MAYBE
627.10/297.11	MAYBE
627.10/297.11	
627.10/297.11	We are left with following problem, upon which TcT provides the
627.10/297.11	certificate MAYBE.
627.10/297.11	
627.10/297.11	Strict Trs:
627.10/297.11	  { active(f(X1, X2, X3)) -> f(X1, active(X2), X3)
627.10/297.11	  , active(f(b(), X, c())) -> mark(f(X, c(), X))
627.10/297.11	  , active(c()) -> mark(b())
627.10/297.11	  , f(X1, mark(X2), X3) -> mark(f(X1, X2, X3))
627.10/297.11	  , f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3))
627.10/297.11	  , proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3))
627.10/297.11	  , proper(b()) -> ok(b())
627.10/297.11	  , proper(c()) -> ok(c())
627.10/297.11	  , top(mark(X)) -> top(proper(X))
627.10/297.11	  , top(ok(X)) -> top(active(X)) }
627.10/297.11	Obligation:
627.10/297.11	  runtime complexity
627.10/297.11	Answer:
627.10/297.11	  MAYBE
627.10/297.11	
627.10/297.11	None of the processors succeeded.
627.10/297.11	
627.10/297.11	Details of failed attempt(s):
627.10/297.11	-----------------------------
627.10/297.11	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
627.10/297.11	   following reason:
627.10/297.11	   
627.10/297.11	   Computation stopped due to timeout after 297.0 seconds.
627.10/297.11	
627.10/297.11	2) 'Best' failed due to the following reason:
627.10/297.11	   
627.10/297.11	   None of the processors succeeded.
627.10/297.11	   
627.10/297.11	   Details of failed attempt(s):
627.10/297.11	   -----------------------------
627.10/297.11	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
627.10/297.11	      seconds)' failed due to the following reason:
627.10/297.11	      
627.10/297.11	      Computation stopped due to timeout after 148.0 seconds.
627.10/297.11	   
627.10/297.11	   2) 'Best' failed due to the following reason:
627.10/297.11	      
627.10/297.11	      None of the processors succeeded.
627.10/297.11	      
627.10/297.11	      Details of failed attempt(s):
627.10/297.11	      -----------------------------
627.10/297.11	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
627.10/297.11	         following reason:
627.10/297.11	         
627.10/297.11	         The processor is inapplicable, reason:
627.10/297.11	           Processor only applicable for innermost runtime complexity analysis
627.10/297.11	      
627.10/297.11	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
627.10/297.11	         to the following reason:
627.10/297.11	         
627.10/297.11	         The processor is inapplicable, reason:
627.10/297.11	           Processor only applicable for innermost runtime complexity analysis
627.10/297.11	      
627.10/297.11	   
627.10/297.11	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
627.10/297.11	      failed due to the following reason:
627.10/297.11	      
627.10/297.11	      None of the processors succeeded.
627.10/297.11	      
627.10/297.11	      Details of failed attempt(s):
627.10/297.11	      -----------------------------
627.10/297.11	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
627.10/297.11	         failed due to the following reason:
627.10/297.11	         
627.10/297.11	         match-boundness of the problem could not be verified.
627.10/297.11	      
627.10/297.11	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
627.10/297.11	         failed due to the following reason:
627.10/297.11	         
627.10/297.11	         match-boundness of the problem could not be verified.
627.10/297.11	      
627.10/297.11	   
627.10/297.11	
627.10/297.11	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
627.10/297.11	   the following reason:
627.10/297.11	   
627.10/297.11	   We add the following weak dependency pairs:
627.10/297.11	   
627.10/297.11	   Strict DPs:
627.10/297.11	     { active^#(f(X1, X2, X3)) -> c_1(f^#(X1, active(X2), X3))
627.10/297.11	     , active^#(f(b(), X, c())) -> c_2(f^#(X, c(), X))
627.10/297.11	     , active^#(c()) -> c_3()
627.10/297.11	     , f^#(X1, mark(X2), X3) -> c_4(f^#(X1, X2, X3))
627.10/297.11	     , f^#(ok(X1), ok(X2), ok(X3)) -> c_5(f^#(X1, X2, X3))
627.10/297.11	     , proper^#(f(X1, X2, X3)) ->
627.10/297.11	       c_6(f^#(proper(X1), proper(X2), proper(X3)))
627.10/297.11	     , proper^#(b()) -> c_7()
627.10/297.11	     , proper^#(c()) -> c_8()
627.10/297.11	     , top^#(mark(X)) -> c_9(top^#(proper(X)))
627.10/297.11	     , top^#(ok(X)) -> c_10(top^#(active(X))) }
627.10/297.11	   
627.10/297.11	   and mark the set of starting terms.
627.10/297.11	   
627.10/297.11	   We are left with following problem, upon which TcT provides the
627.10/297.11	   certificate MAYBE.
