MAYBE

Problem:
 active(f(X)) -> mark(if(X,c(),f(true())))
 active(if(true(),X,Y)) -> mark(X)
 active(if(false(),X,Y)) -> mark(Y)
 mark(f(X)) -> active(f(mark(X)))
 mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
 mark(c()) -> active(c())
 mark(true()) -> active(true())
 mark(false()) -> active(false())
 f(mark(X)) -> f(X)
 f(active(X)) -> f(X)
 if(mark(X1),X2,X3) -> if(X1,X2,X3)
 if(X1,mark(X2),X3) -> if(X1,X2,X3)
 if(X1,X2,mark(X3)) -> if(X1,X2,X3)
 if(active(X1),X2,X3) -> if(X1,X2,X3)
 if(X1,active(X2),X3) -> if(X1,X2,X3)
 if(X1,X2,active(X3)) -> if(X1,X2,X3)

Proof:
 DP Processor:
  DPs:
   active#(f(X)) -> f#(true())
   active#(f(X)) -> if#(X,c(),f(true()))
   active#(f(X)) -> mark#(if(X,c(),f(true())))
   active#(if(true(),X,Y)) -> mark#(X)
   active#(if(false(),X,Y)) -> mark#(Y)
   mark#(f(X)) -> mark#(X)
   mark#(f(X)) -> f#(mark(X))
   mark#(f(X)) -> active#(f(mark(X)))
   mark#(if(X1,X2,X3)) -> mark#(X2)
   mark#(if(X1,X2,X3)) -> mark#(X1)
   mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3)
   mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3))
   mark#(c()) -> active#(c())
   mark#(true()) -> active#(true())
   mark#(false()) -> active#(false())
   f#(mark(X)) -> f#(X)
   f#(active(X)) -> f#(X)
   if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
   if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
   if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
   if#(active(X1),X2,X3) -> if#(X1,X2,X3)
   if#(X1,active(X2),X3) -> if#(X1,X2,X3)
   if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
  TRS:
   active(f(X)) -> mark(if(X,c(),f(true())))
   active(if(true(),X,Y)) -> mark(X)
   active(if(false(),X,Y)) -> mark(Y)
   mark(f(X)) -> active(f(mark(X)))
   mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
   mark(c()) -> active(c())
   mark(true()) -> active(true())
   mark(false()) -> active(false())
   f(mark(X)) -> f(X)
   f(active(X)) -> f(X)
   if(mark(X1),X2,X3) -> if(X1,X2,X3)
   if(X1,mark(X2),X3) -> if(X1,X2,X3)
   if(X1,X2,mark(X3)) -> if(X1,X2,X3)
   if(active(X1),X2,X3) -> if(X1,X2,X3)
   if(X1,active(X2),X3) -> if(X1,X2,X3)
   if(X1,X2,active(X3)) -> if(X1,X2,X3)
  EDG Processor:
   DPs:
    active#(f(X)) -> f#(true())
    active#(f(X)) -> if#(X,c(),f(true()))
    active#(f(X)) -> mark#(if(X,c(),f(true())))
    active#(if(true(),X,Y)) -> mark#(X)
    active#(if(false(),X,Y)) -> mark#(Y)
    mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> f#(mark(X))
    mark#(f(X)) -> active#(f(mark(X)))
    mark#(if(X1,X2,X3)) -> mark#(X2)
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3)
    mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3))
    mark#(c()) -> active#(c())
    mark#(true()) -> active#(true())
    mark#(false()) -> active#(false())
    f#(mark(X)) -> f#(X)
    f#(active(X)) -> f#(X)
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
    if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
    if#(active(X1),X2,X3) -> if#(X1,X2,X3)
    if#(X1,active(X2),X3) -> if#(X1,X2,X3)
    if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
   TRS:
    active(f(X)) -> mark(if(X,c(),f(true())))
    active(if(true(),X,Y)) -> mark(X)
    active(if(false(),X,Y)) -> mark(Y)
    mark(f(X)) -> active(f(mark(X)))
    mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
    mark(c()) -> active(c())
    mark(true()) -> active(true())
    mark(false()) -> active(false())
    f(mark(X)) -> f(X)
    f(active(X)) -> f(X)
