MAYBE
1072.85/297.03	MAYBE
1072.85/297.03	
1072.85/297.03	We are left with following problem, upon which TcT provides the
1072.85/297.03	certificate MAYBE.
1072.85/297.03	
1072.85/297.03	Strict Trs:
1072.85/297.03	  { active(f(X1, X2, X3)) -> f(X1, X2, active(X3))
1072.85/297.03	  , active(f(a(), b(), X)) -> mark(f(X, X, X))
1072.85/297.03	  , active(c()) -> mark(a())
1072.85/297.03	  , active(c()) -> mark(b())
1072.85/297.03	  , f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3))
1072.85/297.03	  , f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3))
1072.85/297.03	  , proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3))
1072.85/297.03	  , proper(a()) -> ok(a())
1072.85/297.03	  , proper(b()) -> ok(b())
1072.85/297.03	  , proper(c()) -> ok(c())
1072.85/297.03	  , top(mark(X)) -> top(proper(X))
1072.85/297.03	  , top(ok(X)) -> top(active(X)) }
1072.85/297.03	Obligation:
1072.85/297.03	  runtime complexity
1072.85/297.03	Answer:
1072.85/297.03	  MAYBE
1072.85/297.03	
1072.85/297.03	None of the processors succeeded.
1072.85/297.03	
1072.85/297.03	Details of failed attempt(s):
1072.85/297.03	-----------------------------
1072.85/297.03	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
1072.85/297.03	   following reason:
1072.85/297.03	   
1072.85/297.03	   Computation stopped due to timeout after 297.0 seconds.
1072.85/297.03	
1072.85/297.03	2) 'Best' failed due to the following reason:
1072.85/297.03	   
1072.85/297.03	   None of the processors succeeded.
1072.85/297.03	   
1072.85/297.03	   Details of failed attempt(s):
1072.85/297.03	   -----------------------------
1072.85/297.03	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
1072.85/297.03	      seconds)' failed due to the following reason:
1072.85/297.03	      
1072.85/297.03	      Computation stopped due to timeout after 148.0 seconds.
1072.85/297.03	   
1072.85/297.03	   2) 'Best' failed due to the following reason:
1072.85/297.03	      
1072.85/297.03	      None of the processors succeeded.
1072.85/297.03	      
1072.85/297.03	      Details of failed attempt(s):
1072.85/297.03	      -----------------------------
1072.85/297.03	      1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
1072.85/297.03	         to the following reason:
1072.85/297.03	         
1072.85/297.03	         The processor is inapplicable, reason:
1072.85/297.03	           Processor only applicable for innermost runtime complexity analysis
1072.85/297.03	      
1072.85/297.03	      2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
1072.85/297.03	         following reason:
1072.85/297.03	         
1072.85/297.03	         The processor is inapplicable, reason:
1072.85/297.03	           Processor only applicable for innermost runtime complexity analysis
1072.85/297.03	      
1072.85/297.03	   
1072.85/297.03	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
1072.85/297.03	      failed due to the following reason:
1072.85/297.03	      
1072.85/297.03	      None of the processors succeeded.
1072.85/297.03	      
1072.85/297.03	      Details of failed attempt(s):
1072.85/297.03	      -----------------------------
1072.85/297.03	      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
1072.85/297.03	         failed due to the following reason:
1072.85/297.03	         
1072.85/297.03	         match-boundness of the problem could not be verified.
1072.85/297.03	      
1072.85/297.03	      2) 'Bounds with minimal-enrichment and initial automaton 'match''
1072.85/297.03	         failed due to the following reason:
1072.85/297.03	         
1072.85/297.03	         match-boundness of the problem could not be verified.
1072.85/297.03	      
1072.85/297.03	   
1072.85/297.03	
1072.85/297.03	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
1072.85/297.03	   the following reason:
1072.85/297.03	   
1072.85/297.03	   We add the following weak dependency pairs:
1072.85/297.03	   
1072.85/297.03	   Strict DPs:
1072.85/297.03	     { active^#(f(X1, X2, X3)) -> c_1(f^#(X1, X2, active(X3)))
1072.85/297.03	     , active^#(f(a(), b(), X)) -> c_2(f^#(X, X, X))
1072.85/297.03	     , active^#(c()) -> c_3()
1072.85/297.03	     , active^#(c()) -> c_4()
1072.85/297.03	     , f^#(X1, X2, mark(X3)) -> c_5(f^#(X1, X2, X3))
1072.85/297.03	     , f^#(ok(X1), ok(X2), ok(X3)) -> c_6(f^#(X1, X2, X3))
1072.85/297.03	     , proper^#(f(X1, X2, X3)) ->
1072.85/297.03	       c_7(f^#(proper(X1), proper(X2), proper(X3)))
1072.85/297.03	     , proper^#(a()) -> c_8()
1072.85/297.03	     , proper^#(b()) -> c_9()
1072.85/297.03	     , proper^#(c()) -> c_10()
1072.85/297.03	     , top^#(mark(X)) -> c_11(top^#(proper(X)))
1072.85/297.03	     , top^#(ok(X)) -> c_12(top^#(active(X))) }
1072.85/297.03	   
1072.85/297.03	   and mark the set of starting terms.
