/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:
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            gen(x,y,z) -> if(ge(z,x),x,y,z)
            generate(x,y) -> gen(x,y,0())
            if(false(),x,y,z) -> cons(y,gen(x,y,s(z)))
            if(true(),x,y,z) -> nil()
            sum(cons(0(),xs)) -> sum(xs)
            sum(cons(s(x),xs)) -> s(sum(cons(x,xs)))
            sum(nil()) -> 0()
            times(x,y) -> sum(generate(x,y))
        - Signature:
            {ge/2,gen/3,generate/2,if/4,sum/1,times/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {ge,gen,generate,if,sum,times} and constructors {0,cons,false,nil,s
            ,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            gen(x,y,z) -> if(ge(z,x),x,y,z)
            generate(x,y) -> gen(x,y,0())
            if(false(),x,y,z) -> cons(y,gen(x,y,s(z)))
            if(true(),x,y,z) -> nil()
            sum(cons(0(),xs)) -> sum(xs)
            sum(cons(s(x),xs)) -> s(sum(cons(x,xs)))
            sum(nil()) -> 0()
            times(x,y) -> sum(generate(x,y))
        - Signature:
            {ge/2,gen/3,generate/2,if/4,sum/1,times/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {ge,gen,generate,if,sum,times} and constructors {0,cons,false,nil,s
            ,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            gen(x,y,z) -> if(ge(z,x),x,y,z)
            generate(x,y) -> gen(x,y,0())
            if(false(),x,y,z) -> cons(y,gen(x,y,s(z)))
            if(true(),x,y,z) -> nil()
            sum(cons(0(),xs)) -> sum(xs)
            sum(cons(s(x),xs)) -> s(sum(cons(x,xs)))
            sum(nil()) -> 0()
            times(x,y) -> sum(generate(x,y))
        - Signature:
            {ge/2,gen/3,generate/2,if/4,sum/1,times/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {ge,gen,generate,if,sum,times} and constructors {0,cons,false,nil,s
            ,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          ge(x,y){x -> s(x),y -> s(y)} =
            ge(s(x),s(y)) ->^+ ge(x,y)
              = C[ge(x,y) = ge(x,y){}]

WORST_CASE(Omega(n^1),?)