    if(mark(X1),X2,X3) -> if(X1,X2,X3)
    if(X1,mark(X2),X3) -> if(X1,X2,X3)
    if(X1,X2,mark(X3)) -> if(X1,X2,X3)
    if(active(X1),X2,X3) -> if(X1,X2,X3)
    if(X1,active(X2),X3) -> if(X1,X2,X3)
    if(X1,X2,active(X3)) -> if(X1,X2,X3)
   graph:
    mark#(if(X1,X2,X3)) -> mark#(X2) -> mark#(f(X)) -> mark#(X)
    mark#(if(X1,X2,X3)) -> mark#(X2) -> mark#(f(X)) -> f#(mark(X))
    mark#(if(X1,X2,X3)) -> mark#(X2) ->
    mark#(f(X)) -> active#(f(mark(X)))
    mark#(if(X1,X2,X3)) -> mark#(X2) ->
    mark#(if(X1,X2,X3)) -> mark#(X2)
    mark#(if(X1,X2,X3)) -> mark#(X2) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(if(X1,X2,X3)) -> mark#(X2) ->
    mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3)
    mark#(if(X1,X2,X3)) -> mark#(X2) ->
    mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3))
    mark#(if(X1,X2,X3)) -> mark#(X2) -> mark#(c()) -> active#(c())
    mark#(if(X1,X2,X3)) -> mark#(X2) ->
    mark#(true()) -> active#(true())
    mark#(if(X1,X2,X3)) -> mark#(X2) ->
    mark#(false()) -> active#(false())
    mark#(if(X1,X2,X3)) -> mark#(X1) -> mark#(f(X)) -> mark#(X)
    mark#(if(X1,X2,X3)) -> mark#(X1) -> mark#(f(X)) -> f#(mark(X))
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(f(X)) -> active#(f(mark(X)))
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> mark#(X2)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3)
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3))
    mark#(if(X1,X2,X3)) -> mark#(X1) -> mark#(c()) -> active#(c())
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(true()) -> active#(true())
    mark#(if(X1,X2,X3)) -> mark#(X1) ->
    mark#(false()) -> active#(false())
    mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3) ->
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3) ->
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
    mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3) ->
    if#(active(X1),X2,X3) -> if#(X1,X2,X3)
    mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3) ->
    if#(X1,active(X2),X3) -> if#(X1,X2,X3)
    mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3)) ->
    active#(f(X)) -> f#(true())
    mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3)) ->
    active#(f(X)) -> if#(X,c(),f(true()))
    mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3)) ->
    active#(f(X)) -> mark#(if(X,c(),f(true())))
    mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3)) ->
    active#(if(true(),X,Y)) -> mark#(X)
    mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3)) ->
    active#(if(false(),X,Y)) -> mark#(Y)
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> f#(mark(X))
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> active#(f(mark(X)))
    mark#(f(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X2)
    mark#(f(X)) -> mark#(X) -> mark#(if(X1,X2,X3)) -> mark#(X1)
    mark#(f(X)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3)
    mark#(f(X)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3))
    mark#(f(X)) -> mark#(X) -> mark#(c()) -> active#(c())
    mark#(f(X)) -> mark#(X) -> mark#(true()) -> active#(true())
    mark#(f(X)) -> mark#(X) -> mark#(false()) -> active#(false())
    mark#(f(X)) -> f#(mark(X)) -> f#(mark(X)) -> f#(X)
    mark#(f(X)) -> f#(mark(X)) -> f#(active(X)) -> f#(X)
    mark#(f(X)) -> active#(f(mark(X))) ->
    active#(f(X)) -> f#(true())
    mark#(f(X)) -> active#(f(mark(X))) ->
    active#(f(X)) -> if#(X,c(),f(true()))
