/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /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:
            and(x,false()) -> false()
            and(false(),x) -> false()
            and(true(),true()) -> true()
            cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
            cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
            cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            gr(s(x),s(y)) -> gr(x,y)
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {and/2,cond1/3,cond2/3,eq/2,gr/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,cond1,cond2,eq,gr,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:
            and(x,false()) -> false()
            and(false(),x) -> false()
            and(true(),true()) -> true()
            cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
            cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
            cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            gr(s(x),s(y)) -> gr(x,y)
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {and/2,cond1/3,cond2/3,eq/2,gr/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,cond1,cond2,eq,gr,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:
            and(x,false()) -> false()
            and(false(),x) -> false()
            and(true(),true()) -> true()
            cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
            cond2(false(),x,y) -> cond1(and(eq(x,y),gr(x,0())),x,y)
            cond2(true(),x,y) -> cond2(gr(y,0()),p(x),p(y))
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            gr(0(),x) -> false()
            gr(s(x),0()) -> true()
            gr(s(x),s(y)) -> gr(x,y)
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {and/2,cond1/3,cond2/3,eq/2,gr/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {and,cond1,cond2,eq,gr,p} and constructors {0,false,s
            ,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          eq(x,y){x -> s(x),y -> s(y)} =
            eq(s(x),s(y)) ->^+ eq(x,y)
              = C[eq(x,y) = eq(x,y){}]

WORST_CASE(Omega(n^1),?)