WORST_CASE(?,O(1))
* 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: PredecessorEstimation 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:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,4}
        by application of
          Pre({1,3,4}) = {2}.
        Here rules are labelled as follows:
          1: *#(x,0()) -> c_1()
          2: *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
          3: *#(1(),y) -> c_3()
          4: *#(i(x),x) -> c_4()
* Step 4: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
        - Weak DPs:
            *#(x,0()) -> c_1()
            *#(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:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:*#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
             -->_2 *#(i(x),x) -> c_4():4
             -->_1 *#(i(x),x) -> c_4():4
             -->_2 *#(1(),y) -> c_3():3
             -->_1 *#(1(),y) -> c_3():3
             -->_2 *#(x,0()) -> c_1():2
             -->_1 *#(x,0()) -> c_1():2
             -->_2 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
             -->_1 *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z)):1
          
          2:W:*#(x,0()) -> c_1()
             
          
          3:W:*#(1(),y) -> c_3()
             
          
          4:W:*#(i(x),x) -> c_4()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: *#(x,0()) -> c_1()
          3: *#(1(),y) -> c_3()
          4: *#(i(x),x) -> c_4()
* Step 5: RemoveInapplicable WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
        - 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:
        RemoveInapplicable
    + Details:
        Only the nodes
          {}
        are reachable from nodes
          {}
        that start derivation from marked basic terms.
        The nodes not reachable are removed from the problem.
* Step 6: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - 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:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))