WORST_CASE(?,O(1))
* Step 1: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            a(b(x)) -> a(c(b(x)))
        - Signature:
            {a/1} / {b/1,c/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a} and constructors {b,c}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          a#(b(x)) -> c_1(a#(c(b(x))))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            a#(b(x)) -> c_1(a#(c(b(x))))
        - Weak TRS:
            a(b(x)) -> a(c(b(x)))
        - Signature:
            {a/1,a#/1} / {b/1,c/1,c_1/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#} and constructors {b,c}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {}.
        Here rules are labelled as follows:
          1: a#(b(x)) -> c_1(a#(c(b(x))))
* Step 3: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            a#(b(x)) -> c_1(a#(c(b(x))))
        - Weak TRS:
            a(b(x)) -> a(c(b(x)))
        - Signature:
            {a/1,a#/1} / {b/1,c/1,c_1/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#} and constructors {b,c}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:a#(b(x)) -> c_1(a#(c(b(x))))
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: a#(b(x)) -> c_1(a#(c(b(x))))
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a(b(x)) -> a(c(b(x)))
        - Signature:
            {a/1,a#/1} / {b/1,c/1,c_1/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#} and constructors {b,c}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))