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

WORST_CASE(Omega(n^1),?)