/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:
            del(x,cons(y,z)) -> if(eq(x,y),z,cons(y,del(x,z)))
            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)
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            min(x,cons(y,z)) -> if(le(x,y),min(x,z),min(y,z))
            min(x,nil()) -> x
            minsort(cons(x,y)) -> cons(min(x,y),minsort(del(min(x,y),cons(x,y))))
            minsort(nil()) -> nil()
        - Signature:
            {del/2,eq/2,if/3,le/2,min/2,minsort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {del,eq,if,le,min,minsort} 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,z)) -> if(eq(x,y),z,cons(y,del(x,z)))
            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)
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            min(x,cons(y,z)) -> if(le(x,y),min(x,z),min(y,z))
            min(x,nil()) -> x
            minsort(cons(x,y)) -> cons(min(x,y),minsort(del(min(x,y),cons(x,y))))
            minsort(nil()) -> nil()
        - Signature:
            {del/2,eq/2,if/3,le/2,min/2,minsort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {del,eq,if,le,min,minsort} 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,z)) -> if(eq(x,y),z,cons(y,del(x,z)))
            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)
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            min(x,cons(y,z)) -> if(le(x,y),min(x,z),min(y,z))
            min(x,nil()) -> x
            minsort(cons(x,y)) -> cons(min(x,y),minsort(del(min(x,y),cons(x,y))))
            minsort(nil()) -> nil()
        - Signature:
            {del/2,eq/2,if/3,le/2,min/2,minsort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {del,eq,if,le,min,minsort} and constructors {0,cons,false,nil,s
            ,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          del(x,z){z -> cons(y,z)} =
            del(x,cons(y,z)) ->^+ if(eq(x,y),z,cons(y,del(x,z)))
              = C[del(x,z) = del(x,z){}]

WORST_CASE(Omega(n^1),?)