Debugger: Errors at searching path for included makefiles

I have a directory [aaa] with Makefile & sub-directory as illustrated.

(The directory was compressed and please download from aaa.tar.gz )

At the beginnig, invoke remake in folder [aaa].
In folder [aaa], Makefile[1] would be read , and invoke remake in foler [bbb] with searching path added (-I'absolute_path'/aaa).
In folder [bbb], Makefile[2] would be read, include another.mk in folder [aaa] with searching path, and invoke remake in folder [ccc].
In folder [ccc], Makefile[2] would be re-read again, and include anotther.mk in folder [aaa] with searching path.
Without debugger, all is fine; however, with debugger step by step executed, the the path of included another.mk in Makefile[2] is wrong at first (but still includable) in folder [bbb]. Finally, in folder [ccc], the another.mk in Makefile[2] is not includable and debugger catch an error.

The following is the message given by remake. I also print the variable [.INCLUDE_DIRS] in every recipe in Makefile[1] & [2] to inspect the searching path of included files. It seems that the searching path was not correctly added to sub-folders.

remake -X
Reading makefiles...
Updating makefiles...
-> (/home/kwlee/aaa/another.mk:1)
Makefile:
remake<0> s
Updating goal targets...
-> (/home/kwlee/aaa/Makefile:1)
all:
remake<1> s
File 'all' does not exist.
Must remake target 'all'.
/usr/local/include /usr/local/include /usr/include
Makefile:2: target 'all' does not exist
##>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
remake -I/home/kwlee/aaa -C bbb
##<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
++ (/home/kwlee/aaa/Makefile:1)
all
remake<2> s
Reading makefiles...
remake[1]: Entering directory '/home/kwlee/aaa/bbb'
Updating makefiles...
-> (/home/kwlee/aaa/bbb/another.mk:1)
Makefile:
remake<<0>> s
Updating goal targets...
-> (/home/kwlee/aaa/bbb/Makefile:8)
all:
remake<<1>> s
File 'all' does not exist.
Must remake target 'all'.
/home/kwlee/aaa /usr/local/include /usr/local/include /usr/include
Makefile:9: target 'all' does not exist
##>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
remake -C ccc -f ../Makefile
##<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
++ (/home/kwlee/aaa/bbb/Makefile:8)
all
remake<<2>> s
Reading makefiles...
remake[2]: Entering directory '/home/kwlee/aaa/bbb/ccc'
Updating makefiles...
File 'another.mk' does not exist.
Must remake target 'another.mk'.
../Makefile:14: another.mk: No such file or directory
remake[2]: *** No rule to make target 'another.mk'. Stop.
remake[2]: Leaving directory '/home/kwlee/aaa/bbb/ccc'
Makefile:9: *** [all] error 2
#0 all at /home/kwlee/aaa/bbb/Makefile:8
***Entering debugger because we encountered a fatal error.
** Exiting the debugger will exit make with exit code 2.
!! (/home/kwlee/aaa/bbb/Makefile:8)
all

Download the aaa.tar.gz reproduction and run remake -X from aaa, following the nested -I and -C invocations into bbb and ccc. Compare .INCLUDE_DIRS and the resolution of another.mk with and without debugger stepping. Done means nested execution keeps the intended include path so another.mk remains includable in ccc.