MAYBE
(ignored inputs)COMMENT reduction failed
Rewrite Rules:
   [ f(f(?x,a),a) -> f(f(f(f(a,?x),a),a),a) ]
Apply Direct Methods...
Inner CPs:
   [ f(f(f(f(f(a,?x),a),a),a),a) = f(f(f(f(a,f(?x,a)),a),a),a) ]
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:
   [ f(f(f(f(f(a,?x_1),a),a),a),a) = f(f(f(f(a,f(?x_1,a)),a),a),a),
     f(f(f(f(a,f(f(f(f(a,?x_1),a),a),a)),a),a),a) = f(f(f(f(f(a,f(?x_1,a)),a),a),a),a),
     f(f(f(f(a,f(?x,a)),a),a),a) = f(f(f(f(f(a,?x),a),a),a),a) ]
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 <f(f(f(f(f(a,?x),a),a),a),a), f(f(f(f(a,f(?x,a)),a),a),a)> by Rules <0, 0> preceded by [(f,1)]
unknown Diagram Decreasing
check Non-Confluence...
obtain 3 rules by 3 steps unfolding
obtain 100 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (failure)
check by Interpretation(mod2) (failure)
check by Descendants-Approximation, check by Ordering(poly) (failure)
unknown Non-Confluence
unknown Huet (modulo AC)
check by Reduction-Preserving Completion...
STEP: 1 (parallel)
S:
   [ ]
P:
   [ f(f(?x,a),a) -> f(f(f(f(a,?x),a),a),a) ]
P: not reversible
failure(Step 1)
STEP: 2 (linear)
S:
   [ ]
P:
   [ f(f(?x,a),a) -> f(f(f(f(a,?x),a),a),a) ]
P: not reversible
failure(Step 2)
STEP: 3 (relative)
S:
   [ ]
P:
   [ f(f(?x,a),a) -> f(f(f(f(a,?x),a),a),a) ]
P: not reversible
failure(Step 3)
failure(no possibility remains)
unknown Reduction-Preserving Completion
check by Ordered Rewriting...
remove redundants rules and split
R-part:
   [ f(f(?x,a),a) -> f(f(f(f(a,?x),a),a),a) ]
E-part:
   [ ]
...failed to find a suitable LPO.
unknown Confluence by Ordered Rewriting
Direct Methods: Can't judge

Try Persistent Decomposition for...
   [ f(f(?x,a),a) -> f(f(f(f(a,?x),a),a),a) ]
Sort Assignment:
 a : =>3
 f : 3*3=>3
maximal types: {3}
Persistent Decomposition failed: Can't judge

Try Layer Preserving Decomposition for...
   [ f(f(?x,a),a) -> f(f(f(f(a,?x),a),a),a) ]
Layer Preserving Decomposition failed: Can't judge

Try Commutative Decomposition for...
   [ f(f(?x,a),a) -> f(f(f(f(a,?x),a),a),a) ]
Commutative Decomposition failed: Can't judge
No further decomposition possible


Combined result: Can't judge
/tmp/file5psz0u.trs: Failure(unknown CR)
(12523 msec.)