YES
(ignored inputs)COMMENT TPDB SRS_Standard/Secret_06_SRS/aprove07
Rewrite Rules:
   [ foo(0(?x)) -> 0(s(p(p(p(s(s(s(p(s(?x)))))))))),
     foo(s(?x)) -> p(s(p(p(p(s(s(p(s(s(p(s(foo(p(p(s(s(p(s(bar(p(p(s(s(p(s(?x)))))))))))))))))))))))))),
     bar(0(?x)) -> 0(p(s(s(s(?x))))),
     bar(s(?x)) -> p(s(p(p(s(s(foo(s(p(p(s(s(?x)))))))))))),
     p(p(s(?x))) -> p(?x),
     p(s(?x)) -> ?x,
     p(0(?x)) -> 0(s(s(s(s(?x))))) ]
Apply Direct Methods...
Inner CPs:
   [ p(?x_5) = p(?x_5) ]
Outer CPs:
   [  ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
Development Closed
Direct Methods: CR

Combined result: CR
977.trs: Success(CR)
(201 msec.)