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

WORST_CASE(Omega(n^1),?)