    mark#(f(X)) -> active#(f(mark(X))) ->
    active#(f(X)) -> mark#(if(X,c(),f(true())))
    mark#(f(X)) -> active#(f(mark(X))) ->
    active#(if(true(),X,Y)) -> mark#(X)
    mark#(f(X)) -> active#(f(mark(X))) ->
    active#(if(false(),X,Y)) -> mark#(Y)
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(active(X1),X2,X3) -> if#(X1,X2,X3)
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(X1,active(X2),X3) -> if#(X1,X2,X3)
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
    if#(active(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    if#(active(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
    if#(active(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
    if#(active(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(active(X1),X2,X3) -> if#(X1,X2,X3)
    if#(active(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(X1,active(X2),X3) -> if#(X1,X2,X3)
    if#(active(X1),X2,X3) -> if#(X1,X2,X3) ->
    if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3) ->
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3) ->
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3) ->
    if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3) ->
    if#(active(X1),X2,X3) -> if#(X1,X2,X3)
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3) ->
    if#(X1,active(X2),X3) -> if#(X1,X2,X3)
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3) ->
    if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
    if#(X1,active(X2),X3) -> if#(X1,X2,X3) ->
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    if#(X1,active(X2),X3) -> if#(X1,X2,X3) ->
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
    if#(X1,active(X2),X3) -> if#(X1,X2,X3) ->
    if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
    if#(X1,active(X2),X3) -> if#(X1,X2,X3) ->
    if#(active(X1),X2,X3) -> if#(X1,X2,X3)
    if#(X1,active(X2),X3) -> if#(X1,X2,X3) ->
    if#(X1,active(X2),X3) -> if#(X1,X2,X3)
    if#(X1,active(X2),X3) -> if#(X1,X2,X3) ->
    if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
    if#(X1,X2,mark(X3)) -> if#(X1,X2,X3) ->
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    if#(X1,X2,mark(X3)) -> if#(X1,X2,X3) ->
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
    if#(X1,X2,mark(X3)) -> if#(X1,X2,X3) ->
    if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
    if#(X1,X2,mark(X3)) -> if#(X1,X2,X3) ->
    if#(active(X1),X2,X3) -> if#(X1,X2,X3)
    if#(X1,X2,mark(X3)) -> if#(X1,X2,X3) ->
    if#(X1,active(X2),X3) -> if#(X1,X2,X3)
    if#(X1,X2,mark(X3)) -> if#(X1,X2,X3) ->
    if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
    if#(X1,X2,active(X3)) -> if#(X1,X2,X3) ->
    if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    if#(X1,X2,active(X3)) -> if#(X1,X2,X3) ->
    if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
    if#(X1,X2,active(X3)) -> if#(X1,X2,X3) ->
    if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
    if#(X1,X2,active(X3)) -> if#(X1,X2,X3) ->
    if#(active(X1),X2,X3) -> if#(X1,X2,X3)
    if#(X1,X2,active(X3)) -> if#(X1,X2,X3) ->
    if#(X1,active(X2),X3) -> if#(X1,X2,X3)
    if#(X1,X2,active(X3)) -> if#(X1,X2,X3) ->
    if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
    f#(mark(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    f#(mark(X)) -> f#(X) -> f#(active(X)) -> f#(X)
    f#(active(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    f#(active(X)) -> f#(X) -> f#(active(X)) -> f#(X)
