(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
c(0, x) → x
c(x, c(y, z)) → c(+(x, y), z)
+(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))
*(0, 0) → 0
*(0, 1) → 0
*(0, 2) → 0
*(0, 3) → 0
*(0, 4) → 0
*(0, 5) → 0
*(0, 6) → 0
*(0, 7) → 0
*(0, 8) → 0
*(0, 9) → 0
*(1, 0) → 0
*(1, 1) → 1
*(1, 2) → 2
*(1, 3) → 3
*(1, 4) → 4
*(1, 5) → 5
*(1, 6) → 6
*(1, 7) → 7
*(1, 8) → 8
*(1, 9) → 9
*(2, 0) → 0
*(2, 1) → 2
*(2, 2) → 4
*(2, 3) → 6
*(2, 4) → 8
*(2, 5) → c(1, 0)
*(2, 6) → c(1, 2)
*(2, 7) → c(1, 4)
*(2, 8) → c(1, 6)
*(2, 9) → c(1, 8)
*(3, 0) → 0
*(3, 1) → 3
*(3, 2) → 6
*(3, 3) → 9
*(3, 4) → c(1, 2)
*(3, 5) → c(1, 5)
*(3, 6) → c(1, 8)
*(3, 7) → c(2, 1)
*(3, 8) → c(2, 4)
*(3, 9) → c(2, 7)
*(4, 0) → 0
*(4, 1) → 4
*(4, 2) → 8
*(4, 3) → c(1, 2)
*(4, 4) → c(1, 6)
*(4, 5) → c(2, 0)
*(4, 6) → c(2, 4)
*(4, 7) → c(2, 8)
*(4, 8) → c(3, 2)
*(4, 9) → c(3, 6)
*(5, 0) → 0
*(5, 1) → 5
*(5, 2) → c(1, 0)
*(5, 3) → c(1, 5)
*(5, 4) → c(2, 0)
*(5, 5) → c(2, 5)
*(5, 6) → c(3, 0)
*(5, 7) → c(3, 5)
*(5, 8) → c(4, 0)
*(5, 9) → c(4, 5)
*(6, 0) → 0
*(6, 1) → 6
*(6, 2) → c(1, 2)
*(6, 3) → c(1, 8)
*(6, 4) → c(2, 4)
*(6, 5) → c(3, 0)
*(6, 6) → c(3, 6)
*(6, 7) → c(4, 2)
*(6, 8) → c(4, 8)
*(6, 9) → c(5, 4)
*(7, 0) → 0
*(7, 1) → 7
*(7, 2) → c(1, 4)
*(7, 3) → c(2, 1)
*(7, 4) → c(2, 8)
*(7, 5) → c(3, 5)
*(7, 6) → c(4, 2)
*(7, 7) → c(4, 9)
*(7, 8) → c(5, 6)
*(7, 9) → c(6, 3)
*(8, 0) → 0
*(8, 1) → 8
*(8, 2) → c(1, 8)
*(8, 3) → c(2, 4)
*(8, 4) → c(3, 2)
*(8, 5) → c(4, 0)
*(8, 6) → c(4, 8)
*(8, 7) → c(5, 6)
*(8, 8) → c(6, 4)
*(8, 9) → c(7, 2)
*(9, 0) → 0
*(9, 1) → 9
*(9, 2) → c(1, 8)
*(9, 3) → c(2, 7)
*(9, 4) → c(3, 6)
*(9, 5) → c(4, 5)
*(9, 6) → c(5, 4)
*(9, 7) → c(6, 3)
*(9, 8) → c(7, 2)
*(9, 9) → c(8, 1)
*(x, c(y, z)) → c(*(x, y), *(x, z))
*(c(x, y), z) → c(*(x, z), *(y, z))
Q is empty.