/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:
            div(x,y) -> quot(x,y,y)
            div(0(),y) -> 0()
            quot(x,0(),s(z)) -> s(div(x,s(z)))
            quot(0(),s(y),z) -> 0()
            quot(s(x),s(y),z) -> quot(x,y,z)
        - Signature:
            {div/2,quot/3} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {div,quot} 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(x,y) -> quot(x,y,y)
            div(0(),y) -> 0()
            quot(x,0(),s(z)) -> s(div(x,s(z)))
            quot(0(),s(y),z) -> 0()
            quot(s(x),s(y),z) -> quot(x,y,z)
        - Signature:
            {div/2,quot/3} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {div,quot} 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(x,y) -> quot(x,y,y)
            div(0(),y) -> 0()
            quot(x,0(),s(z)) -> s(div(x,s(z)))
            quot(0(),s(y),z) -> 0()
            quot(s(x),s(y),z) -> quot(x,y,z)
        - Signature:
            {div/2,quot/3} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {div,quot} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          quot(x,y,z){x -> s(x),y -> s(y)} =
            quot(s(x),s(y),z) ->^+ quot(x,y,z)
              = C[quot(x,y,z) = quot(x,y,z){}]

WORST_CASE(Omega(n^1),?)