WORST_CASE(?,O(1))
* Step 1: Sum.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            GCD(z0,0()) -> c()
            GCD(0(),z0) -> c1()
            GCD(s(z0),s(z1)) -> c2(GCD(s(z0),-(z1,z0)))
            GCD(s(z0),s(z1)) -> c3(GCD(-(z0,z1),s(z1)))
        - Weak TRS:
            gcd(z0,0()) -> z0
            gcd(0(),z0) -> z0
            gcd(s(z0),s(z1)) -> if(<(z0,z1),gcd(s(z0),-(z1,z0)),gcd(-(z0,z1),s(z1)))
        - Signature:
            {GCD/2,gcd/2} / {-/2,0/0,</2,c/0,c1/0,c2/1,c3/1,if/3,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {GCD,gcd} and constructors {-,0,<,c,c1,c2,c3,if,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            GCD(z0,0()) -> c()
            GCD(0(),z0) -> c1()
            GCD(s(z0),s(z1)) -> c2(GCD(s(z0),-(z1,z0)))
            GCD(s(z0),s(z1)) -> c3(GCD(-(z0,z1),s(z1)))
        - Weak TRS:
            gcd(z0,0()) -> z0
            gcd(0(),z0) -> z0
            gcd(s(z0),s(z1)) -> if(<(z0,z1),gcd(s(z0),-(z1,z0)),gcd(-(z0,z1),s(z1)))
        - Signature:
            {GCD/2,gcd/2} / {-/2,0/0,</2,c/0,c1/0,c2/1,c3/1,if/3,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {GCD,gcd} and constructors {-,0,<,c,c1,c2,c3,if,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          GCD#(z0,0()) -> c_1()
          GCD#(0(),z0) -> c_2()
          GCD#(s(z0),s(z1)) -> c_3(GCD#(s(z0),-(z1,z0)))
          GCD#(s(z0),s(z1)) -> c_4(GCD#(-(z0,z1),s(z1)))
        Weak DPs
          gcd#(z0,0()) -> c_5()
          gcd#(0(),z0) -> c_6()
          gcd#(s(z0),s(z1)) -> c_7(gcd#(s(z0),-(z1,z0)),gcd#(-(z0,z1),s(z1)))
        
