/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:
            a__div(X1,X2) -> div(X1,X2)
            a__div(0(),s(Y)) -> 0()
            a__div(s(X),s(Y)) -> a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0())
            a__geq(X,0()) -> true()
            a__geq(X1,X2) -> geq(X1,X2)
            a__geq(0(),s(Y)) -> false()
            a__geq(s(X),s(Y)) -> a__geq(X,Y)
            a__if(X1,X2,X3) -> if(X1,X2,X3)
            a__if(false(),X,Y) -> mark(Y)
            a__if(true(),X,Y) -> mark(X)
            a__minus(X1,X2) -> minus(X1,X2)
            a__minus(0(),Y) -> 0()
            a__minus(s(X),s(Y)) -> a__minus(X,Y)
            mark(0()) -> 0()
            mark(div(X1,X2)) -> a__div(mark(X1),X2)
            mark(false()) -> false()
            mark(geq(X1,X2)) -> a__geq(X1,X2)
            mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
            mark(minus(X1,X2)) -> a__minus(X1,X2)
            mark(s(X)) -> s(mark(X))
            mark(true()) -> true()
        - Signature:
            {a__div/2,a__geq/2,a__if/3,a__minus/2,mark/1} / {0/0,div/2,false/0,geq/2,if/3,minus/2,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__div,a__geq,a__if,a__minus,mark} and constructors {0,div,false
            ,geq,if,minus,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__div(X1,X2) -> div(X1,X2)
            a__div(0(),s(Y)) -> 0()
            a__div(s(X),s(Y)) -> a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0())
            a__geq(X,0()) -> true()
            a__geq(X1,X2) -> geq(X1,X2)
            a__geq(0(),s(Y)) -> false()
            a__geq(s(X),s(Y)) -> a__geq(X,Y)
            a__if(X1,X2,X3) -> if(X1,X2,X3)
            a__if(false(),X,Y) -> mark(Y)
            a__if(true(),X,Y) -> mark(X)
            a__minus(X1,X2) -> minus(X1,X2)
            a__minus(0(),Y) -> 0()
            a__minus(s(X),s(Y)) -> a__minus(X,Y)
            mark(0()) -> 0()
            mark(div(X1,X2)) -> a__div(mark(X1),X2)
            mark(false()) -> false()
            mark(geq(X1,X2)) -> a__geq(X1,X2)
            mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
            mark(minus(X1,X2)) -> a__minus(X1,X2)
            mark(s(X)) -> s(mark(X))
            mark(true()) -> true()
        - Signature:
            {a__div/2,a__geq/2,a__if/3,a__minus/2,mark/1} / {0/0,div/2,false/0,geq/2,if/3,minus/2,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__div,a__geq,a__if,a__minus,mark} and constructors {0,div,false
            ,geq,if,minus,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__div(X1,X2) -> div(X1,X2)
            a__div(0(),s(Y)) -> 0()
            a__div(s(X),s(Y)) -> a__if(a__geq(X,Y),s(div(minus(X,Y),s(Y))),0())
            a__geq(X,0()) -> true()
            a__geq(X1,X2) -> geq(X1,X2)
            a__geq(0(),s(Y)) -> false()
            a__geq(s(X),s(Y)) -> a__geq(X,Y)
            a__if(X1,X2,X3) -> if(X1,X2,X3)
            a__if(false(),X,Y) -> mark(Y)
            a__if(true(),X,Y) -> mark(X)
            a__minus(X1,X2) -> minus(X1,X2)
            a__minus(0(),Y) -> 0()
            a__minus(s(X),s(Y)) -> a__minus(X,Y)
            mark(0()) -> 0()
            mark(div(X1,X2)) -> a__div(mark(X1),X2)
            mark(false()) -> false()
            mark(geq(X1,X2)) -> a__geq(X1,X2)
            mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
            mark(minus(X1,X2)) -> a__minus(X1,X2)
            mark(s(X)) -> s(mark(X))
            mark(true()) -> true()
        - Signature:
            {a__div/2,a__geq/2,a__if/3,a__minus/2,mark/1} / {0/0,div/2,false/0,geq/2,if/3,minus/2,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__div,a__geq,a__if,a__minus,mark} and constructors {0,div,false
            ,geq,if,minus,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          a__geq(x,y){x -> s(x),y -> s(y)} =
            a__geq(s(x),s(y)) ->^+ a__geq(x,y)
              = C[a__geq(x,y) = a__geq(x,y){}]

WORST_CASE(Omega(n^1),?)