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

WORST_CASE(Omega(n^1),?)