/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:
            if(false(),b,x,y) -> logZeroError()
            if(true(),false(),x,s(y)) -> y
            if(true(),true(),x,y) -> logIter(x,y)
            inc(0()) -> s(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) -> logIter(x,0())
            logIter(x,y) -> if(le(s(0()),x),le(s(s(0())),x),quot(x,s(s(0()))),inc(y))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {if/4,inc/1,le/2,log/1,logIter/2,minus/2,quot/2} / {0/0,false/0,logZeroError/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if,inc,le,log,logIter,minus,quot} and constructors {0,false
            ,logZeroError,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            if(false(),b,x,y) -> logZeroError()
            if(true(),false(),x,s(y)) -> y
            if(true(),true(),x,y) -> logIter(x,y)
            inc(0()) -> s(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) -> logIter(x,0())
            logIter(x,y) -> if(le(s(0()),x),le(s(s(0())),x),quot(x,s(s(0()))),inc(y))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {if/4,inc/1,le/2,log/1,logIter/2,minus/2,quot/2} / {0/0,false/0,logZeroError/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if,inc,le,log,logIter,minus,quot} and constructors {0,false
            ,logZeroError,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            if(false(),b,x,y) -> logZeroError()
            if(true(),false(),x,s(y)) -> y
            if(true(),true(),x,y) -> logIter(x,y)
            inc(0()) -> s(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) -> logIter(x,0())
            logIter(x,y) -> if(le(s(0()),x),le(s(s(0())),x),quot(x,s(s(0()))),inc(y))
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {if/4,inc/1,le/2,log/1,logIter/2,minus/2,quot/2} / {0/0,false/0,logZeroError/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if,inc,le,log,logIter,minus,quot} and constructors {0,false
            ,logZeroError,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          inc(x){x -> s(x)} =
            inc(s(x)) ->^+ s(inc(x))
              = C[inc(x) = inc(x){}]

WORST_CASE(Omega(n^1),?)