MAYBE

Problem:
 ge(x,0()) -> true()
 ge(0(),s(y)) -> false()
 ge(s(x),s(y)) -> ge(x,y)
 rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
 if(x,true(),z,c,l) -> z
 if(x,false(),z,c,l) -> help(s(c),l,x,z)
 help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
 append(nil(),y) -> y
 append(cons(x,y),z) -> cons(x,append(y,z))
 length(nil()) -> 0()
 length(cons(x,y)) -> s(length(y))

Proof:
 DP Processor:
  DPs:
   ge#(s(x),s(y)) -> ge#(x,y)
   rev#(x) -> length#(x)
   rev#(x) -> if#(x,eq(0(),length(x)),nil(),0(),length(x))
   if#(x,false(),z,c,l) -> help#(s(c),l,x,z)
   help#(c,l,cons(x,y),z) -> ge#(c,l)
   help#(c,l,cons(x,y),z) -> append#(y,cons(x,nil()))
   help#(c,l,cons(x,y),z) -> if#(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
   append#(cons(x,y),z) -> append#(y,z)
   length#(cons(x,y)) -> length#(y)
  TRS:
   ge(x,0()) -> true()
   ge(0(),s(y)) -> false()
   ge(s(x),s(y)) -> ge(x,y)
   rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
   if(x,true(),z,c,l) -> z
   if(x,false(),z,c,l) -> help(s(c),l,x,z)
   help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
   append(nil(),y) -> y
   append(cons(x,y),z) -> cons(x,append(y,z))
   length(nil()) -> 0()
   length(cons(x,y)) -> s(length(y))
  TDG Processor:
   DPs:
    ge#(s(x),s(y)) -> ge#(x,y)
    rev#(x) -> length#(x)
    rev#(x) -> if#(x,eq(0(),length(x)),nil(),0(),length(x))
    if#(x,false(),z,c,l) -> help#(s(c),l,x,z)
    help#(c,l,cons(x,y),z) -> ge#(c,l)
    help#(c,l,cons(x,y),z) -> append#(y,cons(x,nil()))
    help#(c,l,cons(x,y),z) -> if#(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
    append#(cons(x,y),z) -> append#(y,z)
    length#(cons(x,y)) -> length#(y)
   TRS:
    ge(x,0()) -> true()
    ge(0(),s(y)) -> false()
    ge(s(x),s(y)) -> ge(x,y)
    rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
    if(x,true(),z,c,l) -> z
    if(x,false(),z,c,l) -> help(s(c),l,x,z)
    help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
    append(nil(),y) -> y
    append(cons(x,y),z) -> cons(x,append(y,z))
    length(nil()) -> 0()
    length(cons(x,y)) -> s(length(y))
   graph:
    append#(cons(x,y),z) -> append#(y,z) ->
    append#(cons(x,y),z) -> append#(y,z)
    help#(c,l,cons(x,y),z) -> append#(y,cons(x,nil())) ->
    append#(cons(x,y),z) -> append#(y,z)
    help#(c,l,cons(x,y),z) -> if#(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l) ->
    if#(x,false(),z,c,l) -> help#(s(c),l,x,z)
    help#(c,l,cons(x,y),z) -> ge#(c,l) ->
    ge#(s(x),s(y)) -> ge#(x,y)
    if#(x,false(),z,c,l) -> help#(s(c),l,x,z) ->
    help#(c,l,cons(x,y),z) -> if#(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
    if#(x,false(),z,c,l) -> help#(s(c),l,x,z) ->
    help#(c,l,cons(x,y),z) -> append#(y,cons(x,nil()))
    if#(x,false(),z,c,l) -> help#(s(c),l,x,z) ->
    help#(c,l,cons(x,y),z) -> ge#(c,l)
    length#(cons(x,y)) -> length#(y) ->
    length#(cons(x,y)) -> length#(y)
    rev#(x) -> if#(x,eq(0(),length(x)),nil(),0(),length(x)) ->
    if#(x,false(),z,c,l) -> help#(s(c),l,x,z)
    rev#(x) -> length#(x) -> length#(cons(x,y)) -> length#(y)
    ge#(s(x),s(y)) -> ge#(x,y) -> ge#(s(x),s(y)) -> ge#(x,y)
   SCC Processor:
    #sccs: 4
    #rules: 5
    #arcs: 11/81
    DPs:
     length#(cons(x,y)) -> length#(y)
    TRS:
     ge(x,0()) -> true()
     ge(0(),s(y)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
     if(x,true(),z,c,l) -> z
     if(x,false(),z,c,l) -> help(s(c),l,x,z)
     help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
     append(nil(),y) -> y
     append(cons(x,y),z) -> cons(x,append(y,z))
     length(nil()) -> 0()
     length(cons(x,y)) -> s(length(y))
    Subterm Criterion Processor:
     simple projection:
      pi(length#) = 0
     problem:
      DPs:
       
