/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:
            sum(cons(0(),x),y) -> sum(x,y)
            sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
            sum(nil(),y) -> y
            weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x)))
            weight(cons(n,nil())) -> n
        - Signature:
            {sum/2,weight/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {sum,weight} 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:
            sum(cons(0(),x),y) -> sum(x,y)
            sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
            sum(nil(),y) -> y
            weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x)))
            weight(cons(n,nil())) -> n
        - Signature:
            {sum/2,weight/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {sum,weight} 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:
            sum(cons(0(),x),y) -> sum(x,y)
            sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
            sum(nil(),y) -> y
            weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x)))
            weight(cons(n,nil())) -> n
        - Signature:
            {sum/2,weight/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {sum,weight} and constructors {0,cons,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          sum(x,y){x -> cons(0(),x)} =
            sum(cons(0(),x),y) ->^+ sum(x,y)
              = C[sum(x,y) = sum(x,y){}]

WORST_CASE(Omega(n^1),?)