/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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

WORST_CASE(Omega(n^1),?)