YES

TRS:

  +(0(),0()) -> 0()
  +(0(),1()) -> 1()
  +(0(),2()) -> 2()
  +(0(),3()) -> 3()
  +(0(),4()) -> 4()
  +(0(),5()) -> 5()
  +(0(),6()) -> 6()
  +(0(),7()) -> 7()
  +(0(),8()) -> 8()
  +(0(),9()) -> 9()
  +(1(),0()) -> 1()
  +(1(),1()) -> 2()
  +(1(),2()) -> 3()
  +(1(),3()) -> 4()
  +(1(),4()) -> 5()
  +(1(),5()) -> 6()
  +(1(),6()) -> 7()
  +(1(),7()) -> 8()
  +(1(),8()) -> 9()
  +(1(),9()) -> c(1(),0())
  +(2(),0()) -> 2()
  +(2(),1()) -> 3()
  +(2(),2()) -> 4()
  +(2(),3()) -> 5()
  +(2(),4()) -> 6()
  +(2(),5()) -> 7()
  +(2(),6()) -> 8()
  +(2(),7()) -> 9()
  +(2(),8()) -> c(1(),0())
  +(2(),9()) -> c(1(),1())
  +(3(),0()) -> 3()
  +(3(),1()) -> 4()
  +(3(),2()) -> 5()
  +(3(),3()) -> 6()
  +(3(),4()) -> 7()
  +(3(),5()) -> 8()
  +(3(),6()) -> 9()
  +(3(),7()) -> c(1(),0())
  +(3(),8()) -> c(1(),1())
  +(3(),9()) -> c(1(),2())
  +(4(),0()) -> 4()
  +(4(),1()) -> 5()
  +(4(),2()) -> 6()
  +(4(),3()) -> 7()
  +(4(),4()) -> 8()
  +(4(),5()) -> 9()
  +(4(),6()) -> c(1(),0())
  +(4(),7()) -> c(1(),1())
  +(4(),8()) -> c(1(),2())
  +(4(),9()) -> c(1(),3())
  +(5(),0()) -> 5()
  +(5(),1()) -> 6()
  +(5(),2()) -> 7()
  +(5(),3()) -> 8()
  +(5(),4()) -> 9()
  +(5(),5()) -> c(1(),0())
  +(5(),6()) -> c(1(),1())
  +(5(),7()) -> c(1(),2())
  +(5(),8()) -> c(1(),3())
  +(5(),9()) -> c(1(),4())
  +(6(),0()) -> 6()
  +(6(),1()) -> 7()
  +(6(),2()) -> 8()
  +(6(),3()) -> 9()
  +(6(),4()) -> c(1(),0())
  +(6(),5()) -> c(1(),1())
  +(6(),6()) -> c(1(),2())
  +(6(),7()) -> c(1(),3())
  +(6(),8()) -> c(1(),4())
  +(6(),9()) -> c(1(),5())
  +(7(),0()) -> 7()
  +(7(),1()) -> 8()
  +(7(),2()) -> 9()
  +(7(),3()) -> c(1(),0())
  +(7(),4()) -> c(1(),1())
  +(7(),5()) -> c(1(),2())
  +(7(),6()) -> c(1(),3())
  +(7(),7()) -> c(1(),4())
  +(7(),8()) -> c(1(),5())
  +(7(),9()) -> c(1(),6())
  +(8(),0()) -> 8()
  +(8(),1()) -> 9()
  +(8(),2()) -> c(1(),0())
  +(8(),3()) -> c(1(),1())
  +(8(),4()) -> c(1(),2())
  +(8(),5()) -> c(1(),3())
  +(8(),6()) -> c(1(),4())
  +(8(),7()) -> c(1(),5())
  +(8(),8()) -> c(1(),6())
  +(8(),9()) -> c(1(),7())
  +(9(),0()) -> 9()
  +(9(),1()) -> c(1(),0())
  +(9(),2()) -> c(1(),1())
  +(9(),3()) -> c(1(),2())
  +(9(),4()) -> c(1(),3())
  +(9(),5()) -> c(1(),4())
  +(9(),6()) -> c(1(),5())
  +(9(),7()) -> c(1(),6())
  +(9(),8()) -> c(1(),7())
  +(9(),9()) -> c(1(),8())
  +(x,c(y,z)) -> c(y,+(x,z))
  +(c(x,y),z) -> c(x,+(y,z))
  c(0(),x) -> x
  c(x,c(y,z)) -> c(+(x,y),z)

linear polynomial interpretations on N:

  +_A(x1,x2) = x1 + x2
  +#_A(x1,x2) = x1 + x2
  0_A = 6
  0#_A = 6
  1_A = 5
  1#_A = 5
  2_A = 9
  2#_A = 9
  3_A = 13
  3#_A = 13
  4_A = 16
  4#_A = 16
  5_A = 20
  5#_A = 20
  6_A = 24
  6#_A = 24
  7_A = 23
  7#_A = 23
  8_A = 27
  8#_A = 27
  9_A = 31
  9#_A = 31
  c_A(x1,x2) = x1 + x2 + 1
  c#_A(x1,x2) = x1 + x2 + 1

precedence:

  + > 9 > 8 > 6 > 5 > 3 > 2 > 7 > 0 > 4 > 1 = c