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

WORST_CASE(Omega(n^1),?)