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

WORST_CASE(Omega(n^1),?)