/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:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__adx(X)) -> adx(X)
            activate(n__incr(X)) -> incr(X)
            activate(n__s(X)) -> s(X)
            activate(n__zeros()) -> zeros()
            adx(X) -> n__adx(X)
            adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y))))
            hd(cons(X,Y)) -> activate(X)
            incr(X) -> n__incr(X)
            incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y)))
            nats() -> adx(zeros())
            s(X) -> n__s(X)
            tl(cons(X,Y)) -> activate(Y)
            zeros() -> cons(n__0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {0/0,activate/1,adx/1,hd/1,incr/1,nats/0,s/1,tl/1,zeros/0} / {cons/2,n__0/0,n__adx/1,n__incr/1,n__s/1
            ,n__zeros/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,adx,hd,incr,nats,s,tl,zeros} and constructors {cons
            ,n__0,n__adx,n__incr,n__s,n__zeros}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__adx(X)) -> adx(X)
            activate(n__incr(X)) -> incr(X)
            activate(n__s(X)) -> s(X)
            activate(n__zeros()) -> zeros()
            adx(X) -> n__adx(X)
            adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y))))
            hd(cons(X,Y)) -> activate(X)
            incr(X) -> n__incr(X)
            incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y)))
            nats() -> adx(zeros())
            s(X) -> n__s(X)
            tl(cons(X,Y)) -> activate(Y)
            zeros() -> cons(n__0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {0/0,activate/1,adx/1,hd/1,incr/1,nats/0,s/1,tl/1,zeros/0} / {cons/2,n__0/0,n__adx/1,n__incr/1,n__s/1
            ,n__zeros/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,adx,hd,incr,nats,s,tl,zeros} and constructors {cons
            ,n__0,n__adx,n__incr,n__s,n__zeros}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__adx(X)) -> adx(X)
            activate(n__incr(X)) -> incr(X)
            activate(n__s(X)) -> s(X)
            activate(n__zeros()) -> zeros()
            adx(X) -> n__adx(X)
            adx(cons(X,Y)) -> incr(cons(activate(X),n__adx(activate(Y))))
            hd(cons(X,Y)) -> activate(X)
            incr(X) -> n__incr(X)
            incr(cons(X,Y)) -> cons(n__s(activate(X)),n__incr(activate(Y)))
            nats() -> adx(zeros())
            s(X) -> n__s(X)
            tl(cons(X,Y)) -> activate(Y)
            zeros() -> cons(n__0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {0/0,activate/1,adx/1,hd/1,incr/1,nats/0,s/1,tl/1,zeros/0} / {cons/2,n__0/0,n__adx/1,n__incr/1,n__s/1
            ,n__zeros/0}
        - Obligation:
             runtime complexity wrt. defined symbols {0,activate,adx,hd,incr,nats,s,tl,zeros} and constructors {cons
            ,n__0,n__adx,n__incr,n__s,n__zeros}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__adx(cons(x,z))} =
            activate(n__adx(cons(x,z))) ->^+ incr(cons(activate(x),n__adx(activate(z))))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)