MAYBE

Problem:
 lcm(x,y) -> lcmIter(x,y,0(),times(x,y))
 lcmIter(x,y,z,u) -> if(or(ge(0(),x),ge(z,u)),x,y,z,u)
 if(true(),x,y,z,u) -> z
 if(false(),x,y,z,u) -> if2(divisible(z,y),x,y,z,u)
 if2(true(),x,y,z,u) -> z
 if2(false(),x,y,z,u) -> lcmIter(x,y,plus(x,z),u)
 plus(0(),y) -> y
 plus(s(x),y) -> s(plus(x,y))
 times(x,y) -> ifTimes(ge(0(),x),x,y)
 ifTimes(true(),x,y) -> 0()
 ifTimes(false(),x,y) -> plus(y,times(y,p(x)))
 p(s(x)) -> x
 p(0()) -> s(s(0()))
 ge(x,0()) -> true()
 ge(0(),s(y)) -> false()
 ge(s(x),s(y)) -> ge(x,y)
 or(true(),y) -> true()
 or(false(),y) -> y
 divisible(0(),s(y)) -> true()
 divisible(s(x),s(y)) -> div(s(x),s(y),s(y))
 div(x,y,0()) -> divisible(x,y)
 div(0(),y,s(z)) -> false()
 div(s(x),y,s(z)) -> div(x,y,z)
 a() -> b()
 a() -> c()

Proof:
 DP Processor:
  DPs:
   lcm#(x,y) -> times#(x,y)
   lcm#(x,y) -> lcmIter#(x,y,0(),times(x,y))
   lcmIter#(x,y,z,u) -> ge#(z,u)
   lcmIter#(x,y,z,u) -> ge#(0(),x)
   lcmIter#(x,y,z,u) -> or#(ge(0(),x),ge(z,u))
   lcmIter#(x,y,z,u) -> if#(or(ge(0(),x),ge(z,u)),x,y,z,u)
   if#(false(),x,y,z,u) -> divisible#(z,y)
   if#(false(),x,y,z,u) -> if2#(divisible(z,y),x,y,z,u)
   if2#(false(),x,y,z,u) -> plus#(x,z)
   if2#(false(),x,y,z,u) -> lcmIter#(x,y,plus(x,z),u)
   plus#(s(x),y) -> plus#(x,y)
   times#(x,y) -> ge#(0(),x)
   times#(x,y) -> ifTimes#(ge(0(),x),x,y)
   ifTimes#(false(),x,y) -> p#(x)
   ifTimes#(false(),x,y) -> times#(y,p(x))
   ifTimes#(false(),x,y) -> plus#(y,times(y,p(x)))
   ge#(s(x),s(y)) -> ge#(x,y)
   divisible#(s(x),s(y)) -> div#(s(x),s(y),s(y))
   div#(x,y,0()) -> divisible#(x,y)
   div#(s(x),y,s(z)) -> div#(x,y,z)
  TRS:
   lcm(x,y) -> lcmIter(x,y,0(),times(x,y))
   lcmIter(x,y,z,u) -> if(or(ge(0(),x),ge(z,u)),x,y,z,u)
   if(true(),x,y,z,u) -> z
   if(false(),x,y,z,u) -> if2(divisible(z,y),x,y,z,u)
   if2(true(),x,y,z,u) -> z
   if2(false(),x,y,z,u) -> lcmIter(x,y,plus(x,z),u)
   plus(0(),y) -> y
   plus(s(x),y) -> s(plus(x,y))
   times(x,y) -> ifTimes(ge(0(),x),x,y)
   ifTimes(true(),x,y) -> 0()
   ifTimes(false(),x,y) -> plus(y,times(y,p(x)))
   p(s(x)) -> x
   p(0()) -> s(s(0()))
   ge(x,0()) -> true()
   ge(0(),s(y)) -> false()
   ge(s(x),s(y)) -> ge(x,y)
   or(true(),y) -> true()
   or(false(),y) -> y
   divisible(0(),s(y)) -> true()
   divisible(s(x),s(y)) -> div(s(x),s(y),s(y))
   div(x,y,0()) -> divisible(x,y)
   div(0(),y,s(z)) -> false()
   div(s(x),y,s(z)) -> div(x,y,z)
   a() -> b()
   a() -> c()
  Usable Rule Processor:
   DPs:
    lcm#(x,y) -> times#(x,y)
    lcm#(x,y) -> lcmIter#(x,y,0(),times(x,y))
    lcmIter#(x,y,z,u) -> ge#(z,u)
    lcmIter#(x,y,z,u) -> ge#(0(),x)
    lcmIter#(x,y,z,u) -> or#(ge(0(),x),ge(z,u))
    lcmIter#(x,y,z,u) -> if#(or(ge(0(),x),ge(z,u)),x,y,z,u)
    if#(false(),x,y,z,u) -> divisible#(z,y)
    if#(false(),x,y,z,u) -> if2#(divisible(z,y),x,y,z,u)
    if2#(false(),x,y,z,u) -> plus#(x,z)
    if2#(false(),x,y,z,u) -> lcmIter#(x,y,plus(x,z),u)
    plus#(s(x),y) -> plus#(x,y)
    times#(x,y) -> ge#(0(),x)
    times#(x,y) -> ifTimes#(ge(0(),x),x,y)
    ifTimes#(false(),x,y) -> p#(x)
    ifTimes#(false(),x,y) -> times#(y,p(x))
    ifTimes#(false(),x,y) -> plus#(y,times(y,p(x)))
    ge#(s(x),s(y)) -> ge#(x,y)
    divisible#(s(x),s(y)) -> div#(s(x),s(y),s(y))
    div#(x,y,0()) -> divisible#(x,y)
    div#(s(x),y,s(z)) -> div#(x,y,z)
   TRS:
    times(x,y) -> ifTimes(ge(0(),x),x,y)
    ifTimes(true(),x,y) -> 0()
    ifTimes(false(),x,y) -> plus(y,times(y,p(x)))
    ge(x,0()) -> true()
    ge(0(),s(y)) -> false()
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(x,y))
    p(s(x)) -> x
    p(0()) -> s(s(0()))
    ge(s(x),s(y)) -> ge(x,y)
    or(true(),y) -> true()
    or(false(),y) -> y
    divisible(0(),s(y)) -> true()
    divisible(s(x),s(y)) -> div(s(x),s(y),s(y))
    div(s(x),y,s(z)) -> div(x,y,z)
    div(x,y,0()) -> divisible(x,y)
    div(0(),y,s(z)) -> false()
   Open