MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { f(X) -> if(X, c(), f(true()))
  , if(true(), X, Y) -> X
  , if(false(), X, Y) -> Y }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We use the processor 'matrix interpretation of dimension 1' to
orient following rules strictly.

Trs: { if(false(), X, Y) -> Y }

The induced complexity on above rules (modulo remaining rules) is
YES(?,O(n^1)) . These rules are moved into the corresponding weak
component(s).

Sub-proof:
----------
  TcT has computed the following constructor-based matrix
  interpretation satisfying not(EDA).
  
             [f](x1) = [3] x1 + [3]                  
                                                     
    [if](x1, x2, x3) = [3] x1 + [3] x2 + [1] x3 + [0]
                                                     
                 [c] = [0]                           
                                                     
              [true] = [0]                           
                                                     
             [false] = [1]                           
  
  This order satisfies the following ordering constraints:
  
                 [f(X)] =  [3] X + [3]            
                        >= [3] X + [3]            
                        =  [if(X, c(), f(true()))]
                                                  
     [if(true(), X, Y)] =  [3] X + [1] Y + [0]    
                        >= [1] X + [0]            
                        =  [X]                    
                                                  
    [if(false(), X, Y)] =  [3] X + [1] Y + [3]    
                        >  [1] Y + [0]            
                        =  [Y]                    
                                                  

We return to the main proof.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { f(X) -> if(X, c(), f(true()))
  , if(true(), X, Y) -> X }
Weak Trs: { if(false(), X, Y) -> Y }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Empty strict component of the problem is NOT empty.

Arrrr..