0.00/0.07	MAYBE
0.00/0.07	(ignored inputs)COMMENT [121] Example 7.37 submitted by: Thomas Sternagel
0.00/0.07	Conditional Rewrite Rules:
0.00/0.07	   [ g(?x) -> g(?x) | g(?x) == f(a,b),
0.00/0.07	     g(?x) -> f(?x,?x) ]
0.00/0.07	Check whether all rules are type 3
0.00/0.07	OK
0.00/0.07	Check whether the input is deterministic
0.00/0.07	OK
0.00/0.07	Result of unraveling:
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     U0(f(a,b),?x) -> g(?x),
0.00/0.07	     g(?x) -> f(?x,?x) ]
0.00/0.07	Check whether U(R) is terminating
0.00/0.07	failed to show termination
0.00/0.07	Check whether the input is weakly left-linear
0.00/0.07	OK
0.00/0.07	Conditional critical pairs (CCPs):
0.00/0.07	   [ f(?x_1,?x_1) = g(?x_1) | g(?x_1) == f(a,b),
0.00/0.07	     g(?x) = f(?x,?x) | g(?x) == f(a,b) ]
0.00/0.07	Check whether the input is almost orthogonale
0.00/0.07	not almost orthogonal
0.00/0.07	OK
0.00/0.07	Check U(R) is confluent
0.00/0.07	Rewrite Rules:
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     U0(f(a,b),?x) -> g(?x),
0.00/0.07	     g(?x) -> f(?x,?x) ]
0.00/0.07	Apply Direct Methods...
0.00/0.07	Inner CPs:
0.00/0.07	   [  ]
0.00/0.07	Outer CPs:
0.00/0.07	   [ U0(g(?x),?x) = f(?x,?x) ]
0.00/0.07	Overlay, check Innermost Termination...
0.00/0.07	unknown Innermost Terminating
0.00/0.07	unknown Knuth & Bendix
0.00/0.07	Left-Linear, not Right-Linear
0.00/0.07	unknown Development Closed
0.00/0.07	unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
0.00/0.07	unknown Upside-Parallel-Closed/Outside-Closed
0.00/0.07	(inner) Parallel CPs: (not computed)
0.00/0.07	unknown Toyama (Parallel CPs)
0.00/0.07	Simultaneous CPs:
0.00/0.07	   [ f(?x,?x) = U0(g(?x),?x),
0.00/0.07	     U0(g(?x),?x) = f(?x,?x) ]
0.00/0.07	unknown Okui (Simultaneous CPs)
0.00/0.07	unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
0.00/0.07	unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
0.00/0.07	check Locally Decreasing Diagrams by Rule Labelling...
0.00/0.07	Critical Pair <f(?x_2,?x_2), U0(g(?x_2),?x_2)> by Rules <2, 0> preceded by []
0.00/0.07	unknown Diagram Decreasing
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     U0(f(a,b),?x_1) -> g(?x_1),
0.00/0.07	     g(?x_2) -> f(?x_2,?x_2) ]
0.00/0.07	Sort Assignment:
0.00/0.07	 a : =>7
0.00/0.07	 b : =>7
0.00/0.07	 f : 7*7=>14
0.00/0.07	 g : 7=>14
0.00/0.07	 U0 : 14*7=>14
0.00/0.07	non-linear variables: {?x,?x_2}
0.00/0.07	non-linear types: {7}
0.00/0.07	types leq non-linear types: {7}
0.00/0.07	rules applicable to terms of non-linear types:
0.00/0.07	   [ ]
0.00/0.07	Rnl:
0.00/0.07	0: {}
0.00/0.07	1: {}
0.00/0.07	2: {}
0.00/0.07	terms of non-linear types are innermost terminating
0.00/0.07	Critical Pair <f(?x_2,?x_2), U0(g(?x_2),?x_2)> by Rules <2, 0>
0.00/0.07	no joinable sequence for some critical pairs
0.00/0.07	unknown Quasi-Linear & Linearized-Decreasing
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     U0(f(a,b),?x_1) -> g(?x_1),
0.00/0.07	     g(?x_2) -> f(?x_2,?x_2) ]
0.00/0.07	Sort Assignment:
0.00/0.07	 a : =>7
0.00/0.07	 b : =>7
0.00/0.07	 f : 7*7=>14
0.00/0.07	 g : 7=>14
0.00/0.07	 U0 : 14*7=>14
0.00/0.07	non-linear variables: {?x,?x_2}
0.00/0.07	non-linear types: {7}
0.00/0.07	types leq non-linear types: {7}
0.00/0.07	rules applicable to terms of non-linear types:
0.00/0.07	   [ ]
0.00/0.07	terms of non-linear types are terminating
0.00/0.07	Check Joinablility of CP from NLR:
0.00/0.07	done.
