/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /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:
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            half(x) -> if(ge(x,s(s(0()))),x)
            if(false(),x) -> 0()
            if(true(),x) -> s(half(p(p(x))))
            log(0()) -> 0()
            log(s(x)) -> s(log(half(s(x))))
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {ge/2,half/1,if/2,log/1,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ge,half,if,log,p} 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:
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            half(x) -> if(ge(x,s(s(0()))),x)
            if(false(),x) -> 0()
            if(true(),x) -> s(half(p(p(x))))
            log(0()) -> 0()
            log(s(x)) -> s(log(half(s(x))))
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {ge/2,half/1,if/2,log/1,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ge,half,if,log,p} 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:
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            half(x) -> if(ge(x,s(s(0()))),x)
            if(false(),x) -> 0()
            if(true(),x) -> s(half(p(p(x))))
            log(0()) -> 0()
            log(s(x)) -> s(log(half(s(x))))
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {ge/2,half/1,if/2,log/1,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {ge,half,if,log,p} 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),?)