627.10/297.11	   
627.10/297.11	   Strict DPs:
627.10/297.11	     { active^#(f(X1, X2, X3)) -> c_1(f^#(X1, active(X2), X3))
627.10/297.11	     , active^#(f(b(), X, c())) -> c_2(f^#(X, c(), X))
627.10/297.11	     , active^#(c()) -> c_3()
627.10/297.11	     , f^#(X1, mark(X2), X3) -> c_4(f^#(X1, X2, X3))
627.10/297.11	     , f^#(ok(X1), ok(X2), ok(X3)) -> c_5(f^#(X1, X2, X3))
627.10/297.11	     , proper^#(f(X1, X2, X3)) ->
627.10/297.11	       c_6(f^#(proper(X1), proper(X2), proper(X3)))
627.10/297.11	     , proper^#(b()) -> c_7()
627.10/297.11	     , proper^#(c()) -> c_8()
627.10/297.11	     , top^#(mark(X)) -> c_9(top^#(proper(X)))
627.10/297.11	     , top^#(ok(X)) -> c_10(top^#(active(X))) }
627.10/297.11	   Strict Trs:
627.10/297.11	     { active(f(X1, X2, X3)) -> f(X1, active(X2), X3)
627.10/297.11	     , active(f(b(), X, c())) -> mark(f(X, c(), X))
627.10/297.11	     , active(c()) -> mark(b())
627.10/297.11	     , f(X1, mark(X2), X3) -> mark(f(X1, X2, X3))
627.10/297.11	     , f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3))
627.10/297.11	     , proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3))
627.10/297.11	     , proper(b()) -> ok(b())
627.10/297.11	     , proper(c()) -> ok(c())
627.10/297.11	     , top(mark(X)) -> top(proper(X))
627.10/297.11	     , top(ok(X)) -> top(active(X)) }
627.10/297.11	   Obligation:
627.10/297.11	     runtime complexity
627.10/297.11	   Answer:
627.10/297.11	     MAYBE
627.10/297.11	   
627.10/297.11	   Consider the dependency graph:
627.10/297.11	   
627.10/297.11	     1: active^#(f(X1, X2, X3)) -> c_1(f^#(X1, active(X2), X3))
627.10/297.11	        -->_1 f^#(ok(X1), ok(X2), ok(X3)) -> c_5(f^#(X1, X2, X3)) :5
627.10/297.11	        -->_1 f^#(X1, mark(X2), X3) -> c_4(f^#(X1, X2, X3)) :4
627.10/297.11	     
627.10/297.11	     2: active^#(f(b(), X, c())) -> c_2(f^#(X, c(), X))
627.10/297.11	     
627.10/297.11	     3: active^#(c()) -> c_3()
627.10/297.11	     
627.10/297.11	     4: f^#(X1, mark(X2), X3) -> c_4(f^#(X1, X2, X3))
627.10/297.11	        -->_1 f^#(ok(X1), ok(X2), ok(X3)) -> c_5(f^#(X1, X2, X3)) :5
627.10/297.11	        -->_1 f^#(X1, mark(X2), X3) -> c_4(f^#(X1, X2, X3)) :4
627.10/297.11	     
627.10/297.11	     5: f^#(ok(X1), ok(X2), ok(X3)) -> c_5(f^#(X1, X2, X3))
627.10/297.11	        -->_1 f^#(ok(X1), ok(X2), ok(X3)) -> c_5(f^#(X1, X2, X3)) :5
627.10/297.11	        -->_1 f^#(X1, mark(X2), X3) -> c_4(f^#(X1, X2, X3)) :4
627.10/297.11	     
627.10/297.11	     6: proper^#(f(X1, X2, X3)) ->
627.10/297.11	        c_6(f^#(proper(X1), proper(X2), proper(X3)))
627.10/297.11	        -->_1 f^#(ok(X1), ok(X2), ok(X3)) -> c_5(f^#(X1, X2, X3)) :5
627.10/297.11	        -->_1 f^#(X1, mark(X2), X3) -> c_4(f^#(X1, X2, X3)) :4
627.10/297.11	     
627.10/297.11	     7: proper^#(b()) -> c_7()
627.10/297.11	     
627.10/297.11	     8: proper^#(c()) -> c_8()
627.10/297.11	     
627.10/297.11	     9: top^#(mark(X)) -> c_9(top^#(proper(X)))
627.10/297.11	        -->_1 top^#(ok(X)) -> c_10(top^#(active(X))) :10
627.10/297.11	        -->_1 top^#(mark(X)) -> c_9(top^#(proper(X))) :9
627.10/297.11	     
627.10/297.11	     10: top^#(ok(X)) -> c_10(top^#(active(X)))
627.10/297.11	        -->_1 top^#(ok(X)) -> c_10(top^#(active(X))) :10
627.10/297.11	        -->_1 top^#(mark(X)) -> c_9(top^#(proper(X))) :9
627.10/297.11	     
627.10/297.11	   
627.10/297.11	   Only the nodes {3,4,5,7,8,9,10} are reachable from nodes
627.10/297.11	   {3,4,5,7,8,9,10} that start derivation from marked basic terms. The
627.10/297.11	   nodes not reachable are removed from the problem.
