/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:
            a__adx(X) -> adx(X)
            a__adx(cons(X,L)) -> a__incr(cons(mark(X),adx(L)))
            a__adx(nil()) -> nil()
            a__head(X) -> head(X)
            a__head(cons(X,L)) -> mark(X)
            a__incr(X) -> incr(X)
            a__incr(cons(X,L)) -> cons(s(mark(X)),incr(L))
            a__incr(nil()) -> nil()
            a__nats() -> a__adx(a__zeros())
            a__nats() -> nats()
            a__tail(X) -> tail(X)
            a__tail(cons(X,L)) -> mark(L)
            a__zeros() -> cons(0(),zeros())
            a__zeros() -> zeros()
            mark(0()) -> 0()
            mark(adx(X)) -> a__adx(mark(X))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(head(X)) -> a__head(mark(X))
            mark(incr(X)) -> a__incr(mark(X))
            mark(nats()) -> a__nats()
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
            mark(tail(X)) -> a__tail(mark(X))
            mark(zeros()) -> a__zeros()
        - Signature:
            {a__adx/1,a__head/1,a__incr/1,a__nats/0,a__tail/1,a__zeros/0,mark/1} / {0/0,adx/1,cons/2,head/1,incr/1
            ,nats/0,nil/0,s/1,tail/1,zeros/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__adx,a__head,a__incr,a__nats,a__tail,a__zeros
            ,mark} and constructors {0,adx,cons,head,incr,nats,nil,s,tail,zeros}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__adx(X) -> adx(X)
            a__adx(cons(X,L)) -> a__incr(cons(mark(X),adx(L)))
            a__adx(nil()) -> nil()
            a__head(X) -> head(X)
            a__head(cons(X,L)) -> mark(X)
            a__incr(X) -> incr(X)
            a__incr(cons(X,L)) -> cons(s(mark(X)),incr(L))
            a__incr(nil()) -> nil()
            a__nats() -> a__adx(a__zeros())
            a__nats() -> nats()
            a__tail(X) -> tail(X)
            a__tail(cons(X,L)) -> mark(L)
            a__zeros() -> cons(0(),zeros())
            a__zeros() -> zeros()
            mark(0()) -> 0()
            mark(adx(X)) -> a__adx(mark(X))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(head(X)) -> a__head(mark(X))
            mark(incr(X)) -> a__incr(mark(X))
            mark(nats()) -> a__nats()
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
            mark(tail(X)) -> a__tail(mark(X))
            mark(zeros()) -> a__zeros()
        - Signature:
            {a__adx/1,a__head/1,a__incr/1,a__nats/0,a__tail/1,a__zeros/0,mark/1} / {0/0,adx/1,cons/2,head/1,incr/1
            ,nats/0,nil/0,s/1,tail/1,zeros/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__adx,a__head,a__incr,a__nats,a__tail,a__zeros
            ,mark} and constructors {0,adx,cons,head,incr,nats,nil,s,tail,zeros}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__adx(X) -> adx(X)
            a__adx(cons(X,L)) -> a__incr(cons(mark(X),adx(L)))
            a__adx(nil()) -> nil()
            a__head(X) -> head(X)
            a__head(cons(X,L)) -> mark(X)
            a__incr(X) -> incr(X)
            a__incr(cons(X,L)) -> cons(s(mark(X)),incr(L))
            a__incr(nil()) -> nil()
            a__nats() -> a__adx(a__zeros())
            a__nats() -> nats()
            a__tail(X) -> tail(X)
            a__tail(cons(X,L)) -> mark(L)
            a__zeros() -> cons(0(),zeros())
            a__zeros() -> zeros()
            mark(0()) -> 0()
            mark(adx(X)) -> a__adx(mark(X))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(head(X)) -> a__head(mark(X))
            mark(incr(X)) -> a__incr(mark(X))
            mark(nats()) -> a__nats()
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
            mark(tail(X)) -> a__tail(mark(X))
            mark(zeros()) -> a__zeros()
        - Signature:
            {a__adx/1,a__head/1,a__incr/1,a__nats/0,a__tail/1,a__zeros/0,mark/1} / {0/0,adx/1,cons/2,head/1,incr/1
            ,nats/0,nil/0,s/1,tail/1,zeros/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__adx,a__head,a__incr,a__nats,a__tail,a__zeros
            ,mark} and constructors {0,adx,cons,head,incr,nats,nil,s,tail,zeros}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> adx(x)} =
            mark(adx(x)) ->^+ a__adx(mark(x))
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)