/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(x,y,z) -> if(lt(x,y),x,y,inc(z))
            division(x,y) -> div(x,y,0())
            if(false(),x,s(y),z) -> div(minus(x,s(y)),s(y),z)
            if(true(),x,y,z) -> z
            inc(0()) -> s(0())
            inc(s(x)) -> s(inc(x))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
        - Signature:
            {div/3,division/2,if/4,inc/1,lt/2,minus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {div,division,if,inc,lt,minus} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            div(x,y,z) -> if(lt(x,y),x,y,inc(z))
            division(x,y) -> div(x,y,0())
            if(false(),x,s(y),z) -> div(minus(x,s(y)),s(y),z)
            if(true(),x,y,z) -> z
            inc(0()) -> s(0())
            inc(s(x)) -> s(inc(x))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
        - Signature:
            {div/3,division/2,if/4,inc/1,lt/2,minus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {div,division,if,inc,lt,minus} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            div(x,y,z) -> if(lt(x,y),x,y,inc(z))
            division(x,y) -> div(x,y,0())
            if(false(),x,s(y),z) -> div(minus(x,s(y)),s(y),z)
            if(true(),x,y,z) -> z
            inc(0()) -> s(0())
            inc(s(x)) -> s(inc(x))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
        - Signature:
            {div/3,division/2,if/4,inc/1,lt/2,minus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {div,division,if,inc,lt,minus} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          inc(x){x -> s(x)} =
            inc(s(x)) ->^+ s(inc(x))
              = C[inc(x) = inc(x){}]

WORST_CASE(Omega(n^1),?)