/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:
            average(x,y) -> if(le(x,0()),le(y,0()),le(y,s(0())),le(y,s(s(0()))),x,y)
            if(false(),b1,b2,b3,x,y) -> average(p(x),s(y))
            if(true(),b1,b2,b3,x,y) -> if2(b1,b2,b3,x,y)
            if2(false(),b2,b3,x,y) -> if3(b2,b3,x,y)
            if2(true(),b2,b3,x,y) -> 0()
            if3(false(),b3,x,y) -> if4(b3,x,y)
            if3(true(),b3,x,y) -> 0()
            if4(false(),x,y) -> average(s(x),p(p(y)))
            if4(true(),x,y) -> s(0())
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {average/2,if/6,if2/5,if3/4,if4/3,le/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {average,if,if2,if3,if4,le,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:
            average(x,y) -> if(le(x,0()),le(y,0()),le(y,s(0())),le(y,s(s(0()))),x,y)
            if(false(),b1,b2,b3,x,y) -> average(p(x),s(y))
            if(true(),b1,b2,b3,x,y) -> if2(b1,b2,b3,x,y)
            if2(false(),b2,b3,x,y) -> if3(b2,b3,x,y)
            if2(true(),b2,b3,x,y) -> 0()
            if3(false(),b3,x,y) -> if4(b3,x,y)
            if3(true(),b3,x,y) -> 0()
            if4(false(),x,y) -> average(s(x),p(p(y)))
            if4(true(),x,y) -> s(0())
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {average/2,if/6,if2/5,if3/4,if4/3,le/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {average,if,if2,if3,if4,le,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:
            average(x,y) -> if(le(x,0()),le(y,0()),le(y,s(0())),le(y,s(s(0()))),x,y)
            if(false(),b1,b2,b3,x,y) -> average(p(x),s(y))
            if(true(),b1,b2,b3,x,y) -> if2(b1,b2,b3,x,y)
            if2(false(),b2,b3,x,y) -> if3(b2,b3,x,y)
            if2(true(),b2,b3,x,y) -> 0()
            if3(false(),b3,x,y) -> if4(b3,x,y)
            if3(true(),b3,x,y) -> 0()
            if4(false(),x,y) -> average(s(x),p(p(y)))
            if4(true(),x,y) -> s(0())
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {average/2,if/6,if2/5,if3/4,if4/3,le/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {average,if,if2,if3,if4,le,p} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          le(x,y){x -> s(x),y -> s(y)} =
            le(s(x),s(y)) ->^+ le(x,y)
              = C[le(x,y) = le(x,y){}]

WORST_CASE(Omega(n^1),?)