0.00/0.07	Critical Pair <f(?x_2,?x_2), U0(g(?x_2),?x_2)> by Rules <2, 0>
0.00/0.07	no joinable sequence for some critical pairs
0.00/0.07	unknown Strongly Quasi-Linear & Hierarchically Decreasing
0.00/0.07	unknown Huet (modulo AC)
0.00/0.07	check by Reduction-Preserving Completion...
0.00/0.07	failure(empty P)
0.00/0.07	unknown Reduction-Preserving Completion
0.00/0.07	check by Ordered Rewriting...
0.00/0.07	remove redundants rules and split
0.00/0.07	R-part:
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     U0(f(a,b),?x) -> g(?x),
0.00/0.07	     g(?x) -> f(?x,?x) ]
0.00/0.07	E-part:
0.00/0.07	   [ ]
0.00/0.07	...failed to find a suitable LPO.
0.00/0.07	unknown Confluence by Ordered Rewriting
0.00/0.07	Direct Methods: Can't judge
0.00/0.07	
0.00/0.07	Try Persistent Decomposition for...
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     U0(f(a,b),?x) -> g(?x),
0.00/0.07	     g(?x) -> f(?x,?x) ]
0.00/0.07	Sort Assignment:
0.00/0.07	 a : =>7
0.00/0.07	 b : =>7
0.00/0.07	 f : 7*7=>14
0.00/0.07	 g : 7=>14
0.00/0.07	 U0 : 14*7=>14
0.00/0.07	maximal types: {7,14}
0.00/0.07	Persistent Decomposition failed: Can't judge
0.00/0.07	
0.00/0.07	Try Layer Preserving Decomposition for...
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     U0(f(a,b),?x) -> g(?x),
0.00/0.07	     g(?x) -> f(?x,?x) ]
0.00/0.07	Layer Preserving Decomposition failed: Can't judge
0.00/0.07	
0.00/0.07	Try Commutative Decomposition for...
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     U0(f(a,b),?x) -> g(?x),
0.00/0.07	     g(?x) -> f(?x,?x) ]
0.00/0.07	Outside Critical Pair: <f(?x_2,?x_2), U0(g(?x_2),?x_2)> by Rules <2, 0>
0.00/0.07	develop reducts from lhs term...
0.00/0.07	<{}, f(?x_2,?x_2)>
0.00/0.07	develop reducts from rhs term...
0.00/0.07	<{2}, U0(f(?x_2,?x_2),?x_2)>
0.00/0.07	<{0}, U0(U0(g(?x_2),?x_2),?x_2)>
0.00/0.07	<{}, U0(g(?x_2),?x_2)>
0.00/0.07	Try A Minimal Decomposition {0,2}{1}
0.00/0.07	{0,2}
0.00/0.07	(cm)Rewrite Rules:
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     g(?x) -> f(?x,?x) ]
0.00/0.07	Apply Direct Methods...
0.00/0.07	Inner CPs:
0.00/0.07	   [  ]
0.00/0.07	Outer CPs:
0.00/0.07	   [ U0(g(?x),?x) = f(?x,?x) ]
0.00/0.07	Overlay, check Innermost Termination...
0.00/0.07	unknown Innermost Terminating
0.00/0.07	unknown Knuth & Bendix
0.00/0.07	Left-Linear, not Right-Linear
0.00/0.07	unknown Development Closed
0.00/0.07	unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
0.00/0.07	unknown Upside-Parallel-Closed/Outside-Closed
0.00/0.07	(inner) Parallel CPs: (not computed)
0.00/0.07	unknown Toyama (Parallel CPs)
0.00/0.07	Simultaneous CPs:
0.00/0.07	   [ f(?x,?x) = U0(g(?x),?x),
0.00/0.07	     U0(g(?x),?x) = f(?x,?x) ]
0.00/0.07	unknown Okui (Simultaneous CPs)
0.00/0.07	unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
0.00/0.07	unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
0.00/0.07	check Locally Decreasing Diagrams by Rule Labelling...
