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


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            del(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
            del(x,nil()) -> nil()
            eq(0(),0()) -> true()
            eq(0(),s(y)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            if1(false(),x,y,xs) -> max(cons(y,xs))
            if1(true(),x,y,xs) -> max(cons(x,xs))
            if2(false(),x,y,xs) -> cons(y,del(x,xs))
            if2(true(),x,y,xs) -> xs
            max(cons(x,cons(y,xs))) -> if1(ge(x,y),x,y,xs)
            max(cons(x,nil())) -> x
            max(nil()) -> 0()
            sort(cons(x,xs)) -> cons(max(cons(x,xs)),sort(del(max(cons(x,xs)),cons(x,xs))))
            sort(nil()) -> nil()
        - Signature:
            {del/2,eq/2,ge/2,if1/4,if2/4,max/1,sort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {del,eq,ge,if1,if2,max,sort} 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:
            del(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
            del(x,nil()) -> nil()
            eq(0(),0()) -> true()
            eq(0(),s(y)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            if1(false(),x,y,xs) -> max(cons(y,xs))
            if1(true(),x,y,xs) -> max(cons(x,xs))
            if2(false(),x,y,xs) -> cons(y,del(x,xs))
            if2(true(),x,y,xs) -> xs
            max(cons(x,cons(y,xs))) -> if1(ge(x,y),x,y,xs)
            max(cons(x,nil())) -> x
            max(nil()) -> 0()
            sort(cons(x,xs)) -> cons(max(cons(x,xs)),sort(del(max(cons(x,xs)),cons(x,xs))))
            sort(nil()) -> nil()
        - Signature:
            {del/2,eq/2,ge/2,if1/4,if2/4,max/1,sort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {del,eq,ge,if1,if2,max,sort} 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:
            del(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
            del(x,nil()) -> nil()
            eq(0(),0()) -> true()
            eq(0(),s(y)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            ge(x,0()) -> true()
            ge(0(),s(x)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            if1(false(),x,y,xs) -> max(cons(y,xs))
            if1(true(),x,y,xs) -> max(cons(x,xs))
            if2(false(),x,y,xs) -> cons(y,del(x,xs))
            if2(true(),x,y,xs) -> xs
            max(cons(x,cons(y,xs))) -> if1(ge(x,y),x,y,xs)
            max(cons(x,nil())) -> x
            max(nil()) -> 0()
            sort(cons(x,xs)) -> cons(max(cons(x,xs)),sort(del(max(cons(x,xs)),cons(x,xs))))
            sort(nil()) -> nil()
        - Signature:
            {del/2,eq/2,ge/2,if1/4,if2/4,max/1,sort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {del,eq,ge,if1,if2,max,sort} and constructors {0,cons,false,nil,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),?)