/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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MAYBE

Problem:
 isEmpty(cons(x,xs)) -> false()
 isEmpty(nil()) -> true()
 isZero(0()) -> true()
 isZero(s(x)) -> false()
 head(cons(x,xs)) -> x
 tail(cons(x,xs)) -> xs
 tail(nil()) -> nil()
 append(nil(),x) -> cons(x,nil())
 append(cons(y,ys),x) -> cons(y,append(ys,x))
 p(s(s(x))) -> s(p(s(x)))
 p(s(0())) -> 0()
 p(0()) -> 0()
 inc(s(x)) -> s(inc(x))
 inc(0()) -> s(0())
 addLists(xs,ys,zs) ->
 if(isEmpty(xs),isEmpty(ys),isZero(head(xs)),tail(xs),tail(ys),cons(p(head(xs)),tail(xs)),
    cons(inc(head(ys)),tail(ys)),zs,append(zs,head(ys)))
 if(true(),true(),b,xs,ys,xs2,ys2,zs,zs2) -> zs
 if(true(),false(),b,xs,ys,xs2,ys2,zs,zs2) -> differentLengthError()
 if(false(),true(),b,xs,ys,xs2,ys2,zs,zs2) -> differentLengthError()
 if(false(),false(),false(),xs,ys,xs2,ys2,zs,zs2) -> addLists(xs2,ys2,zs)
 if(false(),false(),true(),xs,ys,xs2,ys2,zs,zs2) -> addLists(xs,ys,zs2)
 addList(xs,ys) -> addLists(xs,ys,nil())

Proof:
 Open