/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(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            from(X) -> cons(X,from(s(X)))
            length(cons(X,Y)) -> s(length1(Y))
            length(nil()) -> 0()
            length1(X) -> length(X)
        - Signature:
            {from/1,length/1,length1/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {from,length,length1} and constructors {0,cons,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            from(X) -> cons(X,from(s(X)))
            length(cons(X,Y)) -> s(length1(Y))
            length(nil()) -> 0()
            length1(X) -> length(X)
        - Signature:
            {from/1,length/1,length1/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {from,length,length1} and constructors {0,cons,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            from(X) -> cons(X,from(s(X)))
            length(cons(X,Y)) -> s(length1(Y))
            length(nil()) -> 0()
            length1(X) -> length(X)
        - Signature:
            {from/1,length/1,length1/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {from,length,length1} and constructors {0,cons,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          length(x){x -> cons(y,x)} =
            length(cons(y,x)) ->^+ s(length(x))
              = C[length(x) = length(x){}]

WORST_CASE(Omega(n^1),?)