/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,z) -> if(ge(y,s(0())),ge(x,y),x,y,z)
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            id_inc(x) -> x
            id_inc(x) -> s(x)
            if(false(),b,x,y,z) -> div_by_zero()
            if(true(),false(),x,y,z) -> z
            if(true(),true(),x,y,z) -> div(minus(x,y),y,id_inc(z))
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            quot(x,y) -> div(x,y,0())
        - Signature:
            {div/3,ge/2,id_inc/1,if/5,minus/2,quot/2} / {0/0,div_by_zero/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {div,ge,id_inc,if,minus,quot} and constructors {0,div_by_zero,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(ge(y,s(0())),ge(x,y),x,y,z)
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            id_inc(x) -> x
            id_inc(x) -> s(x)
            if(false(),b,x,y,z) -> div_by_zero()
            if(true(),false(),x,y,z) -> z
            if(true(),true(),x,y,z) -> div(minus(x,y),y,id_inc(z))
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            quot(x,y) -> div(x,y,0())
        - Signature:
            {div/3,ge/2,id_inc/1,if/5,minus/2,quot/2} / {0/0,div_by_zero/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {div,ge,id_inc,if,minus,quot} and constructors {0,div_by_zero,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(ge(y,s(0())),ge(x,y),x,y,z)
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            id_inc(x) -> x
            id_inc(x) -> s(x)
            if(false(),b,x,y,z) -> div_by_zero()
            if(true(),false(),x,y,z) -> z
            if(true(),true(),x,y,z) -> div(minus(x,y),y,id_inc(z))
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            quot(x,y) -> div(x,y,0())
        - Signature:
            {div/3,ge/2,id_inc/1,if/5,minus/2,quot/2} / {0/0,div_by_zero/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {div,ge,id_inc,if,minus,quot} and constructors {0,div_by_zero,false
            ,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          ge(x,y){x -> s(x),y -> s(y)} =
            ge(s(x),s(y)) ->^+ ge(x,y)
              = C[ge(x,y) = ge(x,y){}]

WORST_CASE(Omega(n^1),?)