/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:
            activate(X) -> X
            activate(n__adx(X)) -> adx(activate(X))
            activate(n__incr(X)) -> incr(activate(X))
            activate(n__zeros()) -> zeros()
            adx(X) -> n__adx(X)
            adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L))))
            adx(nil()) -> nil()
            head(cons(X,L)) -> X
            incr(X) -> n__incr(X)
            incr(cons(X,L)) -> cons(s(X),n__incr(activate(L)))
            incr(nil()) -> nil()
            nats() -> adx(zeros())
            tail(cons(X,L)) -> activate(L)
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {activate/1,adx/1,head/1,incr/1,nats/0,tail/1,zeros/0} / {0/0,cons/2,n__adx/1,n__incr/1,n__zeros/0,nil/0
            ,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,adx,head,incr,nats,tail,zeros} and constructors {0,cons
            ,n__adx,n__incr,n__zeros,nil,s}
    + 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__adx(X)) -> adx(activate(X))
            activate(n__incr(X)) -> incr(activate(X))
            activate(n__zeros()) -> zeros()
            adx(X) -> n__adx(X)
            adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L))))
            adx(nil()) -> nil()
            head(cons(X,L)) -> X
            incr(X) -> n__incr(X)
            incr(cons(X,L)) -> cons(s(X),n__incr(activate(L)))
            incr(nil()) -> nil()
            nats() -> adx(zeros())
            tail(cons(X,L)) -> activate(L)
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {activate/1,adx/1,head/1,incr/1,nats/0,tail/1,zeros/0} / {0/0,cons/2,n__adx/1,n__incr/1,n__zeros/0,nil/0
            ,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,adx,head,incr,nats,tail,zeros} and constructors {0,cons
            ,n__adx,n__incr,n__zeros,nil,s}
    + 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__adx(X)) -> adx(activate(X))
            activate(n__incr(X)) -> incr(activate(X))
            activate(n__zeros()) -> zeros()
            adx(X) -> n__adx(X)
            adx(cons(X,L)) -> incr(cons(X,n__adx(activate(L))))
            adx(nil()) -> nil()
            head(cons(X,L)) -> X
            incr(X) -> n__incr(X)
            incr(cons(X,L)) -> cons(s(X),n__incr(activate(L)))
            incr(nil()) -> nil()
            nats() -> adx(zeros())
            tail(cons(X,L)) -> activate(L)
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {activate/1,adx/1,head/1,incr/1,nats/0,tail/1,zeros/0} / {0/0,cons/2,n__adx/1,n__incr/1,n__zeros/0,nil/0
            ,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,adx,head,incr,nats,tail,zeros} and constructors {0,cons
            ,n__adx,n__incr,n__zeros,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__adx(x)} =
            activate(n__adx(x)) ->^+ adx(activate(x))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)