/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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__add(X1,X2) -> add(X1,X2)
            a__add(0(),X) -> mark(X)
            a__add(s(X),Y) -> s(add(X,Y))
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__fst(X1,X2) -> fst(X1,X2)
            a__fst(0(),Z) -> nil()
            a__fst(s(X),cons(Y,Z)) -> cons(mark(Y),fst(X,Z))
            a__len(X) -> len(X)
            a__len(cons(X,Z)) -> s(len(Z))
            a__len(nil()) -> 0()
            mark(0()) -> 0()
            mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(fst(X1,X2)) -> a__fst(mark(X1),mark(X2))
            mark(len(X)) -> a__len(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(X)
        - Signature:
            {a__add/2,a__from/1,a__fst/2,a__len/1,mark/1} / {0/0,add/2,cons/2,from/1,fst/2,len/1,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a__add,a__from,a__fst,a__len,mark} and constructors {0,add,cons
            ,from,fst,len,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__add(X1,X2) -> add(X1,X2)
            a__add(0(),X) -> mark(X)
            a__add(s(X),Y) -> s(add(X,Y))
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__fst(X1,X2) -> fst(X1,X2)
            a__fst(0(),Z) -> nil()
            a__fst(s(X),cons(Y,Z)) -> cons(mark(Y),fst(X,Z))
            a__len(X) -> len(X)
            a__len(cons(X,Z)) -> s(len(Z))
            a__len(nil()) -> 0()
            mark(0()) -> 0()
            mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(fst(X1,X2)) -> a__fst(mark(X1),mark(X2))
            mark(len(X)) -> a__len(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(X)
        - Signature:
            {a__add/2,a__from/1,a__fst/2,a__len/1,mark/1} / {0/0,add/2,cons/2,from/1,fst/2,len/1,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a__add,a__from,a__fst,a__len,mark} and constructors {0,add,cons
            ,from,fst,len,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__add(X1,X2) -> add(X1,X2)
            a__add(0(),X) -> mark(X)
            a__add(s(X),Y) -> s(add(X,Y))
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            a__fst(X1,X2) -> fst(X1,X2)
            a__fst(0(),Z) -> nil()
            a__fst(s(X),cons(Y,Z)) -> cons(mark(Y),fst(X,Z))
            a__len(X) -> len(X)
            a__len(cons(X,Z)) -> s(len(Z))
            a__len(nil()) -> 0()
            mark(0()) -> 0()
            mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(from(X)) -> a__from(mark(X))
            mark(fst(X1,X2)) -> a__fst(mark(X1),mark(X2))
            mark(len(X)) -> a__len(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(X)
        - Signature:
            {a__add/2,a__from/1,a__fst/2,a__len/1,mark/1} / {0/0,add/2,cons/2,from/1,fst/2,len/1,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a__add,a__from,a__fst,a__len,mark} and constructors {0,add,cons
            ,from,fst,len,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> add(x,y)} =
            mark(add(x,y)) ->^+ a__add(mark(x),mark(y))
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)