YES
(ignored inputs)COMMENT the following rules are removed from the original TRS hd ( : ( x , y ) ) -> x
Rewrite Rules:
   [ inc(tl(nats)) -> tl(inc(nats)),
     nats -> :(0,inc(nats)),
     inc(:(?x,?y)) -> :(s(?x),inc(?y)),
     tl(:(?x,?y)) -> ?y ]
Apply Direct Methods...
Inner CPs:
   [ inc(tl(:(0,inc(nats)))) = tl(inc(nats)) ]
Outer CPs:
   [  ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
inner CP cond (upside-parallel)
innter CP Cond (outside)
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ inc(tl(:(0,inc(nats)))) = tl(inc(nats)),
     tl(inc(nats)) = inc(tl(:(0,inc(nats)))) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair <inc(tl(:(0,inc(nats)))), tl(inc(nats))> by Rules <1, 0> preceded by [(inc,1),(tl,1)]
 joinable by a reduction of rules <[([(inc,1)],3)], [([(tl,1),(inc,1)],1),([(tl,1)],2),([],3)]>
Satisfiable by 1>2,4>3; :(0,0)s(0)tl(0)inc(0); 2,4>1>3
Diagram Decreasing
Direct Methods: CR

Combined result: CR
/tmp/fileSVxMbv.trs: Success(CR)
(0 msec.)