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


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            if(false(),b,x,y) -> if2(b,x,y)
            if(true(),b,x,y) -> log_undefined()
            if2(false(),x,y) -> log2(quot(x,s(s(0()))),y)
            if2(true(),x,s(y)) -> y
            inc(0()) -> 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) -> log2(x,0())
            log2(x,y) -> if(le(x,0()),le(x,s(0())),x,inc(y))
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            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,if2/3,inc/1,le/2,log/1,log2/2,minus/2,quot/2} / {0/0,false/0,log_undefined/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if,if2,inc,le,log,log2,minus,quot} and constructors {0,false
            ,log_undefined,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) -> if2(b,x,y)
            if(true(),b,x,y) -> log_undefined()
            if2(false(),x,y) -> log2(quot(x,s(s(0()))),y)
            if2(true(),x,s(y)) -> y
            inc(0()) -> 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) -> log2(x,0())
            log2(x,y) -> if(le(x,0()),le(x,s(0())),x,inc(y))
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            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,if2/3,inc/1,le/2,log/1,log2/2,minus/2,quot/2} / {0/0,false/0,log_undefined/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if,if2,inc,le,log,log2,minus,quot} and constructors {0,false
            ,log_undefined,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) -> if2(b,x,y)
            if(true(),b,x,y) -> log_undefined()
            if2(false(),x,y) -> log2(quot(x,s(s(0()))),y)
            if2(true(),x,s(y)) -> y
            inc(0()) -> 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) -> log2(x,0())
            log2(x,y) -> if(le(x,0()),le(x,s(0())),x,inc(y))
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            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,if2/3,inc/1,le/2,log/1,log2/2,minus/2,quot/2} / {0/0,false/0,log_undefined/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if,if2,inc,le,log,log2,minus,quot} and constructors {0,false
            ,log_undefined,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),?)