4 year old boxer

Question
QUESTION: we have a boxer that goes poop upstairs in my sons room and occasionally pees in his toy box. harley never barks or whines to be let out. he just gets excited and goes to the door. he'll stare at you and always wants attention when we have visitors and they pet him. he usually has his accidents when we are at work and we usaully don't notice right away because we don't go up there to often. he is free to roam the house when were gone but he usually doesn't chew anything.. occasionaly he will get in the trash and make a mess if there is old food in there.
if the weather is nice he'll stay outside and he will chew things when he is outside until we get home. harley is a male that has been nuetred.. we hoped that would help him from marking his territory. harley really doesn't do much and just sleeps all day. we were thinking about getting rid of him because it is such an irritating habit. he has pooped downstairs before so i don't know what to do.

ANSWER: What type of exercise is Harley getting?

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QUESTION: a normal week for harley he will spend about 4 days outside when we are at work. we have a nice sized back yard that is fenced in to run and jump on. everytime he goes outside he usually runs a lap around the yard. we generally don't run with him. it is rare that we take him in a vehicle anywhere.

ANSWER: Your dog is bored and the solution is very simple, stop banishing him to the backyard and start exercising him.

Many people make the mistake of putting their dogs outside (while home or away) and thinking they 'should' be getting enough exercise.  Running around the yard and leash walking are very different, mentally, for a dog.  Leash walking has a purpose.  It stimulates the mind and tires out the animal.

You have chosen a breed that is extremely people oriented.  They do not do well when left alone outside.  They also don't do well in hot (above 80) and cold (below 45-50) weather.  If you are leaving him out you are putting his health at risk, not to mention running the risk of him digging, jumping or otherwise escaping the fence and looking for stimulation elsewhere.

As for the housebreaking, what steps have you taken to cure this and how old is Harley?

---------- FOLLOW-UP ----------

QUESTION: harley is 4 years old. he has never been trained to go for a walk on a collar. he is a strong dog and likes to run if i remember correctly. he is only outside in mild weather and does have a nice wooden house outside. if the solution is to walk him then why do you ask about what housebreaking steps we have taken? most of the time we cant catch him in the act so nothing is done to stop it.

Answer
It really doesn't matter if he has a nice wooden house out back or a barn all to himself...he'll still be bored and chew.  If you want to stop the behavior, stop letting him out on his own.

I ask because you stated that he's pooping in the house.  The two behaviors are exclusive of each other.  Chewing in the yard and pooping in the house have nothing to do with one another.

If you aren't willing to supervise him properly, there's nothing that will stop his behaviors and it will be kinder to rehome him with someone that has the time and energy to devote to his needs.