/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:
            div(x,y) -> quot(x,y,0())
            if(false(),x,s(y),z) -> quot(minus(x,s(y)),s(y),z)
            if(true(),x,y,z) -> p(z)
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            p(s(x)) -> x
            plus(0(),y) -> y
            plus(s(x),y) -> plus(x,s(y))
            quot(x,y,z) -> if(zero(x),x,y,plus(z,s(0())))
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {div/2,if/4,minus/2,p/1,plus/2,quot/3,zero/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {div,if,minus,p,plus,quot,zero} 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:
            div(x,y) -> quot(x,y,0())
            if(false(),x,s(y),z) -> quot(minus(x,s(y)),s(y),z)
            if(true(),x,y,z) -> p(z)
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            p(s(x)) -> x
            plus(0(),y) -> y
            plus(s(x),y) -> plus(x,s(y))
            quot(x,y,z) -> if(zero(x),x,y,plus(z,s(0())))
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {div/2,if/4,minus/2,p/1,plus/2,quot/3,zero/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {div,if,minus,p,plus,quot,zero} 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:
            div(x,y) -> quot(x,y,0())
            if(false(),x,s(y),z) -> quot(minus(x,s(y)),s(y),z)
            if(true(),x,y,z) -> p(z)
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            p(s(x)) -> x
            plus(0(),y) -> y
            plus(s(x),y) -> plus(x,s(y))
            quot(x,y,z) -> if(zero(x),x,y,plus(z,s(0())))
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {div/2,if/4,minus/2,p/1,plus/2,quot/3,zero/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {div,if,minus,p,plus,quot,zero} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          minus(x,y){x -> s(x),y -> s(y)} =
            minus(s(x),s(y)) ->^+ minus(x,y)
              = C[minus(x,y) = minus(x,y){}]

WORST_CASE(Omega(n^1),?)