/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:
            eq(0(),0()) -> true()
            eq(0(),s(Y)) -> false()
            eq(s(X),0()) -> false()
            eq(s(X),s(Y)) -> eq(X,Y)
            ifmin(false(),cons(N,cons(M,L))) -> min(cons(M,L))
            ifmin(true(),cons(N,cons(M,L))) -> min(cons(N,L))
            ifrepl(false(),N,M,cons(K,L)) -> cons(K,replace(N,M,L))
            ifrepl(true(),N,M,cons(K,L)) -> cons(M,L)
            ifselsort(false(),cons(N,L)) -> cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))
            ifselsort(true(),cons(N,L)) -> cons(N,selsort(L))
            le(0(),Y) -> true()
            le(s(X),0()) -> false()
            le(s(X),s(Y)) -> le(X,Y)
            min(cons(N,cons(M,L))) -> ifmin(le(N,M),cons(N,cons(M,L)))
            min(cons(0(),nil())) -> 0()
            min(cons(s(N),nil())) -> s(N)
            replace(N,M,cons(K,L)) -> ifrepl(eq(N,K),N,M,cons(K,L))
            replace(N,M,nil()) -> nil()
            selsort(cons(N,L)) -> ifselsort(eq(N,min(cons(N,L))),cons(N,L))
            selsort(nil()) -> nil()
        - Signature:
            {eq/2,ifmin/2,ifrepl/4,ifselsort/2,le/2,min/1,replace/3,selsort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {eq,ifmin,ifrepl,ifselsort,le,min,replace
            ,selsort} 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:
            eq(0(),0()) -> true()
            eq(0(),s(Y)) -> false()
            eq(s(X),0()) -> false()
            eq(s(X),s(Y)) -> eq(X,Y)
            ifmin(false(),cons(N,cons(M,L))) -> min(cons(M,L))
            ifmin(true(),cons(N,cons(M,L))) -> min(cons(N,L))
            ifrepl(false(),N,M,cons(K,L)) -> cons(K,replace(N,M,L))
            ifrepl(true(),N,M,cons(K,L)) -> cons(M,L)
            ifselsort(false(),cons(N,L)) -> cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))
            ifselsort(true(),cons(N,L)) -> cons(N,selsort(L))
            le(0(),Y) -> true()
            le(s(X),0()) -> false()
            le(s(X),s(Y)) -> le(X,Y)
            min(cons(N,cons(M,L))) -> ifmin(le(N,M),cons(N,cons(M,L)))
            min(cons(0(),nil())) -> 0()
            min(cons(s(N),nil())) -> s(N)
            replace(N,M,cons(K,L)) -> ifrepl(eq(N,K),N,M,cons(K,L))
            replace(N,M,nil()) -> nil()
            selsort(cons(N,L)) -> ifselsort(eq(N,min(cons(N,L))),cons(N,L))
            selsort(nil()) -> nil()
        - Signature:
            {eq/2,ifmin/2,ifrepl/4,ifselsort/2,le/2,min/1,replace/3,selsort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {eq,ifmin,ifrepl,ifselsort,le,min,replace
            ,selsort} 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:
            eq(0(),0()) -> true()
            eq(0(),s(Y)) -> false()
            eq(s(X),0()) -> false()
            eq(s(X),s(Y)) -> eq(X,Y)
            ifmin(false(),cons(N,cons(M,L))) -> min(cons(M,L))
            ifmin(true(),cons(N,cons(M,L))) -> min(cons(N,L))
            ifrepl(false(),N,M,cons(K,L)) -> cons(K,replace(N,M,L))
            ifrepl(true(),N,M,cons(K,L)) -> cons(M,L)
            ifselsort(false(),cons(N,L)) -> cons(min(cons(N,L)),selsort(replace(min(cons(N,L)),N,L)))
            ifselsort(true(),cons(N,L)) -> cons(N,selsort(L))
            le(0(),Y) -> true()
            le(s(X),0()) -> false()
            le(s(X),s(Y)) -> le(X,Y)
            min(cons(N,cons(M,L))) -> ifmin(le(N,M),cons(N,cons(M,L)))
            min(cons(0(),nil())) -> 0()
            min(cons(s(N),nil())) -> s(N)
            replace(N,M,cons(K,L)) -> ifrepl(eq(N,K),N,M,cons(K,L))
            replace(N,M,nil()) -> nil()
            selsort(cons(N,L)) -> ifselsort(eq(N,min(cons(N,L))),cons(N,L))
            selsort(nil()) -> nil()
        - Signature:
            {eq/2,ifmin/2,ifrepl/4,ifselsort/2,le/2,min/1,replace/3,selsort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {eq,ifmin,ifrepl,ifselsort,le,min,replace
            ,selsort} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          eq(x,y){x -> s(x),y -> s(y)} =
            eq(s(x),s(y)) ->^+ eq(x,y)
              = C[eq(x,y) = eq(x,y){}]

WORST_CASE(Omega(n^1),?)