/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem 1: 

(VAR x y z)
(RULES
*(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
c(x,c(y,z)) -> c(+(x,y),z)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 *#(c(x,y),z) -> *#(x,z)
 *#(c(x,y),z) -> *#(y,z)
 *#(c(x,y),z) -> C(*(x,z),*(y,z))
 *#(x,c(y,z)) -> *#(x,y)
 *#(x,c(y,z)) -> *#(x,z)
 *#(x,c(y,z)) -> C(*(x,y),*(x,z))
 +#(c(x,y),z) -> +#(y,z)
 +#(c(x,y),z) -> C(x,+(y,z))
 +#(x,c(y,z)) -> +#(x,z)
 +#(x,c(y,z)) -> C(y,+(x,z))
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)

Problem 1: 

SCC Processor:
-> Pairs:
 *#(c(x,y),z) -> *#(x,z)
 *#(c(x,y),z) -> *#(y,z)
 *#(c(x,y),z) -> C(*(x,z),*(y,z))
 *#(x,c(y,z)) -> *#(x,y)
 *#(x,c(y,z)) -> *#(x,z)
 *#(x,c(y,z)) -> C(*(x,y),*(x,z))
 +#(c(x,y),z) -> +#(y,z)
 +#(c(x,y),z) -> C(x,+(y,z))
 +#(x,c(y,z)) -> +#(x,z)
 +#(x,c(y,z)) -> C(y,+(x,z))
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 +#(c(x,y),z) -> +#(y,z)
 +#(c(x,y),z) -> C(x,+(y,z))
 +#(x,c(y,z)) -> +#(x,z)
 +#(x,c(y,z)) -> C(y,+(x,z))
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
->->-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->->Cycle:
->->-> Pairs:
 *#(c(x,y),z) -> *#(x,z)
 *#(c(x,y),z) -> *#(y,z)
 *#(x,c(y,z)) -> *#(x,y)
 *#(x,c(y,z)) -> *#(x,z)
->->-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 +#(c(x,y),z) -> +#(y,z)
 +#(c(x,y),z) -> C(x,+(y,z))
 +#(x,c(y,z)) -> +#(x,z)
 +#(x,c(y,z)) -> C(y,+(x,z))
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
-> Usable rules:
 +(c(x,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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[+](X1,X2) = X1 + X2 + 2
[c](X1,X2) = X1 + X2 + 2
[0] = 0
[1] = 0
[2] = 0
[3] = 2
[4] = 0
[5] = 2
[6] = 0
[7] = 2
[8] = 0
[9] = 2
[+#](X1,X2) = 2.X1 + 2.X2
[C](X1,X2) = 2.X1 + 2.X2

Problem 1.1: 

SCC Processor:
-> Pairs:
 +#(c(x,y),z) -> C(x,+(y,z))
 +#(x,c(y,z)) -> +#(x,z)
 +#(x,c(y,z)) -> C(y,+(x,z))
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 +#(c(x,y),z) -> C(x,+(y,z))
 +#(x,c(y,z)) -> +#(x,z)
 +#(x,c(y,z)) -> C(y,+(x,z))
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
->->-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 +#(c(x,y),z) -> C(x,+(y,z))
 +#(x,c(y,z)) -> +#(x,z)
 +#(x,c(y,z)) -> C(y,+(x,z))
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
-> Usable rules:
 +(c(x,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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[+](X1,X2) = X1 + X2 + 2
[c](X1,X2) = X1 + X2 + 2
[0] = 0
[1] = 0
[2] = 0
[3] = 0
[4] = 2
[5] = 2
[6] = 0
[7] = 2
[8] = 2
[9] = 2
[+#](X1,X2) = 2.X1 + 2.X2 + 2
[C](X1,X2) = 2.X1 + 2.X2

Problem 1.1: 

SCC Processor:
-> Pairs:
 +#(x,c(y,z)) -> +#(x,z)
 +#(x,c(y,z)) -> C(y,+(x,z))
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 +#(x,c(y,z)) -> +#(x,z)
 +#(x,c(y,z)) -> C(y,+(x,z))
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
->->-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 +#(x,c(y,z)) -> +#(x,z)
 +#(x,c(y,z)) -> C(y,+(x,z))
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
-> Usable rules:
 +(c(x,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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[+](X1,X2) = X1 + X2 + 2
[c](X1,X2) = X1 + X2 + 2
[0] = 2
[1] = 1
[2] = 2
[3] = 2
[4] = 1
[5] = 2
[6] = 2
[7] = 1
[8] = 2
[9] = 2
[+#](X1,X2) = 2.X1 + 2.X2
[C](X1,X2) = 2.X1 + 2.X2

Problem 1.1: 

SCC Processor:
-> Pairs:
 +#(x,c(y,z)) -> C(y,+(x,z))
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 +#(x,c(y,z)) -> C(y,+(x,z))
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
->->-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)

Problem 1.1: 

Reduction Pair Processor:
-> Pairs:
 +#(x,c(y,z)) -> C(y,+(x,z))
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
-> Usable rules:
 +(c(x,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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[+](X1,X2) = X1 + X2 + 1
[c](X1,X2) = 2.X1 + X2 + 2
[0] = 1
[1] = 0
[2] = 1
[3] = 2
[4] = 2
[5] = 2
[6] = 1
[7] = 2
[8] = 2
[9] = 2
[+#](X1,X2) = 2.X1 + X2 + 2
[C](X1,X2) = 2.X1 + X2

Problem 1.1: 

SCC Processor:
-> Pairs:
 C(x,c(y,z)) -> +#(x,y)
 C(x,c(y,z)) -> C(+(x,y),z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 C(x,c(y,z)) -> C(+(x,y),z)
->->-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)

Problem 1.1: 

Subterm Processor:
-> Pairs:
 C(x,c(y,z)) -> C(+(x,y),z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Projection:
 pi(C) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 *#(c(x,y),z) -> *#(x,z)
 *#(c(x,y),z) -> *#(y,z)
 *#(x,c(y,z)) -> *#(x,y)
 *#(x,c(y,z)) -> *#(x,z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Projection:
 pi(*#) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 *#(x,c(y,z)) -> *#(x,y)
 *#(x,c(y,z)) -> *#(x,z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 *#(x,c(y,z)) -> *#(x,y)
 *#(x,c(y,z)) -> *#(x,z)
->->-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)

Problem 1.2: 

Subterm Processor:
-> Pairs:
 *#(x,c(y,z)) -> *#(x,y)
 *#(x,c(y,z)) -> *#(x,z)
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Projection:
 pi(*#) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 *(c(x,y),z) -> c(*(x,z),*(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,+(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(0,x) -> x
 c(x,c(y,z)) -> c(+(x,y),z)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.