MAYBE

Problem:
 f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,s(y),z)
 f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,y,s(z))
 plus(n,0()) -> n
 plus(n,s(m)) -> s(plus(n,m))
 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,z) -> plus#(y,z)
   f#(true(),x,y,z) -> gt#(x,plus(y,z))
   f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,s(y),z)
   f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,y,s(z))
   plus#(n,s(m)) -> plus#(n,m)
   gt#(s(u),s(v)) -> gt#(u,v)
  TRS:
   f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,s(y),z)
   f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,y,s(z))
   plus(n,0()) -> n
   plus(n,s(m)) -> s(plus(n,m))
   gt(0(),v) -> false()
   gt(s(u),0()) -> true()
   gt(s(u),s(v)) -> gt(u,v)
  TDG Processor:
   DPs:
    f#(true(),x,y,z) -> plus#(y,z)
    f#(true(),x,y,z) -> gt#(x,plus(y,z))
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,s(y),z)
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,y,s(z))
    plus#(n,s(m)) -> plus#(n,m)
    gt#(s(u),s(v)) -> gt#(u,v)
   TRS:
    f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,s(y),z)
    f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,y,s(z))
    plus(n,0()) -> n
    plus(n,s(m)) -> s(plus(n,m))
    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)
    plus#(n,s(m)) -> plus#(n,m) -> plus#(n,s(m)) -> plus#(n,m)
    f#(true(),x,y,z) -> gt#(x,plus(y,z)) ->
    gt#(s(u),s(v)) -> gt#(u,v)
    f#(true(),x,y,z) -> plus#(y,z) ->
    plus#(n,s(m)) -> plus#(n,m)
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,s(y),z) ->
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,y,s(z))
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,s(y),z) ->
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,s(y),z)
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,s(y),z) ->
    f#(true(),x,y,z) -> gt#(x,plus(y,z))
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,s(y),z) ->
    f#(true(),x,y,z) -> plus#(y,z)
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,y,s(z)) ->
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,y,s(z))
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,y,s(z)) ->
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,s(y),z)
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,y,s(z)) ->
    f#(true(),x,y,z) -> gt#(x,plus(y,z))
    f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,y,s(z)) -> f#(true(),x,y,z) -> plus#(y,z)
   SCC Processor:
    #sccs: 3
    #rules: 4
    #arcs: 12/36
    DPs:
     f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,s(y),z)
     f#(true(),x,y,z) -> f#(gt(x,plus(y,z)),x,y,s(z))
    TRS:
     f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,s(y),z)
     f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,y,s(z))
     plus(n,0()) -> n
     plus(n,s(m)) -> s(plus(n,m))
     gt(0(),v) -> false()
     gt(s(u),0()) -> true()
     gt(s(u),s(v)) -> gt(u,v)
    Open
    
    DPs:
     plus#(n,s(m)) -> plus#(n,m)
    TRS:
     f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,s(y),z)
     f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,y,s(z))
     plus(n,0()) -> n
     plus(n,s(m)) -> s(plus(n,m))
     gt(0(),v) -> false()
     gt(s(u),0()) -> true()
     gt(s(u),s(v)) -> gt(u,v)
    KBO Processor:
     argument filtering:
      pi(true) = []
      pi(f) = 1
      pi(plus) = [0,1]
      pi(gt) = 0
      pi(s) = [0]
      pi(0) = []
      pi(false) = []
      pi(plus#) = 1
     weight function:
      w0 = 1
      w(plus#) = w(false) = w(0) = w(s) = w(gt) = w(plus) = w(f) = w(true) = 1
     precedence:
      plus# ~ 0 ~ plus ~ true > false ~ s ~ gt ~ f
     problem:
      DPs:
       
      TRS:
       f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,s(y),z)
       f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,y,s(z))
       plus(n,0()) -> n
       plus(n,s(m)) -> s(plus(n,m))
       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,z) -> f(gt(x,plus(y,z)),x,s(y),z)
     f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,y,s(z))
     plus(n,0()) -> n
     plus(n,s(m)) -> s(plus(n,m))
     gt(0(),v) -> false()
     gt(s(u),0()) -> true()
     gt(s(u),s(v)) -> gt(u,v)
    KBO Processor:
     argument filtering:
      pi(true) = []
      pi(f) = 1
      pi(plus) = [0,1]
      pi(gt) = 0
      pi(s) = [0]
      pi(0) = []
      pi(false) = []
      pi(gt#) = 1
     weight function:
      w0 = 1
      w(gt#) = w(false) = w(0) = w(s) = w(gt) = w(plus) = w(f) = w(true) = 1
     precedence:
      gt# ~ plus > 0 > false ~ s ~ gt ~ f ~ true
     problem:
      DPs:
       
      TRS:
       f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,s(y),z)
       f(true(),x,y,z) -> f(gt(x,plus(y,z)),x,y,s(z))
       plus(n,0()) -> n
       plus(n,s(m)) -> s(plus(n,m))
       gt(0(),v) -> false()
       gt(s(u),0()) -> true()
       gt(s(u),s(v)) -> gt(u,v)
     Qed