      TRS:
       ge(x,0()) -> true()
       ge(0(),s(y)) -> false()
       ge(s(x),s(y)) -> ge(x,y)
       rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
       if(x,true(),z,c,l) -> z
       if(x,false(),z,c,l) -> help(s(c),l,x,z)
       help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
       append(nil(),y) -> y
       append(cons(x,y),z) -> cons(x,append(y,z))
       length(nil()) -> 0()
       length(cons(x,y)) -> s(length(y))
     Qed
    
    DPs:
     help#(c,l,cons(x,y),z) -> if#(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
     if#(x,false(),z,c,l) -> help#(s(c),l,x,z)
    TRS:
     ge(x,0()) -> true()
     ge(0(),s(y)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
     if(x,true(),z,c,l) -> z
     if(x,false(),z,c,l) -> help(s(c),l,x,z)
     help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
     append(nil(),y) -> y
     append(cons(x,y),z) -> cons(x,append(y,z))
     length(nil()) -> 0()
     length(cons(x,y)) -> s(length(y))
    Open
    
    DPs:
     ge#(s(x),s(y)) -> ge#(x,y)
    TRS:
     ge(x,0()) -> true()
     ge(0(),s(y)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
     if(x,true(),z,c,l) -> z
     if(x,false(),z,c,l) -> help(s(c),l,x,z)
     help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
     append(nil(),y) -> y
     append(cons(x,y),z) -> cons(x,append(y,z))
     length(nil()) -> 0()
     length(cons(x,y)) -> s(length(y))
    Subterm Criterion Processor:
     simple projection:
      pi(ge#) = 1
     problem:
      DPs:
       
      TRS:
       ge(x,0()) -> true()
       ge(0(),s(y)) -> false()
       ge(s(x),s(y)) -> ge(x,y)
       rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
       if(x,true(),z,c,l) -> z
       if(x,false(),z,c,l) -> help(s(c),l,x,z)
       help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
       append(nil(),y) -> y
       append(cons(x,y),z) -> cons(x,append(y,z))
       length(nil()) -> 0()
       length(cons(x,y)) -> s(length(y))
     Qed
    
    DPs:
     append#(cons(x,y),z) -> append#(y,z)
    TRS:
     ge(x,0()) -> true()
     ge(0(),s(y)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
     if(x,true(),z,c,l) -> z
     if(x,false(),z,c,l) -> help(s(c),l,x,z)
     help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
     append(nil(),y) -> y
     append(cons(x,y),z) -> cons(x,append(y,z))
     length(nil()) -> 0()
     length(cons(x,y)) -> s(length(y))
    Subterm Criterion Processor:
     simple projection:
      pi(append#) = 0
     problem:
      DPs:
       
      TRS:
       ge(x,0()) -> true()
       ge(0(),s(y)) -> false()
       ge(s(x),s(y)) -> ge(x,y)
       rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
       if(x,true(),z,c,l) -> z
       if(x,false(),z,c,l) -> help(s(c),l,x,z)
       help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
       append(nil(),y) -> y
       append(cons(x,y),z) -> cons(x,append(y,z))
       length(nil()) -> 0()
       length(cons(x,y)) -> s(length(y))
     Qed