        and mark the set of starting terms.
* Step 3: PredecessorEstimation.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            GCD#(z0,0()) -> c_1()
            GCD#(0(),z0) -> c_2()
            GCD#(s(z0),s(z1)) -> c_3(GCD#(s(z0),-(z1,z0)))
            GCD#(s(z0),s(z1)) -> c_4(GCD#(-(z0,z1),s(z1)))
        - Weak DPs:
            gcd#(z0,0()) -> c_5()
            gcd#(0(),z0) -> c_6()
            gcd#(s(z0),s(z1)) -> c_7(gcd#(s(z0),-(z1,z0)),gcd#(-(z0,z1),s(z1)))
        - Weak TRS:
            GCD(z0,0()) -> c()
            GCD(0(),z0) -> c1()
            GCD(s(z0),s(z1)) -> c2(GCD(s(z0),-(z1,z0)))
            GCD(s(z0),s(z1)) -> c3(GCD(-(z0,z1),s(z1)))
            gcd(z0,0()) -> z0
            gcd(0(),z0) -> z0
            gcd(s(z0),s(z1)) -> if(<(z0,z1),gcd(s(z0),-(z1,z0)),gcd(-(z0,z1),s(z1)))
        - Signature:
            {GCD/2,gcd/2,GCD#/2,gcd#/2} / {-/2,0/0,</2,c/0,c1/0,c2/1,c3/1,if/3,s/1,c_1/0,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0
            ,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {GCD#,gcd#} and constructors {-,0,<,c,c1,c2,c3,if,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,3,4}
        by application of
          Pre({1,2,3,4}) = {}.
        Here rules are labelled as follows:
          1: GCD#(z0,0()) -> c_1()
          2: GCD#(0(),z0) -> c_2()
          3: GCD#(s(z0),s(z1)) -> c_3(GCD#(s(z0),-(z1,z0)))
          4: GCD#(s(z0),s(z1)) -> c_4(GCD#(-(z0,z1),s(z1)))
          5: gcd#(z0,0()) -> c_5()
          6: gcd#(0(),z0) -> c_6()
          7: gcd#(s(z0),s(z1)) -> c_7(gcd#(s(z0),-(z1,z0)),gcd#(-(z0,z1),s(z1)))
* Step 4: RemoveWeakSuffixes.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            GCD#(z0,0()) -> c_1()
            GCD#(0(),z0) -> c_2()
            GCD#(s(z0),s(z1)) -> c_3(GCD#(s(z0),-(z1,z0)))
            GCD#(s(z0),s(z1)) -> c_4(GCD#(-(z0,z1),s(z1)))
            gcd#(z0,0()) -> c_5()
            gcd#(0(),z0) -> c_6()
            gcd#(s(z0),s(z1)) -> c_7(gcd#(s(z0),-(z1,z0)),gcd#(-(z0,z1),s(z1)))
        - Weak TRS:
            GCD(z0,0()) -> c()
            GCD(0(),z0) -> c1()
            GCD(s(z0),s(z1)) -> c2(GCD(s(z0),-(z1,z0)))
            GCD(s(z0),s(z1)) -> c3(GCD(-(z0,z1),s(z1)))
            gcd(z0,0()) -> z0
            gcd(0(),z0) -> z0
            gcd(s(z0),s(z1)) -> if(<(z0,z1),gcd(s(z0),-(z1,z0)),gcd(-(z0,z1),s(z1)))
        - Signature:
            {GCD/2,gcd/2,GCD#/2,gcd#/2} / {-/2,0/0,</2,c/0,c1/0,c2/1,c3/1,if/3,s/1,c_1/0,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0
            ,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {GCD#,gcd#} and constructors {-,0,<,c,c1,c2,c3,if,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:GCD#(z0,0()) -> c_1()
             
          
          2:W:GCD#(0(),z0) -> c_2()
             
          
          3:W:GCD#(s(z0),s(z1)) -> c_3(GCD#(s(z0),-(z1,z0)))
             
          
          4:W:GCD#(s(z0),s(z1)) -> c_4(GCD#(-(z0,z1),s(z1)))
             
          
          5:W:gcd#(z0,0()) -> c_5()
             
          
          6:W:gcd#(0(),z0) -> c_6()
             
          
          7:W:gcd#(s(z0),s(z1)) -> c_7(gcd#(s(z0),-(z1,z0)),gcd#(-(z0,z1),s(z1)))
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          7: gcd#(s(z0),s(z1)) -> c_7(gcd#(s(z0),-(z1,z0)),gcd#(-(z0,z1),s(z1)))
          6: gcd#(0(),z0) -> c_6()
          5: gcd#(z0,0()) -> c_5()
          4: GCD#(s(z0),s(z1)) -> c_4(GCD#(-(z0,z1),s(z1)))
          3: GCD#(s(z0),s(z1)) -> c_3(GCD#(s(z0),-(z1,z0)))
          2: GCD#(0(),z0) -> c_2()
          1: GCD#(z0,0()) -> c_1()
* Step 5: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            GCD(z0,0()) -> c()
            GCD(0(),z0) -> c1()
            GCD(s(z0),s(z1)) -> c2(GCD(s(z0),-(z1,z0)))
            GCD(s(z0),s(z1)) -> c3(GCD(-(z0,z1),s(z1)))
            gcd(z0,0()) -> z0
            gcd(0(),z0) -> z0
            gcd(s(z0),s(z1)) -> if(<(z0,z1),gcd(s(z0),-(z1,z0)),gcd(-(z0,z1),s(z1)))
        - Signature:
            {GCD/2,gcd/2,GCD#/2,gcd#/2} / {-/2,0/0,</2,c/0,c1/0,c2/1,c3/1,if/3,s/1,c_1/0,c_2/0,c_3/1,c_4/1,c_5/0,c_6/0
            ,c_7/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {GCD#,gcd#} and constructors {-,0,<,c,c1,c2,c3,if,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))