WORST_CASE(?,O(1))
* Step 1: InnermostRuleRemoval WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w)))
            h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w))))))
            h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x)))))
            t(x) -> x
            t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x)))))
            t(t(x)) -> t(c(t(x),x))
        - Signature:
            {h/3,t/1} / {0/0,c/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h,t} and constructors {0,c,s}
    + Applied Processor:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w)))
          h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w))))))
          h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x)))))
          t(t(x)) -> t(c(t(x),x))
        All above mentioned rules can be savely removed.
* Step 2: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            t(x) -> x
            t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x)))))
        - Signature:
            {h/3,t/1} / {0/0,c/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h,t} and constructors {0,c,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          t#(x) -> c_1()
          t#(x) -> c_2()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            t#(x) -> c_1()
            t#(x) -> c_2()
        - Weak TRS:
            t(x) -> x
            t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x)))))
        - Signature:
            {h/3,t/1,h#/3,t#/1} / {0/0,c/2,s/1,c_1/0,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h#,t#} and constructors {0,c,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          t#(x) -> c_1()
          t#(x) -> c_2()
* Step 4: Trivial WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            t#(x) -> c_1()
            t#(x) -> c_2()
        - Signature:
            {h/3,t/1,h#/3,t#/1} / {0/0,c/2,s/1,c_1/0,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h#,t#} and constructors {0,c,s}
    + Applied Processor:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:t#(x) -> c_1()
             
          
          2:S:t#(x) -> c_2()
             
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 5: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {h/3,t/1,h#/3,t#/1} / {0/0,c/2,s/1,c_1/0,c_2/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h#,t#} and constructors {0,c,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))