(ignored inputs)COMMENT due to Sivakumar , from p.287 of \cite{DJ90}
Rewrite Rules:
[ f(?x,?x) -> g(?x),
f(?x,g(?x)) -> b,
h(c,?y) -> f(h(?y,c),h(?y,?y)) ]
Apply Direct Methods...
Inner CPs:
[ ]
Outer CPs:
[ ]
Overlay, check Innermost Termination...
unknown Innermost Terminating
unknown Knuth&Bendix
not Left-Linear, not Right-Linear
unknown Strongly Depth-Preserving & Non-E-Overlapping
check by Reduction-Preserving Completion...
failure(empty P)
unknown Reduction-Preserving Completion
check Non-Confluence...Unknown
Direct Methods: Can't judge
Try Persistent Decomposition for...
[ f(?x,?x) -> g(?x),
f(?x,g(?x)) -> b,
h(c,?y) -> f(h(?y,c),h(?y,?y)) ]
Sort Assignment:
b : =>14
c : =>11
f : 14*14=>14
g : 14=>14
h : 11*11=>14
maximal types: {11,14}
Persistent Decomposition failed: Can't judge
Try Layer Preserving Decomposition for...
[ f(?x,?x) -> g(?x),
f(?x,g(?x)) -> b,
h(c,?y) -> f(h(?y,c),h(?y,?y)) ]
Layer Preserving Decomposition failed: Can't judge
Try Commutative Decomposition for...
[ f(?x,?x) -> g(?x),
f(?x,g(?x)) -> b,
h(c,?y) -> f(h(?y,c),h(?y,?y)) ]
Commutative Decomposition failed (not left-linear): Can't judge
No further decomposition possible
Final result: Can't judge
/local-scratch/hzankl/2012/cops2012/16.trs: Failure(unknown)
(12 msec.)