WORST_CASE(?,O(1))
* Step 1: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            cons(x,y) -> x
            cons(x,y) -> y
            f(s(a()),s(b()),x) -> f(x,x,x)
            g(f(s(x),s(y),z)) -> g(f(x,y,z))
        - Signature:
            {cons/2,f/3,g/1} / {a/0,b/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons,f,g} and constructors {a,b,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          cons#(x,y) -> c_1()
          cons#(x,y) -> c_2()
          f#(s(a()),s(b()),x) -> c_3(f#(x,x,x))
          g#(f(s(x),s(y),z)) -> c_4(g#(f(x,y,z)),f#(x,y,z))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            cons#(x,y) -> c_1()
            cons#(x,y) -> c_2()
            f#(s(a()),s(b()),x) -> c_3(f#(x,x,x))
            g#(f(s(x),s(y),z)) -> c_4(g#(f(x,y,z)),f#(x,y,z))
        - Weak TRS:
            cons(x,y) -> x
            cons(x,y) -> y
            f(s(a()),s(b()),x) -> f(x,x,x)
            g(f(s(x),s(y),z)) -> g(f(x,y,z))
        - Signature:
            {cons/2,f/3,g/1,cons#/2,f#/3,g#/1} / {a/0,b/0,s/1,c_1/0,c_2/0,c_3/1,c_4/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons#,f#,g#} and constructors {a,b,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          cons#(x,y) -> c_1()
          cons#(x,y) -> c_2()
          f#(s(a()),s(b()),x) -> c_3(f#(x,x,x))
* Step 3: Trivial WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            cons#(x,y) -> c_1()
            cons#(x,y) -> c_2()
            f#(s(a()),s(b()),x) -> c_3(f#(x,x,x))
        - Signature:
            {cons/2,f/3,g/1,cons#/2,f#/3,g#/1} / {a/0,b/0,s/1,c_1/0,c_2/0,c_3/1,c_4/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons#,f#,g#} and constructors {a,b,s}
    + Applied Processor:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:cons#(x,y) -> c_1()
             
          
          2:S:cons#(x,y) -> c_2()
             
          
          3:S:f#(s(a()),s(b()),x) -> c_3(f#(x,x,x))
             
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {cons/2,f/3,g/1,cons#/2,f#/3,g#/1} / {a/0,b/0,s/1,c_1/0,c_2/0,c_3/1,c_4/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons#,f#,g#} and constructors {a,b,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))