/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:
            cond(false(),n,l) -> tail(nthtail(s(n),l))
            cond(true(),n,l) -> l
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            length(cons(x,l)) -> s(length(l))
            length(nil()) -> 0()
            nthtail(n,l) -> cond(ge(n,length(l)),n,l)
            tail(cons(x,l)) -> l
            tail(nil()) -> nil()
        - Signature:
            {cond/3,ge/2,length/1,nthtail/2,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cond,ge,length,nthtail,tail} and constructors {0,cons,false,nil,s
            ,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            cond(false(),n,l) -> tail(nthtail(s(n),l))
            cond(true(),n,l) -> l
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            length(cons(x,l)) -> s(length(l))
            length(nil()) -> 0()
            nthtail(n,l) -> cond(ge(n,length(l)),n,l)
            tail(cons(x,l)) -> l
            tail(nil()) -> nil()
        - Signature:
            {cond/3,ge/2,length/1,nthtail/2,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cond,ge,length,nthtail,tail} and constructors {0,cons,false,nil,s
            ,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            cond(false(),n,l) -> tail(nthtail(s(n),l))
            cond(true(),n,l) -> l
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            length(cons(x,l)) -> s(length(l))
            length(nil()) -> 0()
            nthtail(n,l) -> cond(ge(n,length(l)),n,l)
            tail(cons(x,l)) -> l
            tail(nil()) -> nil()
        - Signature:
            {cond/3,ge/2,length/1,nthtail/2,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cond,ge,length,nthtail,tail} and constructors {0,cons,false,nil,s
            ,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          ge(x,y){x -> s(x),y -> s(y)} =
            ge(s(x),s(y)) ->^+ ge(x,y)
              = C[ge(x,y) = ge(x,y){}]

WORST_CASE(Omega(n^1),?)