YES

> read an ari file for LCTRSs
(FUN  fib : Int -> Int )
(FUN  fib# : Int -> Int )
(RULES
    1 : fib(x) -> +(fib(-(x,1)),fib(-(x,2))) WHEN (>= (- x 2) 0)
    2 : fib(1) -> 1
    3 : fib(x) -> 0 WHEN (<= x 0)
)

(EQUATIONS
)

> Check left-linearity
Yes
> Compute critical pairs
( +(fib(-(x_5,1)),fib(-(x_5,2))), +(fib(-(x_5,1)),fib(-(x_5,2))) [ (and (>= (- x_5 2) 0) (>= (- x_5 2) 0)) ]
( +(fib(-(x_4,1)),fib(-(x_4,2))), +(fib(-(x_4,1)),fib(-(x_4,2))) [ (and (>= (- x_4 2) 0) (>= (- x_4 2) 0)) ]
( 1, 1 [ true ]
( 1, 1 [ true ]
( 0, 0 [ (and (<= x_2 0) (<= x_2 0)) ]
( 0, 0 [ (and (<= x_1 0) (<= x_1 0)) ]
> Check whether all CPs are trivial
Yes

YES