(ignored inputs)COMMENT from p.204 of \cite{Der97}
Rewrite Rules:
[ g(?x,?x,?y) -> ?y,
g(?x,?y,?y) -> ?x,
f(?x,?y,?x,?y,?z) -> f(a,b,?z,?z,?z),
a -> 0,
b -> 0 ]
Apply Direct Methods...
Inner CPs:
[ ]
Outer CPs:
[ ?y = ?y ]
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...
[ g(?x,?x,?y) -> ?y,
g(?x,?y,?y) -> ?x,
f(?x,?y,?x,?y,?z) -> f(a,b,?z,?z,?z),
a -> 0,
b -> 0 ]
Sort Assignment:
0 : =>21
a : =>21
b : =>21
f : 21*21*21*21*21=>23
g : 24*24*24=>24
maximal types: {21,23}{24}
{21,23}
(ps)Rewrite Rules:
[ f(?x,?y,?x,?y,?z) -> f(a,b,?z,?z,?z),
a -> 0,
b -> 0 ]
Apply Direct Methods...
Inner CPs:
[ ]
Outer CPs:
[ ]
Overlay, check Innermost Termination...
unknown Innermost Terminating
unknown Knuth&Bendix
not Left-Linear, not Right-Linear
Strongly Depth-Preserving & Non-E-Overlapping
Direct Methods: CR
{24}
(ps)Rewrite Rules:
[ g(?x,?x,?y) -> ?y,
g(?x,?y,?y) -> ?x ]
Apply Direct Methods...
Inner CPs:
[ ]
Outer CPs:
[ ?y = ?y ]
Overlay, check Innermost Termination...
Innermost Terminating (hence Terminating), WCR
Knuth&Bendix
Direct Methods: CR
Result by Persistent Decomposition: CR
Final result: CR
/local-scratch/hzankl/2012/cops2012/17.trs: Success(CR)
(17 msec.)