(ignored inputs)COMMENT Example 1 of \cite{Tiw02}
Rewrite Rules:
[ a -> f(a,b),
f(a,b) -> f(b,a) ]
Apply Direct Methods...
Inner CPs:
[ f(f(a,b),b) = f(b,a) ]
Outer CPs:
[ ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth&Bendix
Linear
unknown Development Closed
unknown Strongly 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:
[ f(f(a,b),b) = f(b,a),
f(b,a) = f(f(a,b),b) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair by Rules <0, 1> preceded by [(f,1)]
unknown Diagram Decreasing
check by Reduction-Preserving Completion...
STEP: 1 (parallel)
S:
[ a -> f(a,b) ]
P:
[ f(a,b) -> f(b,a) ]
P: not reversible
failure(Step 1)
STEP: 2 (linear)
S:
[ a -> f(a,b) ]
P:
[ f(a,b) -> f(b,a) ]
P: not reversible
failure(Step 2)
STEP: 3 (relative)
S:
[ a -> f(a,b) ]
P:
[ f(a,b) -> f(b,a) ]
P: not reversible
failure(Step 3)
failure(no possibility remains)
unknown Reduction-Preserving Completion
check Non-Confluence...Unknown
Direct Methods: Can't judge
Try Persistent Decomposition for...
[ a -> f(a,b),
f(a,b) -> f(b,a) ]
Sort Assignment:
a : =>6
b : =>6
f : 6*6=>6
maximal types: {6}
Persistent Decomposition failed: Can't judge
Try Layer Preserving Decomposition for...
[ a -> f(a,b),
f(a,b) -> f(b,a) ]
Layer Preserving Decomposition failed: Can't judge
Try Commutative Decomposition for...
[ a -> f(a,b),
f(a,b) -> f(b,a) ]
Inside Critical Pair: by Rules <0, 1>
develop reducts from lhs term...
<{1}, f(f(b,a),b)>
<{0}, f(f(f(a,b),b),b)>
<{}, f(f(a,b),b)>
develop reducts from rhs term...
<{0}, f(b,f(a,b))>
<{}, f(b,a)>
Commutative Decomposition failed: Can't judge
No further decomposition possible
Final result: Can't judge
/local-scratch/hzankl/2012/cops2012/80.trs: Failure(unknown)
(3 msec.)