/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:
            add(0(),x) -> x
            add(s(x),y) -> s(add(x,y))
            cond1(true(),x,y,z) -> cond2(gr(x,0()),x,y,z)
            cond2(false(),x,y,z) -> cond3(gr(y,0()),x,y,z)
            cond2(true(),x,y,z) -> cond1(gr(add(x,y),z),p(x),y,z)
            cond3(false(),x,y,z) -> cond1(gr(add(x,y),z),x,y,z)
            cond3(true(),x,y,z) -> cond1(gr(add(x,y),z),x,p(y),z)
            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:
            {add/2,cond1/4,cond2/4,cond3/4,gr/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {add,cond1,cond2,cond3,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:
            add(0(),x) -> x
            add(s(x),y) -> s(add(x,y))
            cond1(true(),x,y,z) -> cond2(gr(x,0()),x,y,z)
            cond2(false(),x,y,z) -> cond3(gr(y,0()),x,y,z)
            cond2(true(),x,y,z) -> cond1(gr(add(x,y),z),p(x),y,z)
            cond3(false(),x,y,z) -> cond1(gr(add(x,y),z),x,y,z)
            cond3(true(),x,y,z) -> cond1(gr(add(x,y),z),x,p(y),z)
            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:
            {add/2,cond1/4,cond2/4,cond3/4,gr/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {add,cond1,cond2,cond3,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:
            add(0(),x) -> x
            add(s(x),y) -> s(add(x,y))
            cond1(true(),x,y,z) -> cond2(gr(x,0()),x,y,z)
            cond2(false(),x,y,z) -> cond3(gr(y,0()),x,y,z)
            cond2(true(),x,y,z) -> cond1(gr(add(x,y),z),p(x),y,z)
            cond3(false(),x,y,z) -> cond1(gr(add(x,y),z),x,y,z)
            cond3(true(),x,y,z) -> cond1(gr(add(x,y),z),x,p(y),z)
            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:
            {add/2,cond1/4,cond2/4,cond3/4,gr/2,p/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {add,cond1,cond2,cond3,gr,p} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          add(x,y){x -> s(x)} =
            add(s(x),y) ->^+ s(add(x,y))
              = C[add(x,y) = add(x,y){}]

WORST_CASE(Omega(n^1),?)