/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:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            help(x,y) -> ifb(lt(y,x),x,y)
            ifa(false(),x) -> logZeroError()
            ifa(true(),x) -> help(x,1())
            ifb(false(),x,y) -> y
            ifb(true(),x,y) -> help(half(x),s(y))
            logarithm(x) -> ifa(lt(0(),x),x)
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {half/1,help/2,ifa/2,ifb/3,logarithm/1,lt/2} / {0/0,1/0,false/0,logZeroError/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {half,help,ifa,ifb,logarithm,lt} and constructors {0,1,false
            ,logZeroError,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))
            help(x,y) -> ifb(lt(y,x),x,y)
            ifa(false(),x) -> logZeroError()
            ifa(true(),x) -> help(x,1())
            ifb(false(),x,y) -> y
            ifb(true(),x,y) -> help(half(x),s(y))
            logarithm(x) -> ifa(lt(0(),x),x)
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {half/1,help/2,ifa/2,ifb/3,logarithm/1,lt/2} / {0/0,1/0,false/0,logZeroError/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {half,help,ifa,ifb,logarithm,lt} and constructors {0,1,false
            ,logZeroError,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))
            help(x,y) -> ifb(lt(y,x),x,y)
            ifa(false(),x) -> logZeroError()
            ifa(true(),x) -> help(x,1())
            ifb(false(),x,y) -> y
            ifb(true(),x,y) -> help(half(x),s(y))
            logarithm(x) -> ifa(lt(0(),x),x)
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {half/1,help/2,ifa/2,ifb/3,logarithm/1,lt/2} / {0/0,1/0,false/0,logZeroError/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {half,help,ifa,ifb,logarithm,lt} and constructors {0,1,false
            ,logZeroError,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),?)