1072.85/297.03	   
1072.85/297.03	   We are left with following problem, upon which TcT provides the
1072.85/297.03	   certificate MAYBE.
1072.85/297.03	   
1072.85/297.03	   Strict DPs:
1072.85/297.03	     { active^#(f(X1, X2, X3)) -> c_1(f^#(X1, X2, active(X3)))
1072.85/297.03	     , active^#(f(a(), b(), X)) -> c_2(f^#(X, X, X))
1072.85/297.03	     , active^#(c()) -> c_3()
1072.85/297.03	     , active^#(c()) -> c_4()
1072.85/297.03	     , f^#(X1, X2, mark(X3)) -> c_5(f^#(X1, X2, X3))
1072.85/297.03	     , f^#(ok(X1), ok(X2), ok(X3)) -> c_6(f^#(X1, X2, X3))
1072.85/297.03	     , proper^#(f(X1, X2, X3)) ->
1072.85/297.03	       c_7(f^#(proper(X1), proper(X2), proper(X3)))
1072.85/297.03	     , proper^#(a()) -> c_8()
1072.85/297.03	     , proper^#(b()) -> c_9()
1072.85/297.03	     , proper^#(c()) -> c_10()
1072.85/297.03	     , top^#(mark(X)) -> c_11(top^#(proper(X)))
1072.85/297.03	     , top^#(ok(X)) -> c_12(top^#(active(X))) }
1072.85/297.03	   Strict Trs:
1072.85/297.03	     { active(f(X1, X2, X3)) -> f(X1, X2, active(X3))
1072.85/297.03	     , active(f(a(), b(), X)) -> mark(f(X, X, X))
1072.85/297.03	     , active(c()) -> mark(a())
1072.85/297.03	     , active(c()) -> mark(b())
1072.85/297.03	     , f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3))
1072.85/297.03	     , f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3))
1072.85/297.03	     , proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3))
1072.85/297.03	     , proper(a()) -> ok(a())
1072.85/297.03	     , proper(b()) -> ok(b())
1072.85/297.03	     , proper(c()) -> ok(c())
1072.85/297.03	     , top(mark(X)) -> top(proper(X))
1072.85/297.03	     , top(ok(X)) -> top(active(X)) }
1072.85/297.03	   Obligation:
1072.85/297.03	     runtime complexity
1072.85/297.03	   Answer:
1072.85/297.03	     MAYBE
1072.85/297.03	   
1072.85/297.03	   Consider the dependency graph:
1072.85/297.03	   
1072.85/297.03	     1: active^#(f(X1, X2, X3)) -> c_1(f^#(X1, X2, active(X3)))
1072.85/297.03	        -->_1 f^#(ok(X1), ok(X2), ok(X3)) -> c_6(f^#(X1, X2, X3)) :6
1072.85/297.03	        -->_1 f^#(X1, X2, mark(X3)) -> c_5(f^#(X1, X2, X3)) :5
1072.85/297.03	     
1072.85/297.03	     2: active^#(f(a(), b(), X)) -> c_2(f^#(X, X, X))
1072.85/297.03	        -->_1 f^#(ok(X1), ok(X2), ok(X3)) -> c_6(f^#(X1, X2, X3)) :6
1072.85/297.03	        -->_1 f^#(X1, X2, mark(X3)) -> c_5(f^#(X1, X2, X3)) :5
1072.85/297.03	     
1072.85/297.03	     3: active^#(c()) -> c_3()
1072.85/297.03	     
1072.85/297.03	     4: active^#(c()) -> c_4()
1072.85/297.03	     
1072.85/297.03	     5: f^#(X1, X2, mark(X3)) -> c_5(f^#(X1, X2, X3))
1072.85/297.03	        -->_1 f^#(ok(X1), ok(X2), ok(X3)) -> c_6(f^#(X1, X2, X3)) :6
1072.85/297.03	        -->_1 f^#(X1, X2, mark(X3)) -> c_5(f^#(X1, X2, X3)) :5
1072.85/297.03	     
1072.85/297.03	     6: f^#(ok(X1), ok(X2), ok(X3)) -> c_6(f^#(X1, X2, X3))
1072.85/297.03	        -->_1 f^#(ok(X1), ok(X2), ok(X3)) -> c_6(f^#(X1, X2, X3)) :6
1072.85/297.03	        -->_1 f^#(X1, X2, mark(X3)) -> c_5(f^#(X1, X2, X3)) :5
1072.85/297.03	     
1072.85/297.03	     7: proper^#(f(X1, X2, X3)) ->
1072.85/297.03	        c_7(f^#(proper(X1), proper(X2), proper(X3)))
1072.85/297.03	        -->_1 f^#(ok(X1), ok(X2), ok(X3)) -> c_6(f^#(X1, X2, X3)) :6
1072.85/297.03	        -->_1 f^#(X1, X2, mark(X3)) -> c_5(f^#(X1, X2, X3)) :5
1072.85/297.03	     
1072.85/297.03	     8: proper^#(a()) -> c_8()
1072.85/297.03	     
1072.85/297.03	     9: proper^#(b()) -> c_9()
1072.85/297.03	     
1072.85/297.03	     10: proper^#(c()) -> c_10()
1072.85/297.03	     
1072.85/297.03	     11: top^#(mark(X)) -> c_11(top^#(proper(X)))
1072.85/297.03	        -->_1 top^#(ok(X)) -> c_12(top^#(active(X))) :12
1072.85/297.03	        -->_1 top^#(mark(X)) -> c_11(top^#(proper(X))) :11
1072.85/297.03	     
1072.85/297.03	     12: top^#(ok(X)) -> c_12(top^#(active(X)))
1072.85/297.03	        -->_1 top^#(ok(X)) -> c_12(top^#(active(X))) :12
1072.85/297.03	        -->_1 top^#(mark(X)) -> c_11(top^#(proper(X))) :11
1072.85/297.03	     
1072.85/297.03	   
1072.85/297.03	   Only the nodes {3,4,5,6,8,9,10,11,12} are reachable from nodes
1072.85/297.03	   {3,4,5,6,8,9,10,11,12} that start derivation from marked basic
1072.85/297.03	   terms. The nodes not reachable are removed from the problem.
