0.00/0.07	MAYBE
0.00/0.07	(ignored inputs)COMMENT submitted by: Nao Hirokawa
0.00/0.07	Conditional Rewrite Rules:
0.00/0.07	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x,0) -> 0 | 0 == ?x,
0.00/0.07	     +(?x,?y) -> +(?y,?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	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x,0) -> U0(0,?x),
0.00/0.07	     U0(?x,?x) -> 0,
0.00/0.07	     +(?x,?y) -> +(?y,?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	   [ 0 = 0 | 0 == 0,
0.00/0.07	     +(?y_2,0) = ?y_2,
0.00/0.07	     0 = 0 | 0 == 0,
0.00/0.07	     +(0,?x_2) = 0 | 0 == ?x_2,
0.00/0.07	     ?x = +(?x,0),
0.00/0.07	     0 = +(0,?x_1) | 0 == ?x_1 ]
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	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x,0) -> U0(0,?x),
0.00/0.07	     U0(?x,?x) -> 0,
0.00/0.07	     +(?x,?y) -> +(?y,?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 = U0(0,0),
0.00/0.07	     ?x = +(?x,0),
0.00/0.07	     U0(0,?x_1) = +(0,?x_1) ]
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	not Left-Linear, Right-Linear
0.00/0.07	unknown Simple-Right-Linear
0.00/0.07	unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
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	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x_1,0) -> U0(0,?x_1),
0.00/0.07	     U0(?x_2,?x_2) -> 0,
0.00/0.07	     +(?x_3,?y_3) -> +(?y_3,?x_3) ]
0.00/0.07	Sort Assignment:
0.00/0.07	 + : 13*13=>13
0.00/0.07	 0 : =>13
0.00/0.07	 U0 : 13*13=>13
0.00/0.07	non-linear variables: {?x_2}
0.00/0.07	non-linear types: {13}
0.00/0.07	types leq non-linear types: {13}
0.00/0.07	rules applicable to terms of non-linear types:
0.00/0.07	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x_1,0) -> U0(0,?x_1),
0.00/0.07	     U0(?x_2,?x_2) -> 0,
0.00/0.07	     +(?x_3,?y_3) -> +(?y_3,?x_3) ]
0.00/0.07	unknown innermost-termination for terms of non-linear types
0.00/0.07	unknown Quasi-Left-Linear & Parallel-Closed
0.00/0.07	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x_1,0) -> U0(0,?x_1),
0.00/0.07	     U0(?x_2,?x_2) -> 0,
0.00/0.07	     +(?x_3,?y_3) -> +(?y_3,?x_3) ]
0.00/0.07	Sort Assignment:
0.00/0.07	 + : 13*13=>13
0.00/0.07	 0 : =>13
0.00/0.07	 U0 : 13*13=>13
0.00/0.07	non-linear variables: {?x_2}
0.00/0.07	non-linear types: {13}
0.00/0.07	types leq non-linear types: {13}
0.00/0.07	rules applicable to terms of non-linear types:
0.00/0.07	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x_1,0) -> U0(0,?x_1),
0.00/0.07	     U0(?x_2,?x_2) -> 0,
0.00/0.07	     +(?x_3,?y_3) -> +(?y_3,?x_3) ]
0.00/0.07	Rnl:
0.00/0.07	0: {}
0.00/0.07	1: {}
0.00/0.07	2: {0,1,2,3}
0.00/0.07	3: {}
0.00/0.07	unknown innermost-termination for terms of non-linear types
0.00/0.07	unknown Quasi-Linear & Linearized-Decreasing
0.00/0.07	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x_1,0) -> U0(0,?x_1),
0.00/0.07	     U0(?x_2,?x_2) -> 0,
0.00/0.07	     +(?x_3,?y_3) -> +(?y_3,?x_3) ]
0.00/0.07	Sort Assignment:
0.00/0.07	 + : 13*13=>13
0.00/0.07	 0 : =>13
0.00/0.07	 U0 : 13*13=>13
0.00/0.07	non-linear variables: {?x_2}
0.00/0.07	non-linear types: {13}
0.00/0.07	types leq non-linear types: {13}
0.00/0.07	rules applicable to terms of non-linear types:
0.00/0.07	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x_1,0) -> U0(0,?x_1),
0.00/0.07	     U0(?x_2,?x_2) -> 0,
0.00/0.07	     +(?x_3,?y_3) -> +(?y_3,?x_3) ]
0.00/0.07	unknown innermost-termination for terms of non-linear types
0.00/0.07	unknown Strongly Quasi-Linear & Hierarchically Decreasing
0.00/0.07	unknown Weight-Decreasing Joinable
0.00/0.07	check by Reduction-Preserving Completion...
0.00/0.07	STEP: 1 (parallel)
0.00/0.07	S:
0.00/0.07	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x,0) -> U0(0,?x),
0.00/0.07	     U0(?x,?x) -> 0 ]
0.00/0.07	P:
0.00/0.07	   [ +(?x,?y) -> +(?y,?x) ]
0.00/0.07	S: not left-linear
0.00/0.07	failure(Step 1)
0.00/0.07	STEP: 2 (linear)
0.00/0.07	S:
0.00/0.07	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x,0) -> U0(0,?x),
0.00/0.07	     U0(?x,?x) -> 0 ]
0.00/0.07	P:
0.00/0.07	   [ +(?x,?y) -> +(?y,?x) ]
0.00/0.07	S: not linear
0.00/0.07	failure(Step 2)
0.00/0.07	STEP: 3 (relative)
0.00/0.07	S:
0.00/0.07	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x,0) -> U0(0,?x),
0.00/0.07	     U0(?x,?x) -> 0 ]
0.00/0.07	P:
0.00/0.07	   [ +(?x,?y) -> +(?y,?x) ]
0.00/0.07	failure(Step 3)
0.00/0.07	failure(no possibility remains)
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	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x,0) -> U0(0,?x),
0.00/0.07	     U0(?x,?x) -> 0 ]
0.00/0.07	E-part:
0.00/0.07	   [ +(?x,?y) -> +(?y,?x) ]
0.00/0.07	Perform abstraction and check...
0.00/0.07	Increase tree depth and check...
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	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x,0) -> U0(0,?x),
0.00/0.07	     U0(?x,?x) -> 0,
0.00/0.07	     +(?x,?y) -> +(?y,?x) ]
0.00/0.07	Sort Assignment:
0.00/0.07	 + : 13*13=>13
0.00/0.07	 0 : =>13
0.00/0.07	 U0 : 13*13=>13
0.00/0.07	maximal types: {13}
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	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x,0) -> U0(0,?x),
0.00/0.07	     U0(?x,?x) -> 0,
0.00/0.07	     +(?x,?y) -> +(?y,?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	   [ +(0,?x) -> ?x,
0.00/0.07	     +(?x,0) -> U0(0,?x),
0.00/0.07	     U0(?x,?x) -> 0,
0.00/0.07	     +(?x,?y) -> +(?y,?x) ]
0.00/0.07	Commutative Decomposition failed (not left-linear): 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	(13 msec.)
0.00/0.07	EOF