(ignored inputs)COMMENT Example 1 of \cite{GOO98} Rewrite Rules: [ f(?x,?x) -> h(?x,?x), f(g(?x),?x) -> a, c -> g(c), h(g(?x),?x) -> a ] 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) -> h(?x,?x), f(g(?x),?x) -> a, c -> g(c), h(g(?x),?x) -> a ] Sort Assignment: a : =>14 c : =>15 f : 15*15=>14 g : 15=>15 h : 15*15=>14 maximal types: {14,15} Persistent Decomposition failed: Can't judge Try Layer Preserving Decomposition for... [ f(?x,?x) -> h(?x,?x), f(g(?x),?x) -> a, c -> g(c), h(g(?x),?x) -> a ] Layer Preserving Decomposition failed: Can't judge Try Commutative Decomposition for... [ f(?x,?x) -> h(?x,?x), f(g(?x),?x) -> a, c -> g(c), h(g(?x),?x) -> a ] Commutative Decomposition failed (not left-linear): Can't judge No further decomposition possible Final result: Can't judge /local-scratch/hzankl/2012/cops2012/27.trs: Failure(unknown) (2 msec.)