/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            if(false(),x,y) -> log2(half(x),y)
            if(true(),x,s(y)) -> y
            inc(0()) -> 0()
            inc(s(x)) -> s(inc(x))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            log(x) -> log2(x,0())
            log2(x,y) -> if(le(x,s(0())),x,inc(y))
        - Signature:
            {half/1,if/3,inc/1,le/2,log/1,log2/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {half,if,inc,le,log,log2} 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:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            if(false(),x,y) -> log2(half(x),y)
            if(true(),x,s(y)) -> y
            inc(0()) -> 0()
            inc(s(x)) -> s(inc(x))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            log(x) -> log2(x,0())
            log2(x,y) -> if(le(x,s(0())),x,inc(y))
        - Signature:
            {half/1,if/3,inc/1,le/2,log/1,log2/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {half,if,inc,le,log,log2} 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:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            if(false(),x,y) -> log2(half(x),y)
            if(true(),x,s(y)) -> y
            inc(0()) -> 0()
            inc(s(x)) -> s(inc(x))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            log(x) -> log2(x,0())
            log2(x,y) -> if(le(x,s(0())),x,inc(y))
        - Signature:
            {half/1,if/3,inc/1,le/2,log/1,log2/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {half,if,inc,le,log,log2} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          half(x){x -> s(s(x))} =
            half(s(s(x))) ->^+ s(half(x))
              = C[half(x) = half(x){}]

WORST_CASE(Omega(n^1),?)