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

WORST_CASE(Omega(n^1),?)