WORST_CASE(?,O(1))
* Step 1: Sum 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:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: 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 3: PredecessorEstimation 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:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,3}
        by application of
          Pre({1,2,3}) = {4}.
        Here rules are labelled as follows:
          1: cons#(x,y) -> c_1()
          2: cons#(x,y) -> c_2()
          3: f#(s(a()),s(b()),x) -> c_3(f#(x,x,x))
          4: g#(f(s(x),s(y),z)) -> c_4(g#(f(x,y,z)),f#(x,y,z))
* Step 4: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            g#(f(s(x),s(y),z)) -> c_4(g#(f(x,y,z)),f#(x,y,z))
        - Weak DPs:
            cons#(x,y) -> c_1()
            cons#(x,y) -> c_2()
            f#(s(a()),s(b()),x) -> c_3(f#(x,x,x))
        - 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:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:g#(f(s(x),s(y),z)) -> c_4(g#(f(x,y,z)),f#(x,y,z))
             -->_2 f#(s(a()),s(b()),x) -> c_3(f#(x,x,x)):4
             -->_1 g#(f(s(x),s(y),z)) -> c_4(g#(f(x,y,z)),f#(x,y,z)):1
          
          2:W:cons#(x,y) -> c_1()
             
          
          3:W:cons#(x,y) -> c_2()
             
          
          4:W:f#(s(a()),s(b()),x) -> c_3(f#(x,x,x))
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: cons#(x,y) -> c_2()
          2: cons#(x,y) -> c_1()
          4: f#(s(a()),s(b()),x) -> c_3(f#(x,x,x))
* Step 5: SimplifyRHS WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            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:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:g#(f(s(x),s(y),z)) -> c_4(g#(f(x,y,z)),f#(x,y,z))
             -->_1 g#(f(s(x),s(y),z)) -> c_4(g#(f(x,y,z)),f#(x,y,z)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          g#(f(s(x),s(y),z)) -> c_4(g#(f(x,y,z)))
* Step 6: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            g#(f(s(x),s(y),z)) -> c_4(g#(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_4/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cons#,f#,g#} and constructors {a,b,s}
    + Applied Processor:
        UsableRules
    + Details:
        No rule is usable, rules are removed from the input problem.
* Step 7: 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_4/1}
        - 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))