MAYBE

Problem:
 plus(0(),x) -> x
 plus(s(x),y) -> s(plus(x,y))
 times(0(),y) -> 0()
 times(s(x),y) -> plus(y,times(x,y))
 exp(x,0()) -> s(0())
 exp(x,s(y)) -> times(x,exp(x,y))
 ge(x,0()) -> true()
 ge(0(),s(x)) -> false()
 ge(s(x),s(y)) -> ge(x,y)
 tower(x,y) -> towerIter(0(),x,y,s(0()))
 towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
 help(true(),c,x,y,z) -> z
 help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))

Proof:
 DP Processor:
  DPs:
   plus#(s(x),y) -> plus#(x,y)
   times#(s(x),y) -> times#(x,y)
   times#(s(x),y) -> plus#(y,times(x,y))
   exp#(x,s(y)) -> exp#(x,y)
   exp#(x,s(y)) -> times#(x,exp(x,y))
   ge#(s(x),s(y)) -> ge#(x,y)
   tower#(x,y) -> towerIter#(0(),x,y,s(0()))
   towerIter#(c,x,y,z) -> ge#(c,x)
   towerIter#(c,x,y,z) -> help#(ge(c,x),c,x,y,z)
   help#(false(),c,x,y,z) -> exp#(y,z)
   help#(false(),c,x,y,z) -> towerIter#(s(c),x,y,exp(y,z))
  TRS:
   plus(0(),x) -> x
   plus(s(x),y) -> s(plus(x,y))
   times(0(),y) -> 0()
   times(s(x),y) -> plus(y,times(x,y))
   exp(x,0()) -> s(0())
   exp(x,s(y)) -> times(x,exp(x,y))
   ge(x,0()) -> true()
   ge(0(),s(x)) -> false()
   ge(s(x),s(y)) -> ge(x,y)
   tower(x,y) -> towerIter(0(),x,y,s(0()))
   towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
   help(true(),c,x,y,z) -> z
   help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
  TDG Processor:
   DPs:
    plus#(s(x),y) -> plus#(x,y)
    times#(s(x),y) -> times#(x,y)
    times#(s(x),y) -> plus#(y,times(x,y))
    exp#(x,s(y)) -> exp#(x,y)
    exp#(x,s(y)) -> times#(x,exp(x,y))
    ge#(s(x),s(y)) -> ge#(x,y)
    tower#(x,y) -> towerIter#(0(),x,y,s(0()))
    towerIter#(c,x,y,z) -> ge#(c,x)
    towerIter#(c,x,y,z) -> help#(ge(c,x),c,x,y,z)
    help#(false(),c,x,y,z) -> exp#(y,z)
    help#(false(),c,x,y,z) -> towerIter#(s(c),x,y,exp(y,z))
   TRS:
    plus(0(),x) -> x
    plus(s(x),y) -> s(plus(x,y))
    times(0(),y) -> 0()
    times(s(x),y) -> plus(y,times(x,y))
    exp(x,0()) -> s(0())
    exp(x,s(y)) -> times(x,exp(x,y))
    ge(x,0()) -> true()
    ge(0(),s(x)) -> false()
    ge(s(x),s(y)) -> ge(x,y)
    tower(x,y) -> towerIter(0(),x,y,s(0()))
    towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
    help(true(),c,x,y,z) -> z