    active#(if(false(),X,Y)) -> mark#(Y) ->
    mark#(f(X)) -> mark#(X)
    active#(if(false(),X,Y)) -> mark#(Y) ->
    mark#(f(X)) -> f#(mark(X))
    active#(if(false(),X,Y)) -> mark#(Y) ->
    mark#(f(X)) -> active#(f(mark(X)))
    active#(if(false(),X,Y)) -> mark#(Y) ->
    mark#(if(X1,X2,X3)) -> mark#(X2)
    active#(if(false(),X,Y)) -> mark#(Y) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    active#(if(false(),X,Y)) -> mark#(Y) ->
    mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3)
    active#(if(false(),X,Y)) -> mark#(Y) ->
    mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3))
    active#(if(false(),X,Y)) -> mark#(Y) ->
    mark#(c()) -> active#(c())
    active#(if(false(),X,Y)) -> mark#(Y) ->
    mark#(true()) -> active#(true())
    active#(if(false(),X,Y)) -> mark#(Y) ->
    mark#(false()) -> active#(false())
    active#(if(true(),X,Y)) -> mark#(X) ->
    mark#(f(X)) -> mark#(X)
    active#(if(true(),X,Y)) -> mark#(X) ->
    mark#(f(X)) -> f#(mark(X))
    active#(if(true(),X,Y)) -> mark#(X) ->
    mark#(f(X)) -> active#(f(mark(X)))
    active#(if(true(),X,Y)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> mark#(X2)
    active#(if(true(),X,Y)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    active#(if(true(),X,Y)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3)
    active#(if(true(),X,Y)) -> mark#(X) ->
    mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3))
    active#(if(true(),X,Y)) -> mark#(X) ->
    mark#(c()) -> active#(c())
    active#(if(true(),X,Y)) -> mark#(X) ->
    mark#(true()) -> active#(true())
    active#(if(true(),X,Y)) -> mark#(X) ->
    mark#(false()) -> active#(false())
    active#(f(X)) -> mark#(if(X,c(),f(true()))) ->
    mark#(f(X)) -> mark#(X)
    active#(f(X)) -> mark#(if(X,c(),f(true()))) ->
    mark#(f(X)) -> f#(mark(X))
    active#(f(X)) -> mark#(if(X,c(),f(true()))) ->
    mark#(f(X)) -> active#(f(mark(X)))
    active#(f(X)) -> mark#(if(X,c(),f(true()))) ->
    mark#(if(X1,X2,X3)) -> mark#(X2)
    active#(f(X)) -> mark#(if(X,c(),f(true()))) ->
    mark#(if(X1,X2,X3)) -> mark#(X1)
    active#(f(X)) -> mark#(if(X,c(),f(true()))) ->
    mark#(if(X1,X2,X3)) -> if#(mark(X1),mark(X2),X3)
    active#(f(X)) -> mark#(if(X,c(),f(true()))) ->
    mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3))
   SCC Processor:
    #sccs: 3
    #rules: 16
    #arcs: 113/529
    DPs:
     mark#(if(X1,X2,X3)) -> mark#(X2)
     mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3))
     active#(if(false(),X,Y)) -> mark#(Y)
     mark#(if(X1,X2,X3)) -> mark#(X1)
     mark#(f(X)) -> active#(f(mark(X)))
     active#(if(true(),X,Y)) -> mark#(X)
     mark#(f(X)) -> mark#(X)
     active#(f(X)) -> mark#(if(X,c(),f(true())))
    TRS:
     active(f(X)) -> mark(if(X,c(),f(true())))
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     mark(f(X)) -> active(f(mark(X)))
     mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
     mark(c()) -> active(c())
     mark(true()) -> active(true())
     mark(false()) -> active(false())
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
     if(mark(X1),X2,X3) -> if(X1,X2,X3)
     if(X1,mark(X2),X3) -> if(X1,X2,X3)
     if(X1,X2,mark(X3)) -> if(X1,X2,X3)
     if(active(X1),X2,X3) -> if(X1,X2,X3)
     if(X1,active(X2),X3) -> if(X1,X2,X3)
     if(X1,X2,active(X3)) -> if(X1,X2,X3)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [mark#](x0) = x0,
      