627.10/297.11	   
627.10/297.11	   We are left with following problem, upon which TcT provides the
627.10/297.11	   certificate MAYBE.
627.10/297.11	   
627.10/297.11	   Strict DPs:
627.10/297.11	     { active^#(c()) -> c_3()
627.10/297.11	     , f^#(X1, mark(X2), X3) -> c_4(f^#(X1, X2, X3))
627.10/297.11	     , f^#(ok(X1), ok(X2), ok(X3)) -> c_5(f^#(X1, X2, X3))
627.10/297.11	     , proper^#(b()) -> c_7()
627.10/297.11	     , proper^#(c()) -> c_8()
627.10/297.11	     , top^#(mark(X)) -> c_9(top^#(proper(X)))
627.10/297.11	     , top^#(ok(X)) -> c_10(top^#(active(X))) }
627.10/297.11	   Strict Trs:
627.10/297.11	     { active(f(X1, X2, X3)) -> f(X1, active(X2), X3)
627.10/297.11	     , active(f(b(), X, c())) -> mark(f(X, c(), X))
627.10/297.11	     , active(c()) -> mark(b())
627.10/297.11	     , f(X1, mark(X2), X3) -> mark(f(X1, X2, X3))
627.10/297.11	     , f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3))
627.10/297.11	     , proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3))
627.10/297.11	     , proper(b()) -> ok(b())
627.10/297.11	     , proper(c()) -> ok(c())
627.10/297.11	     , top(mark(X)) -> top(proper(X))
627.10/297.11	     , top(ok(X)) -> top(active(X)) }
627.10/297.11	   Obligation:
627.10/297.11	     runtime complexity
627.10/297.11	   Answer:
627.10/297.11	     MAYBE
627.10/297.11	   
627.10/297.11	   We estimate the number of application of {1,4,5} by applications of
627.10/297.11	   Pre({1,4,5}) = {}. Here rules are labeled as follows:
627.10/297.11	   
627.10/297.11	     DPs:
627.10/297.11	       { 1: active^#(c()) -> c_3()
627.10/297.11	       , 2: f^#(X1, mark(X2), X3) -> c_4(f^#(X1, X2, X3))
627.10/297.11	       , 3: f^#(ok(X1), ok(X2), ok(X3)) -> c_5(f^#(X1, X2, X3))
627.10/297.11	       , 4: proper^#(b()) -> c_7()
627.10/297.11	       , 5: proper^#(c()) -> c_8()
627.10/297.11	       , 6: top^#(mark(X)) -> c_9(top^#(proper(X)))
627.10/297.11	       , 7: top^#(ok(X)) -> c_10(top^#(active(X))) }
627.10/297.11	   
627.10/297.11	   We are left with following problem, upon which TcT provides the
627.10/297.11	   certificate MAYBE.
627.10/297.11	   
627.10/297.11	   Strict DPs:
627.10/297.11	     { f^#(X1, mark(X2), X3) -> c_4(f^#(X1, X2, X3))
627.10/297.11	     , f^#(ok(X1), ok(X2), ok(X3)) -> c_5(f^#(X1, X2, X3))
627.10/297.11	     , top^#(mark(X)) -> c_9(top^#(proper(X)))
627.10/297.11	     , top^#(ok(X)) -> c_10(top^#(active(X))) }
627.10/297.11	   Strict Trs:
627.10/297.11	     { active(f(X1, X2, X3)) -> f(X1, active(X2), X3)
627.10/297.11	     , active(f(b(), X, c())) -> mark(f(X, c(), X))
627.10/297.11	     , active(c()) -> mark(b())
627.10/297.11	     , f(X1, mark(X2), X3) -> mark(f(X1, X2, X3))
627.10/297.11	     , f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3))
627.10/297.11	     , proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3))
627.10/297.11	     , proper(b()) -> ok(b())
627.10/297.11	     , proper(c()) -> ok(c())
627.10/297.11	     , top(mark(X)) -> top(proper(X))
627.10/297.11	     , top(ok(X)) -> top(active(X)) }
627.10/297.11	   Weak DPs:
627.10/297.11	     { active^#(c()) -> c_3()
627.10/297.11	     , proper^#(b()) -> c_7()
627.10/297.11	     , proper^#(c()) -> c_8() }
627.10/297.11	   Obligation:
627.10/297.11	     runtime complexity
627.10/297.11	   Answer:
627.10/297.11	     MAYBE
627.10/297.11	   
627.10/297.11	   Empty strict component of the problem is NOT empty.
627.10/297.11	
627.10/297.11	
627.10/297.11	Arrrr..
627.10/297.13	EOF