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

WORST_CASE(Omega(n^1),?)