/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(1))
* Step 1: Sum.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            f(s(x),y,y) -> f(y,x,s(x))
        - Signature:
            {f/3} / {s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            f(s(x),y,y) -> f(y,x,s(x))
        - Signature:
            {f/3} / {s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following weak dependency pairs:
        
        Strict DPs
          f#(s(x),y,y) -> c_1(f#(y,x,s(x)))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: UsableRules.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            f#(s(x),y,y) -> c_1(f#(y,x,s(x)))
        - Strict TRS:
            f(s(x),y,y) -> f(y,x,s(x))
        - Signature:
            {f/3,f#/3} / {s/1,c_1/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f#} and constructors {s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          f#(s(x),y,y) -> c_1(f#(y,x,s(x)))
* Step 4: WeightGap.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            f#(s(x),y,y) -> c_1(f#(y,x,s(x)))
        - Signature:
            {f/3,f#/3} / {s/1,c_1/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f#} and constructors {s}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
          The following argument positions are considered usable:
            none
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
              p(f) = [0]
              p(s) = [0]
             p(f#) = [7]
            p(c_1) = [0]
          
          Following rules are strictly oriented:
          f#(s(x),y,y) = [7]              
                       > [0]              
                       = c_1(f#(y,x,s(x)))
          
          
          Following rules are (at-least) weakly oriented:
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 5: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            f#(s(x),y,y) -> c_1(f#(y,x,s(x)))
        - Signature:
            {f/3,f#/3} / {s/1,c_1/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f#} and constructors {s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))