(ignored inputs)COMMENT Example 3 from [HM11]: doi: http://dx.doi.org/10.1007/s10817-011-9238-x
Rewrite Rules:
   [ nats -> :(0,inc(nats)),
     inc(:(?x,?y)) -> :(s(?x),inc(?y)),
     inc(tl(nats)) -> tl(inc(nats)),
     hd(:(?x,?y)) -> ?x,
     tl(:(?x,?y)) -> ?y,
     d(:(?x,?y)) -> :(?x,:(?x,d(?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
Left-Linear, not Right-Linear
unknown Development Closed
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 & Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair <inc(tl(:(0,inc(nats)))), tl(inc(nats))> by Rules <0, 2> preceded by [(inc,1),(tl,1)]
 joinable by a reduction of rules <[([(inc,1)],4)], [([(tl,1),(inc,1)],0),([(tl,1)],1),([],4)]>
Satisfiable by 3>1,5>2,4,6; :(0,0)d(1)s(0)hd(0)tl(0)inc(0); 3>1,5>2,4,6
Diagram Decreasing
Direct Methods: CR

Final result: CR
/local-scratch/hzankl/2012/cops2012/112.trs: Success(CR)
(3 msec.)