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

WORST_CASE(?,O(1))