(ignored inputs)COMMENT TPDB SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-351
Rewrite Rules:
   [ a(?x) -> b(?x),
     a(b(?x)) -> b(a(c(a(?x)))),
     b(?x) -> c(?x),
     c(c(?x)) -> ?x ]
Apply Direct Methods...
Inner CPs:
   [ a(c(?x_2)) = b(a(c(a(?x_2)))),
     c(?x) = c(?x) ]
Outer CPs:
   [ b(b(?x_1)) = b(a(c(a(?x_1)))) ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ b(a(c(a(?x_1)))) = b(b(?x_1)),
     b(c(?x)) = b(a(c(a(?x)))),
     b(b(?x)) = b(a(c(a(?x)))),
     a(c(?x)) = b(a(c(a(?x)))),
     b(a(c(a(?x)))) = a(c(?x)),
     c(?x_1) = c(?x_1),
     ?x_1 = c(c(?x_1)) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair <a(c(?x_2)), b(a(c(a(?x_2))))> by Rules <2, 1> preceded by [(a,1)]
 joinable by a reduction of rules <[([],0)], [([(b,1),(a,1),(c,1)],0),([(b,1),(a,1),(c,1)],2),([(b,1),(a,1)],3),([(b,1)],0),([(b,1)],2)]>
 joinable by a reduction of rules <[([],0)], [([(b,1),(a,1),(c,1)],0),([(b,1),(a,1),(c,1)],2),([(b,1)],0),([(b,1),(b,1)],3),([(b,1)],2)]>
 joinable by a reduction of rules <[([],0)], [([(b,1),(a,1),(c,1)],0),([(b,1),(a,1),(c,1)],2),([(b,1)],0),([(b,1)],2),([(b,1),(c,1)],3)]>
 joinable by a reduction of rules <[([],0)], [([(b,1),(a,1),(c,1)],0),([(b,1),(a,1),(c,1)],2),([(b,1)],0),([(b,1)],2),([(b,1)],3)]>
 joinable by a reduction of rules <[([],0)], [([(b,1),(a,1),(c,1)],0),([(b,1)],0),([(b,1),(b,1),(c,1)],2),([(b,1),(b,1)],3),([(b,1)],2)]>
 joinable by a reduction of rules <[([],0)], [([(b,1),(a,1),(c,1)],0),([(b,1)],0),([(b,1),(b,1),(c,1)],2),([(b,1)],2),([(b,1),(c,1)],3)]>
 joinable by a reduction of rules <[([],0)], [([(b,1),(a,1),(c,1)],0),([(b,1)],0),([(b,1),(b,1),(c,1)],2),([(b,1)],2),([(b,1)],3)]>
 joinable by a reduction of rules <[([],0)], [([(b,1),(a,1),(c,1)],0),([(b,1)],0),([(b,1)],2),([(b,1),(c,1),(c,1)],2),([(b,1),(c,1)],3)]>
 joinable by a reduction of rules <[([],0)], [([(b,1),(a,1),(c,1)],0),([(b,1)],0),([(b,1)],2),([(b,1),(c,1),(c,1)],2),([(b,1)],3)]>
 joinable by a reduction of rules <[([],0)], [([(b,1),(a,1),(c,1)],0),([(b,1)],0),([(b,1)],2),([(b,1)],3),([(b,1)],2)]>
 joinable by a reduction of rules <[([],0)], [([(b,1)],0),([(b,1),(b,1),(c,1)],0),([(b,1),(b,1),(c,1)],2),([(b,1),(b,1)],3),([(b,1)],2)]>
 joinable by a reduction of rules <[([],0)], [([(b,1)],0),([(b,1),(b,1),(c,1)],0),([(b,1),(b,1),(c,1)],2),([(b,1)],2),([(b,1),(c,1)],3)]>
 joinable by a reduction of rules <[([],0)], [([(b,1)],0),([(b,1),(b,1),(c,1)],0),([(b,1),(b,1),(c,1)],2),([(b,1)],2),([(b,1)],3)]>
 joinable by a reduction of rules <[([],0)], [([(b,1)],0),([(b,1),(b,1),(c,1)],0),([(b,1)],2),([(b,1),(c,1),(c,1)],2),([(b,1),(c,1)],3)]>
 joinable by a reduction of rules <[([],0)], [([(b,1)],0),([(b,1),(b,1),(c,1)],0),([(b,1)],2),([(b,1),(c,1),(c,1)],2),([(b,1)],3)]>
 joinable by a reduction of rules <[([],0)], [([(b,1)],0),([(b,1),(b,1),(c,1)],0),([(b,1)],2),([(b,1)],3),([(b,1)],2)]>
 joinable by a reduction of rules <[([],0)], [([(b,1)],0),([(b,1)],2),([(b,1),(c,1),(c,1)],0),([(b,1),(c,1),(c,1)],2),([(b,1),(c,1)],3)]>
 joinable by a reduction of rules <[([],0)], [([(b,1)],0),([(b,1)],2),([(b,1),(c,1),(c,1)],0),([(b,1),(c,1),(c,1)],2),([(b,1)],3)]>
 joinable by a reduction of rules <[([],0)], [([(b,1)],0),([(b,1)],2),([(b,1),(c,1),(c,1)],0),([(b,1)],3),([(b,1)],2)]>
 joinable by a reduction of rules <[([],0)], [([(b,1)],0),([(b,1)],2),([(b,1)],3),([(b,1)],0),([(b,1)],2)]>
Critical Pair <c(?x), c(?x)> by Rules <3, 3> preceded by [(c,1)]
 joinable by a reduction of rules <[], []>
Critical Pair <b(a(c(a(?x_1)))), b(b(?x_1))> by Rules <1, 0> preceded by []
 joinable by a reduction of rules <[([(b,1),(a,1),(c,1)],0),([(b,1),(a,1),(c,1)],2),([(b,1),(a,1)],3),([(b,1)],0)], []>
 joinable by a reduction of rules <[([(b,1),(a,1),(c,1)],0),([(b,1),(a,1),(c,1)],2),([(b,1)],0),([(b,1),(b,1)],3)], []>
 joinable by a reduction of rules <[([(b,1),(a,1),(c,1)],0),([(b,1)],0),([(b,1),(b,1),(c,1)],2),([(b,1),(b,1)],3)], []>
 joinable by a reduction of rules <[([(b,1),(a,1),(c,1)],0),([(b,1)],0),([(b,1)],2),([(b,1)],3)], []>
 joinable by a reduction of rules <[([(b,1)],0),([(b,1),(b,1),(c,1)],0),([(b,1),(b,1),(c,1)],2),([(b,1),(b,1)],3)], []>
 joinable by a reduction of rules <[([(b,1)],0),([(b,1),(b,1),(c,1)],0),([(b,1)],2),([(b,1)],3)], []>
 joinable by a reduction of rules <[([(b,1)],0),([(b,1)],2),([(b,1),(c,1),(c,1)],0),([(b,1)],3)], []>
 joinable by a reduction of rules <[([(b,1)],0),([(b,1)],2),([(b,1)],3),([(b,1)],0)], []>
Satisfiable by 2>1,4>3; a(0)b(0)c(0); 2>3>1,4
Diagram Decreasing
Direct Methods: CR

Combined result: CR
979.trs: Success(CR)
YES
(55 msec.)