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

WORST_CASE(Omega(n^1),?)