* Step 1: Sum WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            *(x,0()) -> 0()
            *(*(x,y),z) -> *(x,*(y,z))
            *(1(),y) -> y
            *(i(x),x) -> 1()
        - Signature:
            {*/2} / {0/0,1/0,i/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {0,1,i}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            *(x,0()) -> 0()
            *(*(x,y),z) -> *(x,*(y,z))
            *(1(),y) -> y
            *(i(x),x) -> 1()
        - Signature:
            {*/2} / {0/0,1/0,i/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*} and constructors {0,1,i}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          *#(x,0()) -> c_1()
          *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          *#(1(),y) -> c_3()
          *#(i(x),x) -> c_4()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            *#(x,0()) -> c_1()
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
            *#(1(),y) -> c_3()
            *#(i(x),x) -> c_4()
        - Weak TRS:
            *(x,0()) -> 0()
            *(*(x,y),z) -> *(x,*(y,z))
            *(1(),y) -> y
            *(i(x),x) -> 1()
        - Signature:
            {*/2,*#/2} / {0/0,1/0,i/1,c_1/0,c_2/2,c_3/0,c_4/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {0,1,i}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          *#(x,0()) -> c_1()
          *#(1(),y) -> c_3()
          *#(i(x),x) -> c_4()
* Step 4: Trivial WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            *#(x,0()) -> c_1()
            *#(1(),y) -> c_3()
            *#(i(x),x) -> c_4()
        - Signature:
            {*/2,*#/2} / {0/0,1/0,i/1,c_1/0,c_2/2,c_3/0,c_4/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {0,1,i}
    + Applied Processor:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:*#(x,0()) -> c_1()
             
          
          2:S:*#(1(),y) -> c_3()
             
          
          3:S:*#(i(x),x) -> c_4()
             
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 5: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {*/2,*#/2} / {0/0,1/0,i/1,c_1/0,c_2/2,c_3/0,c_4/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#} and constructors {0,1,i}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))