/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1),?)
* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            equal0(a,b) -> equal0[Ite](<(a,b),a,b)
            gcd(x,y) -> gcd[Ite](equal0(x,y),x,y)
            monus(S(x'),S(x)) -> monus(x',x)
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            equal0[Ite](False(),a,b) -> False()
            equal0[Ite](True(),a,b) -> equal0[True][Ite](<(b,a),a,b)
            equal0[True][Ite](False(),a,b) -> False()
            equal0[True][Ite](True(),a,b) -> True()
            gcd[False][Ite](False(),x,y) -> gcd(y,monus(y,x))
            gcd[False][Ite](True(),x,y) -> gcd(monus(x,y),y)
            gcd[Ite](False(),x,y) -> gcd[False][Ite](<(x,y),x,y)
            gcd[Ite](True(),x,y) -> x
        - Signature:
            {</2,equal0/2,equal0[Ite]/3,equal0[True][Ite]/3,gcd/2,gcd[False][Ite]/3,gcd[Ite]/3,monus/2} / {0/0,False/0
            ,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {<,equal0,equal0[Ite],equal0[True][Ite],gcd
            ,gcd[False][Ite],gcd[Ite],monus} and constructors {0,False,S,True}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            equal0(a,b) -> equal0[Ite](<(a,b),a,b)
            gcd(x,y) -> gcd[Ite](equal0(x,y),x,y)
            monus(S(x'),S(x)) -> monus(x',x)
        - Weak TRS:
            <(x,0()) -> False()
            <(0(),S(y)) -> True()
            <(S(x),S(y)) -> <(x,y)
            equal0[Ite](False(),a,b) -> False()
            equal0[Ite](True(),a,b) -> equal0[True][Ite](<(b,a),a,b)
            equal0[True][Ite](False(),a,b) -> False()
            equal0[True][Ite](True(),a,b) -> True()
            gcd[False][Ite](False(),x,y) -> gcd(y,monus(y,x))
            gcd[False][Ite](True(),x,y) -> gcd(monus(x,y),y)
            gcd[Ite](False(),x,y) -> gcd[False][Ite](<(x,y),x,y)
            gcd[Ite](True(),x,y) -> x
        - Signature:
            {</2,equal0/2,equal0[Ite]/3,equal0[True][Ite]/3,gcd/2,gcd[False][Ite]/3,gcd[Ite]/3,monus/2} / {0/0,False/0
            ,S/1,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {<,equal0,equal0[Ite],equal0[True][Ite],gcd
            ,gcd[False][Ite],gcd[Ite],monus} and constructors {0,False,S,True}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          monus(x,y){x -> S(x),y -> S(y)} =
            monus(S(x),S(y)) ->^+ monus(x,y)
              = C[monus(x,y) = monus(x,y){}]

WORST_CASE(Omega(n^1),?)