NO

1 decompositions
 #1 -----------
   4: minus(x3,0()) -> x3
   5: minus(x4,p(x5)) -> s(minus(x4,x5))
   6: minus(x6,s(x7)) -> p(minus(x6,x7))
   7: minus(0(),x8) -> inv(x8)
   8: inv(x9) -> minus(0(),x9)
   9: inv(minus(x10,x11)) -> minus(x11,x10)
  10: s(p(x12)) -> x12
  11: p(s(x13)) -> x13

unjoinable peak
    p(minus(x5,x32))
*<- inv(minus(x32,p(x5))) ->*
    minus(p(x5),x32)
NOTE: input TRS is reduced

original is
   1: inv(0()) -> 0()
   2: inv(s(x1)) -> p(inv(x1))
   3: inv(p(x2)) -> s(inv(x2))
   4: minus(x3,0()) -> x3
   5: minus(x4,p(x5)) -> s(minus(x4,x5))
   6: minus(x6,s(x7)) -> p(minus(x6,x7))
   7: minus(0(),x8) -> inv(x8)
   8: inv(x9) -> minus(0(),x9)
   9: inv(minus(x10,x11)) -> minus(x11,x10)
  10: s(p(x12)) -> x12
  11: p(s(x13)) -> x13

reduced to
   4: minus(x3,0()) -> x3
   5: minus(x4,p(x5)) -> s(minus(x4,x5))
   6: minus(x6,s(x7)) -> p(minus(x6,x7))
   7: minus(0(),x8) -> inv(x8)
   8: inv(x9) -> minus(0(),x9)
   9: inv(minus(x10,x11)) -> minus(x11,x10)
  10: s(p(x12)) -> x12
  11: p(s(x13)) -> x13