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

WORST_CASE(Omega(n^1),?)