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


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            ack_in(0(),n) -> ack_out(s(n))
            ack_in(s(m),0()) -> u11(ack_in(m,s(0())))
            ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
            u11(ack_out(n)) -> ack_out(n)
            u21(ack_out(n),m) -> u22(ack_in(m,n))
            u22(ack_out(n)) -> ack_out(n)
        - Signature:
            {ack_in/2,u11/1,u21/2,u22/1} / {0/0,ack_out/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {ack_in,u11,u21,u22} and constructors {0,ack_out,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            ack_in(0(),n) -> ack_out(s(n))
            ack_in(s(m),0()) -> u11(ack_in(m,s(0())))
            ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
            u11(ack_out(n)) -> ack_out(n)
            u21(ack_out(n),m) -> u22(ack_in(m,n))
            u22(ack_out(n)) -> ack_out(n)
        - Signature:
            {ack_in/2,u11/1,u21/2,u22/1} / {0/0,ack_out/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {ack_in,u11,u21,u22} and constructors {0,ack_out,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            ack_in(0(),n) -> ack_out(s(n))
            ack_in(s(m),0()) -> u11(ack_in(m,s(0())))
            ack_in(s(m),s(n)) -> u21(ack_in(s(m),n),m)
            u11(ack_out(n)) -> ack_out(n)
            u21(ack_out(n),m) -> u22(ack_in(m,n))
            u22(ack_out(n)) -> ack_out(n)
        - Signature:
            {ack_in/2,u11/1,u21/2,u22/1} / {0/0,ack_out/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {ack_in,u11,u21,u22} and constructors {0,ack_out,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          ack_in(s(x),y){y -> s(y)} =
            ack_in(s(x),s(y)) ->^+ u21(ack_in(s(x),y),x)
              = C[ack_in(s(x),y) = ack_in(s(x),y){}]

WORST_CASE(Omega(n^1),?)