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

WORST_CASE(Omega(n^1),?)