/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:
            cond(false(),x,y,z) -> 0()
            cond(true(),x,y,z) -> s(d(x,s(y),plus(s(y),z)))
            d(x,s(y),z) -> cond(ge(x,z),x,y,z)
            div(x,s(y)) -> d(x,s(y),0())
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
        - Signature:
            {cond/4,d/3,div/2,ge/2,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cond,d,div,ge,plus} 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:
            cond(false(),x,y,z) -> 0()
            cond(true(),x,y,z) -> s(d(x,s(y),plus(s(y),z)))
            d(x,s(y),z) -> cond(ge(x,z),x,y,z)
            div(x,s(y)) -> d(x,s(y),0())
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
        - Signature:
            {cond/4,d/3,div/2,ge/2,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cond,d,div,ge,plus} 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:
            cond(false(),x,y,z) -> 0()
            cond(true(),x,y,z) -> s(d(x,s(y),plus(s(y),z)))
            d(x,s(y),z) -> cond(ge(x,z),x,y,z)
            div(x,s(y)) -> d(x,s(y),0())
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
        - Signature:
            {cond/4,d/3,div/2,ge/2,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {cond,d,div,ge,plus} and constructors {0,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),?)