MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            f(X) -> if(X,c(),f(true()))
            if(false(),X,Y) -> Y
            if(true(),X,Y) -> X
        - Signature:
            {f/1,if/3} / {c/0,false/0,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,if} and constructors {c,false,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          f#(X) -> c_1(if#(X,c(),f(true())),f#(true()))
          if#(false(),X,Y) -> c_2()
          if#(true(),X,Y) -> c_3()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(X) -> c_1(if#(X,c(),f(true())),f#(true()))
            if#(false(),X,Y) -> c_2()
            if#(true(),X,Y) -> c_3()
        - Weak TRS:
            f(X) -> if(X,c(),f(true()))
            if(false(),X,Y) -> Y
            if(true(),X,Y) -> X
        - Signature:
            {f/1,if/3,f#/1,if#/3} / {c/0,false/0,true/0,c_1/2,c_2/0,c_3/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,if#} and constructors {c,false,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,3}
        by application of
          Pre({2,3}) = {1}.
        Here rules are labelled as follows:
          1: f#(X) -> c_1(if#(X,c(),f(true())),f#(true()))
          2: if#(false(),X,Y) -> c_2()
          3: if#(true(),X,Y) -> c_3()
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(X) -> c_1(if#(X,c(),f(true())),f#(true()))
        - Weak DPs:
            if#(false(),X,Y) -> c_2()
            if#(true(),X,Y) -> c_3()
        - Weak TRS:
            f(X) -> if(X,c(),f(true()))
            if(false(),X,Y) -> Y
            if(true(),X,Y) -> X
        - Signature:
            {f/1,if/3,f#/1,if#/3} / {c/0,false/0,true/0,c_1/2,c_2/0,c_3/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,if#} and constructors {c,false,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:f#(X) -> c_1(if#(X,c(),f(true())),f#(true()))
             -->_1 if#(true(),X,Y) -> c_3():3
             -->_1 if#(false(),X,Y) -> c_2():2
             -->_2 f#(X) -> c_1(if#(X,c(),f(true())),f#(true())):1
          
          2:W:if#(false(),X,Y) -> c_2()
             
          
          3:W:if#(true(),X,Y) -> c_3()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: if#(false(),X,Y) -> c_2()
          3: if#(true(),X,Y) -> c_3()
* Step 4: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(X) -> c_1(if#(X,c(),f(true())),f#(true()))
        - Weak TRS:
            f(X) -> if(X,c(),f(true()))
            if(false(),X,Y) -> Y
            if(true(),X,Y) -> X
        - Signature:
            {f/1,if/3,f#/1,if#/3} / {c/0,false/0,true/0,c_1/2,c_2/0,c_3/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,if#} and constructors {c,false,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:f#(X) -> c_1(if#(X,c(),f(true())),f#(true()))
             -->_2 f#(X) -> c_1(if#(X,c(),f(true())),f#(true())):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          f#(X) -> c_1(f#(true()))
* Step 5: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            f#(X) -> c_1(f#(true()))
        - Weak TRS:
            f(X) -> if(X,c(),f(true()))
            if(false(),X,Y) -> Y
            if(true(),X,Y) -> X
        - Signature:
            {f/1,if/3,f#/1,if#/3} / {c/0,false/0,true/0,c_1/1,c_2/0,c_3/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#,if#} and constructors {c,false,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          f#(X) -> c_1(f#(true()))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          f#(X) -> c_1(f#(true()))
      - Signature:
          {f/1,if/3,f#/1,if#/3} / {c/0,false/0,true/0,c_1/1,c_2/0,c_3/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {f#,if#} and constructors {c,false,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE