/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            after(0(),XS) -> XS
            after(s(N),cons(X,XS)) -> after(N,XS)
            from(X) -> cons(X,from(s(X)))
        - Signature:
            {after/2,from/1} / {0/0,cons/2,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {after,from} and constructors {0,cons,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            after(0(),XS) -> XS
            after(s(N),cons(X,XS)) -> after(N,XS)
            from(X) -> cons(X,from(s(X)))
        - Signature:
            {after/2,from/1} / {0/0,cons/2,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {after,from} and constructors {0,cons,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            after(0(),XS) -> XS
            after(s(N),cons(X,XS)) -> after(N,XS)
            from(X) -> cons(X,from(s(X)))
        - Signature:
            {after/2,from/1} / {0/0,cons/2,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {after,from} and constructors {0,cons,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          after(x,z){x -> s(x),z -> cons(y,z)} =
            after(s(x),cons(y,z)) ->^+ after(x,z)
              = C[after(x,z) = after(x,z){}]

WORST_CASE(Omega(n^1),?)