/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /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:
            +(X,0()) -> X
            +(X,s(Y)) -> s(+(X,Y))
            f(0(),s(0()),X) -> f(X,+(X,X),X)
            g(X,Y) -> X
            g(X,Y) -> Y
        - Signature:
            {+/2,f/3,g/2} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {+,f,g} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            +(X,0()) -> X
            +(X,s(Y)) -> s(+(X,Y))
            f(0(),s(0()),X) -> f(X,+(X,X),X)
            g(X,Y) -> X
            g(X,Y) -> Y
        - Signature:
            {+/2,f/3,g/2} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {+,f,g} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            +(X,0()) -> X
            +(X,s(Y)) -> s(+(X,Y))
            f(0(),s(0()),X) -> f(X,+(X,X),X)
            g(X,Y) -> X
            g(X,Y) -> Y
        - Signature:
            {+/2,f/3,g/2} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {+,f,g} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          +(x,y){y -> s(y)} =
            +(x,s(y)) ->^+ s(+(x,y))
              = C[+(x,y) = +(x,y){}]

WORST_CASE(Omega(n^1),?)