      [active#](x0) = x0,
      
      [false] = 1,
      
      [mark](x0) = x0,
      
      [if](x0, x1, x2) = x0 + x1 + x2,
      
      [true] = 0,
      
      [c] = 0,
      
      [active](x0) = x0,
      
      [f](x0) = x0
     orientation:
      mark#(if(X1,X2,X3)) = X1 + X2 + X3 >= X2 = mark#(X2)
      
      mark#(if(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active#(if(mark(X1),mark(X2),X3))
      
      active#(if(false(),X,Y)) = X + Y + 1 >= Y = mark#(Y)
      
      mark#(if(X1,X2,X3)) = X1 + X2 + X3 >= X1 = mark#(X1)
      
      mark#(f(X)) = X >= X = active#(f(mark(X)))
      
      active#(if(true(),X,Y)) = X + Y >= X = mark#(X)
      
      mark#(f(X)) = X >= X = mark#(X)
      
      active#(f(X)) = X >= X = mark#(if(X,c(),f(true())))
      
      active(f(X)) = X >= X = mark(if(X,c(),f(true())))
      
      active(if(true(),X,Y)) = X + Y >= X = mark(X)
      
      active(if(false(),X,Y)) = X + Y + 1 >= Y = mark(Y)
      
      mark(f(X)) = X >= X = active(f(mark(X)))
      
      mark(if(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(if(mark(X1),mark(X2),X3))
      
      mark(c()) = 0 >= 0 = active(c())
      
      mark(true()) = 0 >= 0 = active(true())
      
      mark(false()) = 1 >= 1 = active(false())
      
      f(mark(X)) = X >= X = f(X)
      
      f(active(X)) = X >= X = f(X)
      
      if(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = if(X1,X2,X3)
      
      if(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = if(X1,X2,X3)
      
      if(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = if(X1,X2,X3)
      
      if(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = if(X1,X2,X3)
      
      if(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = if(X1,X2,X3)
      
      if(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = if(X1,X2,X3)
     problem:
      DPs:
       mark#(if(X1,X2,X3)) -> mark#(X2)
       mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3))
       mark#(if(X1,X2,X3)) -> mark#(X1)
       mark#(f(X)) -> active#(f(mark(X)))
       active#(if(true(),X,Y)) -> mark#(X)
       mark#(f(X)) -> mark#(X)
       active#(f(X)) -> mark#(if(X,c(),f(true())))
      TRS:
       active(f(X)) -> mark(if(X,c(),f(true())))
       active(if(true(),X,Y)) -> mark(X)
       active(if(false(),X,Y)) -> mark(Y)
       mark(f(X)) -> active(f(mark(X)))
       mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
       mark(c()) -> active(c())
       mark(true()) -> active(true())
       mark(false()) -> active(false())
       f(mark(X)) -> f(X)
       f(active(X)) -> f(X)
       if(mark(X1),X2,X3) -> if(X1,X2,X3)
       if(X1,mark(X2),X3) -> if(X1,X2,X3)
       if(X1,X2,mark(X3)) -> if(X1,X2,X3)
       if(active(X1),X2,X3) -> if(X1,X2,X3)
       if(X1,active(X2),X3) -> if(X1,X2,X3)
       if(X1,X2,active(X3)) -> if(X1,X2,X3)
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [mark#](x0) = x0 + 1,
       
       [active#](x0) = x0 + 1,
       
       [false] = 0,
       
       [mark](x0) = x0,
       
       [if](x0, x1, x2) = x0 + x1 + x2,
       
       [true] = 0,
       
       [c] = 0,
       
       [active](x0) = x0,
       
       [f](x0) = x0 + 1
      orientation:
       mark#(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X2 + 1 = mark#(X2)
       
       mark#(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + X2 + X3 + 1 = active#(if(mark(X1),mark(X2),X3))
       
       mark#(if(X1,X2,X3)) = X1 + X2 + X3 + 1 >= X1 + 1 = mark#(X1)
       
       mark#(f(X)) = X + 2 >= X + 2 = active#(f(mark(X)))
       
       active#(if(true(),X,Y)) = X + Y + 1 >= X + 1 = mark#(X)
       
       mark#(f(X)) = X + 2 >= X + 1 = mark#(X)
       
       active#(f(X)) = X + 2 >= X + 2 = mark#(if(X,c(),f(true())))
       
       active(f(X)) = X + 1 >= X + 1 = mark(if(X,c(),f(true())))
       
       active(if(true(),X,Y)) = X + Y >= X = mark(X)
       
       active(if(false(),X,Y)) = X + Y >= Y = mark(Y)
       
       mark(f(X)) = X + 1 >= X + 1 = active(f(mark(X)))
       
       mark(if(X1,X2,X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = active(if(mark(X1),mark(X2),X3))
       
       mark(c()) = 0 >= 0 = active(c())
       
       mark(true()) = 0 >= 0 = active(true())
       
       mark(false()) = 0 >= 0 = active(false())
       
       f(mark(X)) = X + 1 >= X + 1 = f(X)
       