    help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
   graph:
    help#(false(),c,x,y,z) -> towerIter#(s(c),x,y,exp(y,z)) ->
    towerIter#(c,x,y,z) -> help#(ge(c,x),c,x,y,z)
    help#(false(),c,x,y,z) -> towerIter#(s(c),x,y,exp(y,z)) ->
    towerIter#(c,x,y,z) -> ge#(c,x)
    help#(false(),c,x,y,z) -> exp#(y,z) ->
    exp#(x,s(y)) -> times#(x,exp(x,y))
    help#(false(),c,x,y,z) -> exp#(y,z) ->
    exp#(x,s(y)) -> exp#(x,y)
    towerIter#(c,x,y,z) -> help#(ge(c,x),c,x,y,z) ->
    help#(false(),c,x,y,z) -> towerIter#(s(c),x,y,exp(y,z))
    towerIter#(c,x,y,z) -> help#(ge(c,x),c,x,y,z) ->
    help#(false(),c,x,y,z) -> exp#(y,z)
    towerIter#(c,x,y,z) -> ge#(c,x) ->
    ge#(s(x),s(y)) -> ge#(x,y)
    tower#(x,y) -> towerIter#(0(),x,y,s(0())) ->
    towerIter#(c,x,y,z) -> help#(ge(c,x),c,x,y,z)
    tower#(x,y) -> towerIter#(0(),x,y,s(0())) ->
    towerIter#(c,x,y,z) -> ge#(c,x)
    ge#(s(x),s(y)) -> ge#(x,y) -> ge#(s(x),s(y)) -> ge#(x,y)
    exp#(x,s(y)) -> exp#(x,y) -> exp#(x,s(y)) -> times#(x,exp(x,y))
    exp#(x,s(y)) -> exp#(x,y) -> exp#(x,s(y)) -> exp#(x,y)
    exp#(x,s(y)) -> times#(x,exp(x,y)) ->
    times#(s(x),y) -> plus#(y,times(x,y))
    exp#(x,s(y)) -> times#(x,exp(x,y)) ->
    times#(s(x),y) -> times#(x,y)
    times#(s(x),y) -> times#(x,y) ->
    times#(s(x),y) -> plus#(y,times(x,y))
    times#(s(x),y) -> times#(x,y) ->
    times#(s(x),y) -> times#(x,y)
    times#(s(x),y) -> plus#(y,times(x,y)) -> plus#(s(x),y) -> plus#(x,y)
    plus#(s(x),y) -> plus#(x,y) -> plus#(s(x),y) -> plus#(x,y)
   SCC Processor:
    #sccs: 5
    #rules: 6
    #arcs: 18/121
    DPs:
     help#(false(),c,x,y,z) -> towerIter#(s(c),x,y,exp(y,z))
     towerIter#(c,x,y,z) -> help#(ge(c,x),c,x,y,z)
    TRS:
     plus(0(),x) -> x
     plus(s(x),y) -> s(plus(x,y))
     times(0(),y) -> 0()
     times(s(x),y) -> plus(y,times(x,y))
     exp(x,0()) -> s(0())
     exp(x,s(y)) -> times(x,exp(x,y))
     ge(x,0()) -> true()
     ge(0(),s(x)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     tower(x,y) -> towerIter(0(),x,y,s(0()))
     towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
     help(true(),c,x,y,z) -> z
     help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
    Open
    
