/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /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) -> h(s(f(h(Y),X)))
        - Signature:
            {f/2} / {h/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {h,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            f(s(X),Y) -> h(s(f(h(Y),X)))
        - Signature:
            {f/2} / {h/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {h,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          f#(s(X),Y) -> c_1(f#(h(Y),X))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: PredecessorEstimation WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            f#(s(X),Y) -> c_1(f#(h(Y),X))
        - Weak TRS:
            f(s(X),Y) -> h(s(f(h(Y),X)))
        - Signature:
            {f/2,f#/2} / {h/1,s/1,c_1/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#} and constructors {h,s}
    + 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: f#(s(X),Y) -> c_1(f#(h(Y),X))
* Step 4: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            f#(s(X),Y) -> c_1(f#(h(Y),X))
        - Weak TRS:
            f(s(X),Y) -> h(s(f(h(Y),X)))
        - Signature:
            {f/2,f#/2} / {h/1,s/1,c_1/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#} and constructors {h,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:f#(s(X),Y) -> c_1(f#(h(Y),X))
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: f#(s(X),Y) -> c_1(f#(h(Y),X))
* Step 5: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(s(X),Y) -> h(s(f(h(Y),X)))
        - Signature:
            {f/2,f#/2} / {h/1,s/1,c_1/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#} and constructors {h,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))