MAYBE

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

Proof:
 DP Processor:
  DPs:
   f#(true(),x,y,z) -> gt#(x,z)
   f#(true(),x,y,z) -> gt#(x,y)
   f#(true(),x,y,z) -> and#(gt(x,y),gt(x,z))
   f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,s(y),z)
   f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,y,s(z))
   gt#(s(u),s(v)) -> gt#(u,v)
  TRS:
   f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,s(y),z)
   f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,y,s(z))
   gt(0(),v) -> false()
   gt(s(u),0()) -> true()
   gt(s(u),s(v)) -> gt(u,v)
   and(x,true()) -> x
   and(x,false()) -> false()
  Usable Rule Processor:
   DPs:
    f#(true(),x,y,z) -> gt#(x,z)
    f#(true(),x,y,z) -> gt#(x,y)
    f#(true(),x,y,z) -> and#(gt(x,y),gt(x,z))
    f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,s(y),z)
    f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,y,s(z))
    gt#(s(u),s(v)) -> gt#(u,v)
   TRS:
    f10(x,y) -> x
    f10(x,y) -> y
    gt(0(),v) -> false()
    gt(s(u),0()) -> true()
    gt(s(u),s(v)) -> gt(u,v)
    and(x,true()) -> x
    and(x,false()) -> false()
   TDG Processor:
    DPs:
     f#(true(),x,y,z) -> gt#(x,z)
     f#(true(),x,y,z) -> gt#(x,y)
     f#(true(),x,y,z) -> and#(gt(x,y),gt(x,z))
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,s(y),z)
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,y,s(z))
     gt#(s(u),s(v)) -> gt#(u,v)
    TRS:
     f10(x,y) -> x
     f10(x,y) -> y
     gt(0(),v) -> false()
     gt(s(u),0()) -> true()
     gt(s(u),s(v)) -> gt(u,v)
     and(x,true()) -> x
     and(x,false()) -> false()
    graph:
     gt#(s(u),s(v)) -> gt#(u,v) -> gt#(s(u),s(v)) -> gt#(u,v)
     f#(true(),x,y,z) -> gt#(x,z) -> gt#(s(u),s(v)) -> gt#(u,v)
     f#(true(),x,y,z) -> gt#(x,y) ->
     gt#(s(u),s(v)) -> gt#(u,v)
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,s(y),z) ->
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,y,s(z))
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,s(y),z) ->
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,s(y),z)
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,s(y),z) ->
     f#(true(),x,y,z) -> and#(gt(x,y),gt(x,z))
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,s(y),z) ->
     f#(true(),x,y,z) -> gt#(x,y)
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,s(y),z) ->
     f#(true(),x,y,z) -> gt#(x,z)
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,y,s(z)) ->
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,y,s(z))
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,y,s(z)) ->
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,s(y),z)
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,y,s(z)) ->
     f#(true(),x,y,z) -> and#(gt(x,y),gt(x,z))
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,y,s(z)) ->
     f#(true(),x,y,z) -> gt#(x,y)
     f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,y,s(z)) -> f#(true(),x,y,z) -> gt#(x,z)
    Restore Modifier:
     DPs:
      f#(true(),x,y,z) -> gt#(x,z)
      f#(true(),x,y,z) -> gt#(x,y)
      f#(true(),x,y,z) -> and#(gt(x,y),gt(x,z))
      f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,s(y),z)
      f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,y,s(z))
      gt#(s(u),s(v)) -> gt#(u,v)
     TRS:
      f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,s(y),z)
      f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,y,s(z))
      gt(0(),v) -> false()
      gt(s(u),0()) -> true()
      gt(s(u),s(v)) -> gt(u,v)
      and(x,true()) -> x
      and(x,false()) -> false()
     SCC Processor:
      #sccs: 2
      #rules: 3
      #arcs: 13/36
      DPs:
       f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,s(y),z)
       f#(true(),x,y,z) -> f#(and(gt(x,y),gt(x,z)),x,y,s(z))
      TRS:
       f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,s(y),z)
       f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,y,s(z))
       gt(0(),v) -> false()
       gt(s(u),0()) -> true()
       gt(s(u),s(v)) -> gt(u,v)
       and(x,true()) -> x
       and(x,false()) -> false()
      Open
      
      DPs:
       gt#(s(u),s(v)) -> gt#(u,v)
      TRS:
       f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,s(y),z)
       f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,y,s(z))
       gt(0(),v) -> false()
       gt(s(u),0()) -> true()
       gt(s(u),s(v)) -> gt(u,v)
       and(x,true()) -> x
       and(x,false()) -> false()
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [gt#](x0, x1) = x0 + 1,
        
        [false] = 0,
        
        [0] = 0,
        
        [s](x0) = x0 + 1,
        
        [and](x0, x1) = x0,
        
        [gt](x0, x1) = 0,
        
        [f](x0, x1, x2, x3) = 0,
        
        [true] = 0
       orientation:
        gt#(s(u),s(v)) = u + 2 >= u + 1 = gt#(u,v)
        
        f(true(),x,y,z) = 0 >= 0 = f(and(gt(x,y),gt(x,z)),x,s(y),z)
        
        f(true(),x,y,z) = 0 >= 0 = f(and(gt(x,y),gt(x,z)),x,y,s(z))
        
        gt(0(),v) = 0 >= 0 = false()
        
        gt(s(u),0()) = 0 >= 0 = true()
        
        gt(s(u),s(v)) = 0 >= 0 = gt(u,v)
        
        and(x,true()) = x >= x = x
        
        and(x,false()) = x >= 0 = false()
       problem:
        DPs:
         
        TRS:
         f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,s(y),z)
         f(true(),x,y,z) -> f(and(gt(x,y),gt(x,z)),x,y,s(z))
         gt(0(),v) -> false()
         gt(s(u),0()) -> true()
         gt(s(u),s(v)) -> gt(u,v)
         and(x,true()) -> x
         and(x,false()) -> false()
       Qed