/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:
            activate(X) -> X
            activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
            activate(n__s(X)) -> s(activate(X))
            activate(n__terms(X)) -> terms(activate(X))
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            dbl(0()) -> 0()
            dbl(s(X)) -> s(s(dbl(X)))
            first(X1,X2) -> n__first(X1,X2)
            first(0(),X) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
            half(0()) -> 0()
            half(dbl(X)) -> X
            half(s(0())) -> 0()
            half(s(s(X))) -> s(half(X))
            s(X) -> n__s(X)
            sqr(0()) -> 0()
            sqr(s(X)) -> s(add(sqr(X),dbl(X)))
            terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
            terms(X) -> n__terms(X)
        - Signature:
            {activate/1,add/2,dbl/1,first/2,half/1,s/1,sqr/1,terms/1} / {0/0,cons/2,n__first/2,n__s/1,n__terms/1,nil/0
            ,recip/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,add,dbl,first,half,s,sqr,terms} and constructors {0,cons
            ,n__first,n__s,n__terms,nil,recip}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
            activate(n__s(X)) -> s(activate(X))
            activate(n__terms(X)) -> terms(activate(X))
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            dbl(0()) -> 0()
            dbl(s(X)) -> s(s(dbl(X)))
            first(X1,X2) -> n__first(X1,X2)
            first(0(),X) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
            half(0()) -> 0()
            half(dbl(X)) -> X
            half(s(0())) -> 0()
            half(s(s(X))) -> s(half(X))
            s(X) -> n__s(X)
            sqr(0()) -> 0()
            sqr(s(X)) -> s(add(sqr(X),dbl(X)))
            terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
            terms(X) -> n__terms(X)
        - Signature:
            {activate/1,add/2,dbl/1,first/2,half/1,s/1,sqr/1,terms/1} / {0/0,cons/2,n__first/2,n__s/1,n__terms/1,nil/0
            ,recip/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,add,dbl,first,half,s,sqr,terms} and constructors {0,cons
            ,n__first,n__s,n__terms,nil,recip}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
            activate(n__s(X)) -> s(activate(X))
            activate(n__terms(X)) -> terms(activate(X))
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            dbl(0()) -> 0()
            dbl(s(X)) -> s(s(dbl(X)))
            first(X1,X2) -> n__first(X1,X2)
            first(0(),X) -> nil()
            first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
            half(0()) -> 0()
            half(dbl(X)) -> X
            half(s(0())) -> 0()
            half(s(s(X))) -> s(half(X))
            s(X) -> n__s(X)
            sqr(0()) -> 0()
            sqr(s(X)) -> s(add(sqr(X),dbl(X)))
            terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
            terms(X) -> n__terms(X)
        - Signature:
            {activate/1,add/2,dbl/1,first/2,half/1,s/1,sqr/1,terms/1} / {0/0,cons/2,n__first/2,n__s/1,n__terms/1,nil/0
            ,recip/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,add,dbl,first,half,s,sqr,terms} and constructors {0,cons
            ,n__first,n__s,n__terms,nil,recip}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__first(x,y)} =
            activate(n__first(x,y)) ->^+ first(activate(x),activate(y))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)