 0
     problem:
      DPs:
       
      TRS:
       f(true(),x,y) -> f(gt(x,y),x,round(s(y)))
       round(0()) -> 0()
       round(s(0())) -> s(s(0()))
       round(s(s(x))) -> s(s(round(x)))
       gt(0(),v) -> false()
       gt(s(u),0()) -> true()
       gt(s(u),s(v)) -> gt(u,v)
     Qed
    
    DPs:
     gt#(s(u),s(v)) -> gt#(u,v)
    TRS:
     f(true(),x,y) -> f(gt(x,y),x,round(s(y)))
     round(0()) -> 0()
     round(s(0())) -> s(s(0()))
     round(s(s(x))) -> s(s(round(x)))
     gt(0(),v) -> false()
     gt(s(u),0()) -> true()
     gt(s(u),s(v)) -> gt(u,v)
    Subterm Criterion Processor:
     simple projection:
      pi(gt#) = 1
     problem:
      DPs:
       
      TRS:
       f(true(),x,y) -> f(gt(x,y),x,round(s(y)))
       round(0()) -> 0()
       round(s(0())) -> s(s(0()))
       round(s(s(x))) -> s(s(round(x)))
       gt(0(),v) -> false()
       gt(s(u),0()) -> true()
       gt(s(u),s(v)) -> gt(u,v)
     Qed