/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() -> b()
            a() -> c()
            div(x,y,0()) -> divisible(x,y)
            div(0(),y,s(z)) -> false()
            div(s(x),y,s(z)) -> div(x,y,z)
            divisible(0(),s(y)) -> true()
            divisible(s(x),s(y)) -> div(s(x),s(y),s(y))
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            if(false(),x,y,z,u) -> if2(divisible(z,y),x,y,z,u)
            if(true(),x,y,z,u) -> z
            if2(false(),x,y,z,u) -> lcmIter(x,y,plus(x,z),u)
            if2(true(),x,y,z,u) -> z
            ifTimes(false(),x,y) -> plus(y,times(y,p(x)))
            ifTimes(true(),x,y) -> 0()
            lcm(x,y) -> lcmIter(x,y,0(),times(x,y))
            lcmIter(x,y,z,u) -> if(or(ge(0(),x),ge(z,u)),x,y,z,u)
            or(false(),y) -> y
            or(true(),y) -> true()
            p(0()) -> s(s(0()))
            p(s(x)) -> x
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(x,y) -> ifTimes(ge(0(),x),x,y)
        - Signature:
            {a/0,div/3,divisible/2,ge/2,if/5,if2/5,ifTimes/3,lcm/2,lcmIter/4,or/2,p/1,plus/2,times/2} / {0/0,b/0,c/0
            ,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a,div,divisible,ge,if,if2,ifTimes,lcm,lcmIter,or,p,plus
            ,times} and constructors {0,b,c,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a() -> b()
            a() -> c()
            div(x,y,0()) -> divisible(x,y)
            div(0(),y,s(z)) -> false()
            div(s(x),y,s(z)) -> div(x,y,z)
            divisible(0(),s(y)) -> true()
            divisible(s(x),s(y)) -> div(s(x),s(y),s(y))
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            if(false(),x,y,z,u) -> if2(divisible(z,y),x,y,z,u)
            if(true(),x,y,z,u) -> z
            if2(false(),x,y,z,u) -> lcmIter(x,y,plus(x,z),u)
            if2(true(),x,y,z,u) -> z
            ifTimes(false(),x,y) -> plus(y,times(y,p(x)))
            ifTimes(true(),x,y) -> 0()
            lcm(x,y) -> lcmIter(x,y,0(),times(x,y))
            lcmIter(x,y,z,u) -> if(or(ge(0(),x),ge(z,u)),x,y,z,u)
            or(false(),y) -> y
            or(true(),y) -> true()
            p(0()) -> s(s(0()))
            p(s(x)) -> x
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(x,y) -> ifTimes(ge(0(),x),x,y)
        - Signature:
            {a/0,div/3,divisible/2,ge/2,if/5,if2/5,ifTimes/3,lcm/2,lcmIter/4,or/2,p/1,plus/2,times/2} / {0/0,b/0,c/0
            ,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a,div,divisible,ge,if,if2,ifTimes,lcm,lcmIter,or,p,plus
            ,times} and constructors {0,b,c,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a() -> b()
            a() -> c()
            div(x,y,0()) -> divisible(x,y)
            div(0(),y,s(z)) -> false()
            div(s(x),y,s(z)) -> div(x,y,z)
            divisible(0(),s(y)) -> true()
            divisible(s(x),s(y)) -> div(s(x),s(y),s(y))
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            if(false(),x,y,z,u) -> if2(divisible(z,y),x,y,z,u)
            if(true(),x,y,z,u) -> z
            if2(false(),x,y,z,u) -> lcmIter(x,y,plus(x,z),u)
            if2(true(),x,y,z,u) -> z
            ifTimes(false(),x,y) -> plus(y,times(y,p(x)))
            ifTimes(true(),x,y) -> 0()
            lcm(x,y) -> lcmIter(x,y,0(),times(x,y))
            lcmIter(x,y,z,u) -> if(or(ge(0(),x),ge(z,u)),x,y,z,u)
            or(false(),y) -> y
            or(true(),y) -> true()
            p(0()) -> s(s(0()))
            p(s(x)) -> x
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(x,y) -> ifTimes(ge(0(),x),x,y)
        - Signature:
            {a/0,div/3,divisible/2,ge/2,if/5,if2/5,ifTimes/3,lcm/2,lcmIter/4,or/2,p/1,plus/2,times/2} / {0/0,b/0,c/0
            ,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a,div,divisible,ge,if,if2,ifTimes,lcm,lcmIter,or,p,plus
            ,times} and constructors {0,b,c,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          div(x,y,z){x -> s(x),z -> s(z)} =
            div(s(x),y,s(z)) ->^+ div(x,y,z)
              = C[div(x,y,z) = div(x,y,z){}]

WORST_CASE(Omega(n^1),?)