    DPs:
     exp#(x,s(y)) -> exp#(x,y)
    TRS:
     plus(0(),x) -> x
     plus(s(x),y) -> s(plus(x,y))
     times(0(),y) -> 0()
     times(s(x),y) -> plus(y,times(x,y))
     exp(x,0()) -> s(0())
     exp(x,s(y)) -> times(x,exp(x,y))
     ge(x,0()) -> true()
     ge(0(),s(x)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     tower(x,y) -> towerIter(0(),x,y,s(0()))
     towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
     help(true(),c,x,y,z) -> z
     help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
    Subterm Criterion Processor:
     simple projection:
      pi(exp#) = 1
     problem:
      DPs:
       
      TRS:
       plus(0(),x) -> x
       plus(s(x),y) -> s(plus(x,y))
       times(0(),y) -> 0()
       times(s(x),y) -> plus(y,times(x,y))
       exp(x,0()) -> s(0())
       exp(x,s(y)) -> times(x,exp(x,y))
       ge(x,0()) -> true()
       ge(0(),s(x)) -> false()
       ge(s(x),s(y)) -> ge(x,y)
       tower(x,y) -> towerIter(0(),x,y,s(0()))
       towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
       help(true(),c,x,y,z) -> z
       help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
     Qed
    
    DPs:
     times#(s(x),y) -> times#(x,y)
    TRS:
     plus(0(),x) -> x
     plus(s(x),y) -> s(plus(x,y))
     times(0(),y) -> 0()
     times(s(x),y) -> plus(y,times(x,y))
     exp(x,0()) -> s(0())
     exp(x,s(y)) -> times(x,exp(x,y))
     ge(x,0()) -> true()
     ge(0(),s(x)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     tower(x,y) -> towerIter(0(),x,y,s(0()))
     towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
     help(true(),c,x,y,z) -> z
     help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
    Subterm Criterion Processor:
     simple projection:
      pi(times#) = 0
     problem:
      DPs:
       
      TRS:
       plus(0(),x) -> x
       plus(s(x),y) -> s(plus(x,y))
       times(0(),y) -> 0()
       times(s(x),y) -> plus(y,times(x,y))
       exp(x,0()) -> s(0())
       exp(x,s(y)) -> times(x,exp(x,y))
       ge(x,0()) -> true()
       ge(0(),s(x)) -> false()
       ge(s(x),s(y)) -> ge(x,y)
       tower(x,y) -> towerIter(0(),x,y,s(0()))
       towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
       help(true(),c,x,y,z) -> z
       help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
     Qed
    
    DPs:
     plus#(s(x),y) -> plus#(x,y)
    TRS:
     plus(0(),x) -> x
     plus(s(x),y) -> s(plus(x,y))
     times(0(),y) -> 0()
     times(s(x),y) -> plus(y,times(x,y))
     exp(x,0()) -> s(0())
     exp(x,s(y)) -> times(x,exp(x,y))
     ge(x,0()) -> true()
     ge(0(),s(x)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     tower(x,y) -> towerIter(0(),x,y,s(0()))
     towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
     help(true(),c,x,y,z) -> z
     help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
    Subterm Criterion Processor:
     simple projection:
      pi(plus#) = 0
     problem:
      DPs:
       
      TRS:
       plus(0(),x) -> x
       plus(s(x),y) -> s(plus(x,y))
       times(0(),y) -> 0()
       times(s(x),y) -> plus(y,times(x,y))
       exp(x,0()) -> s(0())
       exp(x,s(y)) -> times(x,exp(x,y))
       ge(x,0()) -> true()
       ge(0(),s(x)) -> false()
       ge(s(x),s(y)) -> ge(x,y)
       tower(x,y) -> towerIter(0(),x,y,s(0()))
       towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
       help(true(),c,x,y,z) -> z
       help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
     Qed
    
    DPs:
     ge#(s(x),s(y)) -> ge#(x,y)
    TRS:
     plus(0(),x) -> x
     plus(s(x),y) -> s(plus(x,y))
     times(0(),y) -> 0()
     times(s(x),y) -> plus(y,times(x,y))
     exp(x,0()) -> s(0())
     exp(x,s(y)) -> times(x,exp(x,y))
     ge(x,0()) -> true()
     ge(0(),s(x)) -> false()
     ge(s(x),s(y)) -> ge(x,y)
     tower(x,y) -> towerIter(0(),x,y,s(0()))
     towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
     help(true(),c,x,y,z) -> z
     help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
    Subterm Criterion Processor:
     simple projection:
      pi(ge#) = 1
     problem:
      DPs:
       
      TRS:
       plus(0(),x) -> x
       plus(s(x),y) -> s(plus(x,y))
       times(0(),y) -> 0()
       times(s(x),y) -> plus(y,times(x,y))
       exp(x,0()) -> s(0())
       exp(x,s(y)) -> times(x,exp(x,y))
       ge(x,0()) -> true()
       ge(0(),s(x)) -> false()
       ge(s(x),s(y)) -> ge(x,y)
       tower(x,y) -> towerIter(0(),x,y,s(0()))
       towerIter(c,x,y,z) -> help(ge(c,x),c,x,y,z)
       help(true(),c,x,y,z) -> z
       help(false(),c,x,y,z) -> towerIter(s(c),x,y,exp(y,z))
     Qed