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


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


WORST_CASE(Omega(n^1),?)
* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            gt(s(x),s(y)) -> gt(x,y)
            gt(s(x),zero()) -> true()
            gt(zero(),y) -> false()
            id(x) -> x
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            not(x) -> if(x,false(),true())
            plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y))))
            plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
            plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
            plus(zero(),y) -> y
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {gt/2,id/1,if/3,minus/2,not/1,plus/2,quot/2} / {0/0,false/0,s/1,true/0,zero/0}
        - Obligation:
             runtime complexity wrt. defined symbols {gt,id,if,minus,not,plus,quot} and constructors {0,false,s,true
            ,zero}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            gt(s(x),s(y)) -> gt(x,y)
            gt(s(x),zero()) -> true()
            gt(zero(),y) -> false()
            id(x) -> x
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            minus(x,0()) -> x
            minus(s(x),s(y)) -> minus(x,y)
            not(x) -> if(x,false(),true())
            plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y))))
            plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
            plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
            plus(zero(),y) -> y
            quot(0(),s(y)) -> 0()
            quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
        - Signature:
            {gt/2,id/1,if/3,minus/2,not/1,plus/2,quot/2} / {0/0,false/0,s/1,true/0,zero/0}
        - Obligation:
             runtime complexity wrt. defined symbols {gt,id,if,minus,not,plus,quot} and constructors {0,false,s,true
            ,zero}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          gt(x,y){x -> s(x),y -> s(y)} =
            gt(s(x),s(y)) ->^+ gt(x,y)
              = C[gt(x,y) = gt(x,y){}]

WORST_CASE(Omega(n^1),?)