MAYBE

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