       f(active(X)) = X + 1 >= X + 1 = f(X)
       
       if(mark(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = if(X1,X2,X3)
       
       if(X1,mark(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = if(X1,X2,X3)
       
       if(X1,X2,mark(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = if(X1,X2,X3)
       
       if(active(X1),X2,X3) = X1 + X2 + X3 >= X1 + X2 + X3 = if(X1,X2,X3)
       
       if(X1,active(X2),X3) = X1 + X2 + X3 >= X1 + X2 + X3 = if(X1,X2,X3)
       
       if(X1,X2,active(X3)) = X1 + X2 + X3 >= X1 + X2 + X3 = if(X1,X2,X3)
      problem:
       DPs:
        mark#(if(X1,X2,X3)) -> mark#(X2)
        mark#(if(X1,X2,X3)) -> active#(if(mark(X1),mark(X2),X3))
        mark#(if(X1,X2,X3)) -> mark#(X1)
        mark#(f(X)) -> active#(f(mark(X)))
        active#(if(true(),X,Y)) -> mark#(X)
        active#(f(X)) -> mark#(if(X,c(),f(true())))
       TRS:
        active(f(X)) -> mark(if(X,c(),f(true())))
        active(if(true(),X,Y)) -> mark(X)
        active(if(false(),X,Y)) -> mark(Y)
        mark(f(X)) -> active(f(mark(X)))
        mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
        mark(c()) -> active(c())
        mark(true()) -> active(true())
        mark(false()) -> active(false())
        f(mark(X)) -> f(X)
        f(active(X)) -> f(X)
        if(mark(X1),X2,X3) -> if(X1,X2,X3)
        if(X1,mark(X2),X3) -> if(X1,X2,X3)
        if(X1,X2,mark(X3)) -> if(X1,X2,X3)
        if(active(X1),X2,X3) -> if(X1,X2,X3)
        if(X1,active(X2),X3) -> if(X1,X2,X3)
        if(X1,X2,active(X3)) -> if(X1,X2,X3)
      Open
    
    DPs:
     f#(active(X)) -> f#(X)
     f#(mark(X)) -> f#(X)
    TRS:
     active(f(X)) -> mark(if(X,c(),f(true())))
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     mark(f(X)) -> active(f(mark(X)))
     mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
     mark(c()) -> active(c())
     mark(true()) -> active(true())
     mark(false()) -> active(false())
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
     if(mark(X1),X2,X3) -> if(X1,X2,X3)
     if(X1,mark(X2),X3) -> if(X1,X2,X3)
     if(X1,X2,mark(X3)) -> if(X1,X2,X3)
     if(active(X1),X2,X3) -> if(X1,X2,X3)
     if(X1,active(X2),X3) -> if(X1,X2,X3)
     if(X1,X2,active(X3)) -> if(X1,X2,X3)
    Open
    
    DPs:
     if#(X1,active(X2),X3) -> if#(X1,X2,X3)
     if#(X1,X2,active(X3)) -> if#(X1,X2,X3)
     if#(active(X1),X2,X3) -> if#(X1,X2,X3)
     if#(X1,X2,mark(X3)) -> if#(X1,X2,X3)
     if#(X1,mark(X2),X3) -> if#(X1,X2,X3)
     if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
    TRS:
     active(f(X)) -> mark(if(X,c(),f(true())))
     active(if(true(),X,Y)) -> mark(X)
     active(if(false(),X,Y)) -> mark(Y)
     mark(f(X)) -> active(f(mark(X)))
     mark(if(X1,X2,X3)) -> active(if(mark(X1),mark(X2),X3))
     mark(c()) -> active(c())
     mark(true()) -> active(true())
     mark(false()) -> active(false())
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
     if(mark(X1),X2,X3) -> if(X1,X2,X3)
     if(X1,mark(X2),X3) -> if(X1,X2,X3)
     if(X1,X2,mark(X3)) -> if(X1,X2,X3)
     if(active(X1),X2,X3) -> if(X1,X2,X3)
     if(X1,active(X2),X3) -> if(X1,X2,X3)
     if(X1,X2,active(X3)) -> if(X1,X2,X3)
    Open