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

WORST_CASE(Omega(n^1),?)