0.00/0.07	Critical Pair <f(?x_1,?x_1), U0(g(?x_1),?x_1)> by Rules <1, 0> preceded by []
0.00/0.07	unknown Diagram Decreasing
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     g(?x_1) -> f(?x_1,?x_1) ]
0.00/0.07	Sort Assignment:
0.00/0.07	 f : 4*4=>11
0.00/0.07	 g : 4=>11
0.00/0.07	 U0 : 11*4=>11
0.00/0.07	non-linear variables: {?x,?x_1}
0.00/0.07	non-linear types: {4}
0.00/0.07	types leq non-linear types: {4}
0.00/0.07	rules applicable to terms of non-linear types:
0.00/0.07	   [ ]
0.00/0.07	Rnl:
0.00/0.07	0: {}
0.00/0.07	1: {}
0.00/0.07	terms of non-linear types are innermost terminating
0.00/0.07	Critical Pair <f(?x_1,?x_1), U0(g(?x_1),?x_1)> by Rules <1, 0>
0.00/0.07	no joinable sequence for some critical pairs
0.00/0.07	unknown Quasi-Linear & Linearized-Decreasing
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     g(?x_1) -> f(?x_1,?x_1) ]
0.00/0.07	Sort Assignment:
0.00/0.07	 f : 4*4=>11
0.00/0.07	 g : 4=>11
0.00/0.07	 U0 : 11*4=>11
0.00/0.07	non-linear variables: {?x,?x_1}
0.00/0.07	non-linear types: {4}
0.00/0.07	types leq non-linear types: {4}
0.00/0.07	rules applicable to terms of non-linear types:
0.00/0.07	   [ ]
0.00/0.07	terms of non-linear types are terminating
0.00/0.07	Check Joinablility of CP from NLR:
0.00/0.07	done.
0.00/0.07	Critical Pair <f(?x_1,?x_1), U0(g(?x_1),?x_1)> by Rules <1, 0>
0.00/0.07	no joinable sequence for some critical pairs
0.00/0.07	unknown Strongly Quasi-Linear & Hierarchically Decreasing
0.00/0.07	unknown Huet (modulo AC)
0.00/0.07	check by Reduction-Preserving Completion...
0.00/0.07	failure(empty P)
0.00/0.07	unknown Reduction-Preserving Completion
0.00/0.07	check by Ordered Rewriting...
0.00/0.07	remove redundants rules and split
0.00/0.07	R-part:
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     g(?x) -> f(?x,?x) ]
0.00/0.07	E-part:
0.00/0.07	   [ ]
0.00/0.07	...failed to find a suitable LPO.
0.00/0.07	unknown Confluence by Ordered Rewriting
0.00/0.07	Direct Methods: Can't judge
0.00/0.07	
0.00/0.07	Try Persistent Decomposition for...
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     g(?x) -> f(?x,?x) ]
0.00/0.07	Sort Assignment:
0.00/0.07	 f : 4*4=>11
0.00/0.07	 g : 4=>11
0.00/0.07	 U0 : 11*4=>11
0.00/0.07	maximal types: {4,11}
0.00/0.07	Persistent Decomposition failed: Can't judge
0.00/0.07	
0.00/0.07	Try Layer Preserving Decomposition for...
0.00/0.07	   [ g(?x) -> U0(g(?x),?x),
0.00/0.07	     g(?x) -> f(?x,?x) ]
0.00/0.07	Layer Preserving Decomposition failed: Can't judge
0.00/0.07	No further decomposition possible
0.00/0.07	
0.00/0.07	{1}
0.00/0.07	(cm)Rewrite Rules:
0.00/0.07	   [ U0(f(a,b),?x) -> g(?x) ]
0.00/0.07	Apply Direct Methods...
0.00/0.07	Inner CPs:
0.00/0.07	   [  ]
0.00/0.07	Outer CPs:
0.00/0.07	   [  ]
0.00/0.07	Overlay, check Innermost Termination...
0.00/0.07	Innermost Terminating (hence Terminating), WCR
0.00/0.07	Knuth & Bendix
0.00/0.07	Direct Methods: CR
0.00/0.07	Commutative Decomposition failed: Can't judge
0.00/0.07	No further decomposition possible
0.00/0.07	
0.00/0.07	
0.00/0.07	Combined result: Can't judge
0.00/0.07	failed to show confluence of U(R)
0.00/0.07	/export/starexec/sandbox/benchmark/theBenchmark.trs: Failure(unknown CR)
0.00/0.07	(15 msec.)
0.00/0.07	EOF