* Step 1: Sum WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))
            f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
            f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
        - Signature:
            {c/3,f/1} / {a/0,b/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {c,f} and constructors {a,b}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))
            f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
            f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
        - Signature:
            {c/3,f/1} / {a/0,b/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {c,f} and constructors {a,b}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          c#(b(a(),a()),b(y,z),x) -> c_1()
          f#(b(b(x,f(y)),z)) -> c_2(c#(z,x,f(b(b(f(a()),y),y))),f#(b(b(f(a()),y),y)),f#(a()))
          f#(c(c(a(),y,a()),b(x,z),a())) -> c_3(f#(c(f(a()),z,z)),c#(f(a()),z,z),f#(a()))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            c#(b(a(),a()),b(y,z),x) -> c_1()
            f#(b(b(x,f(y)),z)) -> c_2(c#(z,x,f(b(b(f(a()),y),y))),f#(b(b(f(a()),y),y)),f#(a()))
            f#(c(c(a(),y,a()),b(x,z),a())) -> c_3(f#(c(f(a()),z,z)),c#(f(a()),z,z),f#(a()))
        - Weak TRS:
            c(b(a(),a()),b(y,z),x) -> b(a(),b(z,z))
            f(b(b(x,f(y)),z)) -> c(z,x,f(b(b(f(a()),y),y)))
            f(c(c(a(),y,a()),b(x,z),a())) -> b(y,f(c(f(a()),z,z)))
        - Signature:
            {c/3,f/1,c#/3,f#/1} / {a/0,b/2,c_1/0,c_2/3,c_3/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {c#,f#} and constructors {a,b}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          c#(b(a(),a()),b(y,z),x) -> c_1()
* Step 4: Trivial WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            c#(b(a(),a()),b(y,z),x) -> c_1()
        - Signature:
            {c/3,f/1,c#/3,f#/1} / {a/0,b/2,c_1/0,c_2/3,c_3/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {c#,f#} and constructors {a,b}
    + Applied Processor:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:c#(b(a(),a()),b(y,z),x) -> c_1()
             
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 5: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {c/3,f/1,c#/3,f#/1} / {a/0,b/2,c_1/0,c_2/3,c_3/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {c#,f#} and constructors {a,b}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))