/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__incr(X)) -> incr(activate(X))
            activate(n__nats()) -> nats()
            activate(n__odds()) -> odds()
            head(cons(X,XS)) -> X
            incr(X) -> n__incr(X)
            incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
            nats() -> cons(0(),n__incr(n__nats()))
            nats() -> n__nats()
            odds() -> incr(pairs())
            odds() -> n__odds()
            pairs() -> cons(0(),n__incr(n__odds()))
            tail(cons(X,XS)) -> activate(XS)
        - Signature:
            {activate/1,head/1,incr/1,nats/0,odds/0,pairs/0,tail/1} / {0/0,cons/2,n__incr/1,n__nats/0,n__odds/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,head,incr,nats,odds,pairs,tail} and constructors {0,cons
            ,n__incr,n__nats,n__odds,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__incr(X)) -> incr(activate(X))
            activate(n__nats()) -> nats()
            activate(n__odds()) -> odds()
            head(cons(X,XS)) -> X
            incr(X) -> n__incr(X)
            incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
            nats() -> cons(0(),n__incr(n__nats()))
            nats() -> n__nats()
            odds() -> incr(pairs())
            odds() -> n__odds()
            pairs() -> cons(0(),n__incr(n__odds()))
            tail(cons(X,XS)) -> activate(XS)
        - Signature:
            {activate/1,head/1,incr/1,nats/0,odds/0,pairs/0,tail/1} / {0/0,cons/2,n__incr/1,n__nats/0,n__odds/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,head,incr,nats,odds,pairs,tail} and constructors {0,cons
            ,n__incr,n__nats,n__odds,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__incr(X)) -> incr(activate(X))
            activate(n__nats()) -> nats()
            activate(n__odds()) -> odds()
            head(cons(X,XS)) -> X
            incr(X) -> n__incr(X)
            incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
            nats() -> cons(0(),n__incr(n__nats()))
            nats() -> n__nats()
            odds() -> incr(pairs())
            odds() -> n__odds()
            pairs() -> cons(0(),n__incr(n__odds()))
            tail(cons(X,XS)) -> activate(XS)
        - Signature:
            {activate/1,head/1,incr/1,nats/0,odds/0,pairs/0,tail/1} / {0/0,cons/2,n__incr/1,n__nats/0,n__odds/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {activate,head,incr,nats,odds,pairs,tail} and constructors {0,cons
            ,n__incr,n__nats,n__odds,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          activate(x){x -> n__incr(x)} =
            activate(n__incr(x)) ->^+ incr(activate(x))
              = C[activate(x) = activate(x){}]

WORST_CASE(Omega(n^1),?)