WORST_CASE(?,O(1))
* Step 1: Sum WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            a(y,x) -> y
            a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0())
            b(x,y) -> c(a(c(y),a(0(),x)))
        - Signature:
            {a/2,b/2} / {0/0,c/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,b} and constructors {0,c}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            a(y,x) -> y
            a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0())
            b(x,y) -> c(a(c(y),a(0(),x)))
        - Signature:
            {a/2,b/2} / {0/0,c/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,b} and constructors {0,c}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          a#(y,x) -> c_1()
          a#(y,c(b(a(0(),x),0()))) -> c_2(b#(a(c(b(0(),y)),x),0()),a#(c(b(0(),y)),x),b#(0(),y))
          b#(x,y) -> c_3(a#(c(y),a(0(),x)),a#(0(),x))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: PredecessorEstimation WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            a#(y,x) -> c_1()
            a#(y,c(b(a(0(),x),0()))) -> c_2(b#(a(c(b(0(),y)),x),0()),a#(c(b(0(),y)),x),b#(0(),y))
            b#(x,y) -> c_3(a#(c(y),a(0(),x)),a#(0(),x))
        - Weak TRS:
            a(y,x) -> y
            a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0())
            b(x,y) -> c(a(c(y),a(0(),x)))
        - Signature:
            {a/2,b/2,a#/2,b#/2} / {0/0,c/1,c_1/0,c_2/3,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,b#} and constructors {0,c}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2}
        by application of
          Pre({1,2}) = {3}.
        Here rules are labelled as follows:
          1: a#(y,x) -> c_1()
          2: a#(y,c(b(a(0(),x),0()))) -> c_2(b#(a(c(b(0(),y)),x),0()),a#(c(b(0(),y)),x),b#(0(),y))
          3: b#(x,y) -> c_3(a#(c(y),a(0(),x)),a#(0(),x))
* Step 4: PredecessorEstimation WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            b#(x,y) -> c_3(a#(c(y),a(0(),x)),a#(0(),x))
        - Weak DPs:
            a#(y,x) -> c_1()
            a#(y,c(b(a(0(),x),0()))) -> c_2(b#(a(c(b(0(),y)),x),0()),a#(c(b(0(),y)),x),b#(0(),y))
        - Weak TRS:
            a(y,x) -> y
            a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0())
            b(x,y) -> c(a(c(y),a(0(),x)))
        - Signature:
            {a/2,b/2,a#/2,b#/2} / {0/0,c/1,c_1/0,c_2/3,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,b#} and constructors {0,c}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {}.
        Here rules are labelled as follows:
          1: b#(x,y) -> c_3(a#(c(y),a(0(),x)),a#(0(),x))
          2: a#(y,x) -> c_1()
          3: a#(y,c(b(a(0(),x),0()))) -> c_2(b#(a(c(b(0(),y)),x),0()),a#(c(b(0(),y)),x),b#(0(),y))
* Step 5: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            a#(y,x) -> c_1()
            a#(y,c(b(a(0(),x),0()))) -> c_2(b#(a(c(b(0(),y)),x),0()),a#(c(b(0(),y)),x),b#(0(),y))
            b#(x,y) -> c_3(a#(c(y),a(0(),x)),a#(0(),x))
        - Weak TRS:
            a(y,x) -> y
            a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0())
            b(x,y) -> c(a(c(y),a(0(),x)))
        - Signature:
            {a/2,b/2,a#/2,b#/2} / {0/0,c/1,c_1/0,c_2/3,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,b#} and constructors {0,c}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:a#(y,x) -> c_1()
             
          
          2:W:a#(y,c(b(a(0(),x),0()))) -> c_2(b#(a(c(b(0(),y)),x),0()),a#(c(b(0(),y)),x),b#(0(),y))
             
          
          3:W:b#(x,y) -> c_3(a#(c(y),a(0(),x)),a#(0(),x))
             -->_2 a#(y,x) -> c_1():1
             -->_1 a#(y,x) -> c_1():1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: b#(x,y) -> c_3(a#(c(y),a(0(),x)),a#(0(),x))
          2: a#(y,c(b(a(0(),x),0()))) -> c_2(b#(a(c(b(0(),y)),x),0()),a#(c(b(0(),y)),x),b#(0(),y))
          1: a#(y,x) -> c_1()
* Step 6: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a(y,x) -> y
            a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0())
            b(x,y) -> c(a(c(y),a(0(),x)))
        - Signature:
            {a/2,b/2,a#/2,b#/2} / {0/0,c/1,c_1/0,c_2/3,c_3/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,b#} and constructors {0,c}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))