0.78/0.83	NO
0.78/0.83	(ignored inputs)COMMENT doi:10.1007/s10817-011-9238-x [33] Example 8
0.78/0.83	Rewrite Rules:
0.78/0.83	   [ f(a,a) -> c,
0.78/0.83	     f(b,?x) -> f(?x,?x),
0.78/0.83	     f(?x,b) -> f(?x,?x),
0.78/0.83	     a -> b ]
0.78/0.83	Apply Direct Methods...
0.78/0.83	Inner CPs:
0.78/0.83	   [ f(b,a) = c,
0.78/0.83	     f(a,b) = c ]
0.78/0.83	Outer CPs:
0.78/0.83	   [ f(b,b) = f(b,b) ]
0.78/0.83	not Overlay, check Termination...
0.78/0.83	unknown/not Terminating
0.78/0.83	unknown Knuth & Bendix
0.78/0.83	Left-Linear, not Right-Linear
0.78/0.83	unknown Development Closed
0.78/0.83	unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
0.78/0.83	inner CP cond (upside-parallel)
0.78/0.83	innter CP Cond (outside)
0.78/0.83	unknown Upside-Parallel-Closed/Outside-Closed
0.78/0.83	(inner) Parallel CPs: (not computed)
0.78/0.83	unknown Toyama (Parallel CPs)
0.78/0.83	Simultaneous CPs:
0.78/0.83	   [ f(b,b) = c,
0.78/0.83	     f(b,a) = c,
0.78/0.83	     f(a,b) = c,
0.78/0.83	     f(b,b) = f(b,b),
0.78/0.83	     c = f(b,a),
0.78/0.83	     c = f(a,b) ]
0.78/0.83	unknown Okui (Simultaneous CPs)
0.78/0.83	unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
0.78/0.83	unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
0.78/0.83	check Locally Decreasing Diagrams by Rule Labelling...
0.78/0.83	Critical Pair <f(b,a), c> by Rules <3, 0> preceded by [(f,1)]
0.78/0.83	 joinable by a reduction of rules <[([],1),([],0)], []>
0.78/0.83	Critical Pair <f(a,b), c> by Rules <3, 0> preceded by [(f,2)]
0.78/0.83	 joinable by a reduction of rules <[([],2),([],0)], []>
0.78/0.83	Critical Pair <f(b,b), f(b,b)> by Rules <2, 1> preceded by []
0.78/0.83	 joinable by a reduction of rules <[], []>
0.78/0.83	unknown Diagram Decreasing
0.78/0.83	   [ f(a,a) -> c,
0.78/0.83	     f(b,?x) -> f(?x,?x),
0.78/0.83	     f(?x_1,b) -> f(?x_1,?x_1),
0.78/0.83	     a -> b ]
0.78/0.83	Sort Assignment:
0.78/0.83	 a : =>9
0.78/0.83	 b : =>9
0.78/0.83	 c : =>10
0.78/0.83	 f : 9*9=>10
0.78/0.83	non-linear variables: {?x,?x_1}
0.78/0.83	non-linear types: {9}
0.78/0.83	types leq non-linear types: {9}
0.78/0.83	rules applicable to terms of non-linear types:
0.78/0.83	   [ a -> b ]
0.78/0.83	Rnl:
0.78/0.83	0: {}
0.78/0.83	1: {3}
0.78/0.83	2: {3}
0.78/0.83	3: {}
0.78/0.83	terms of non-linear types are innermost terminating
0.78/0.83	Critical Pair <f(b,a), c> by Rules <3, 0>
0.78/0.83	 convertible by a reduction of rules [->(1),->(0)]
0.78/0.83	 convertible by a reduction of rules [->(3),(3)<-,->(2),->(0)]
0.78/0.83	Critical Pair <f(a,b), c> by Rules <3, 0>
0.78/0.83	 convertible by a reduction of rules [->(2),->(0)]
0.78/0.83	 convertible by a reduction of rules [->(3),(3)<-,->(1),->(0)]
0.78/0.83	Critical Pair <f(b,b), f(b,b)> by Rules <2, 1>
0.78/0.83	 convertible by a reduction of rules []
0.78/0.83	Not Satisfiable
0.78/0.83	unknown Quasi-Linear & Linearized-Decreasing
0.78/0.83	   [ f(a,a) -> c,
0.78/0.83	     f(b,?x) -> f(?x,?x),
0.78/0.83	     f(?x_1,b) -> f(?x_1,?x_1),
0.78/0.83	     a -> b ]
0.78/0.83	Sort Assignment:
0.78/0.83	 a : =>9
0.78/0.83	 b : =>9
0.78/0.83	 c : =>10
0.78/0.83	 f : 9*9=>10
0.78/0.83	non-linear variables: {?x,?x_1}
0.78/0.83	non-linear types: {9}
0.78/0.83	types leq non-linear types: {9}
0.78/0.83	rules applicable to terms of non-linear types:
0.78/0.83	   [ a -> b ]
0.78/0.83	terms of non-linear types are terminating
0.78/0.83	Check Joinablility of CP from NLR:
0.78/0.83	done.
0.78/0.83	Critical Pair <f(b,a), c> by Rules <3, 0>
0.78/0.83	 convertible by a reduction of rules [->(1),->(0)]
0.78/0.83	 convertible by a reduction of rules [->(3),(3)<-,->(2),->(0)]
0.78/0.83	Critical Pair <f(a,b), c> by Rules <3, 0>
0.78/0.83	 convertible by a reduction of rules [->(2),->(0)]
0.78/0.83	 convertible by a reduction of rules [->(3),(3)<-,->(1),->(0)]
0.78/0.83	Critical Pair <f(b,b), f(b,b)> by Rules <2, 1>
0.78/0.83	 convertible by a reduction of rules []
0.78/0.83	Not Satisfiable
0.78/0.83	unknown Strongly Quasi-Linear & Hierarchically Decreasing
0.78/0.83	check Non-Confluence...
0.78/0.83	obtain 8 rules by 3 steps unfolding
0.78/0.83	obtain 9 candidates for checking non-joinability
0.78/0.83	check by TCAP-Approximation (failure)
0.78/0.83	check by Ordering(rpo), check by Tree-Automata Approximation (failure)
0.78/0.83	check by Interpretation(mod2) (failure)
0.78/0.83	check by Descendants-Approximation, check by Ordering(poly) (success)
0.78/0.83	Witness for Non-Confluence: <f(b,b) <- f(a,b) -> c>
0.78/0.83	Direct Methods: not CR
0.78/0.83	
0.78/0.83	Combined result: not CR
0.78/0.83	/export/starexec/sandbox/benchmark/theBenchmark.trs: Success(not CR)
0.78/0.83	(371 msec.)
0.78/0.83	EOF