1072.85/297.03	   
1072.85/297.03	   We are left with following problem, upon which TcT provides the
1072.85/297.03	   certificate MAYBE.
1072.85/297.03	   
1072.85/297.03	   Strict DPs:
1072.85/297.03	     { active^#(c()) -> c_3()
1072.85/297.03	     , active^#(c()) -> c_4()
1072.85/297.03	     , f^#(X1, X2, mark(X3)) -> c_5(f^#(X1, X2, X3))
1072.85/297.03	     , f^#(ok(X1), ok(X2), ok(X3)) -> c_6(f^#(X1, X2, X3))
1072.85/297.03	     , proper^#(a()) -> c_8()
1072.85/297.03	     , proper^#(b()) -> c_9()
1072.85/297.03	     , proper^#(c()) -> c_10()
1072.85/297.03	     , top^#(mark(X)) -> c_11(top^#(proper(X)))
1072.85/297.03	     , top^#(ok(X)) -> c_12(top^#(active(X))) }
1072.85/297.03	   Strict Trs:
1072.85/297.03	     { active(f(X1, X2, X3)) -> f(X1, X2, active(X3))
1072.85/297.03	     , active(f(a(), b(), X)) -> mark(f(X, X, X))
1072.85/297.03	     , active(c()) -> mark(a())
1072.85/297.03	     , active(c()) -> mark(b())
1072.85/297.03	     , f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3))
1072.85/297.03	     , f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3))
1072.85/297.03	     , proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3))
1072.85/297.03	     , proper(a()) -> ok(a())
1072.85/297.03	     , proper(b()) -> ok(b())
1072.85/297.03	     , proper(c()) -> ok(c())
1072.85/297.03	     , top(mark(X)) -> top(proper(X))
1072.85/297.03	     , top(ok(X)) -> top(active(X)) }
1072.85/297.03	   Obligation:
1072.85/297.03	     runtime complexity
1072.85/297.03	   Answer:
1072.85/297.03	     MAYBE
1072.85/297.03	   
1072.85/297.03	   We estimate the number of application of {1,2,5,6,7} by
1072.85/297.03	   applications of Pre({1,2,5,6,7}) = {}. Here rules are labeled as
1072.85/297.03	   follows:
1072.85/297.03	   
1072.85/297.03	     DPs:
1072.85/297.03	       { 1: active^#(c()) -> c_3()
1072.85/297.03	       , 2: active^#(c()) -> c_4()
1072.85/297.03	       , 3: f^#(X1, X2, mark(X3)) -> c_5(f^#(X1, X2, X3))
1072.85/297.03	       , 4: f^#(ok(X1), ok(X2), ok(X3)) -> c_6(f^#(X1, X2, X3))
1072.85/297.03	       , 5: proper^#(a()) -> c_8()
1072.85/297.03	       , 6: proper^#(b()) -> c_9()
1072.85/297.03	       , 7: proper^#(c()) -> c_10()
1072.85/297.03	       , 8: top^#(mark(X)) -> c_11(top^#(proper(X)))
1072.85/297.03	       , 9: top^#(ok(X)) -> c_12(top^#(active(X))) }
1072.85/297.03	   
1072.85/297.03	   We are left with following problem, upon which TcT provides the
1072.85/297.03	   certificate MAYBE.
1072.85/297.03	   
1072.85/297.03	   Strict DPs:
1072.85/297.03	     { f^#(X1, X2, mark(X3)) -> c_5(f^#(X1, X2, X3))
1072.85/297.03	     , f^#(ok(X1), ok(X2), ok(X3)) -> c_6(f^#(X1, X2, X3))
1072.85/297.03	     , top^#(mark(X)) -> c_11(top^#(proper(X)))
1072.85/297.03	     , top^#(ok(X)) -> c_12(top^#(active(X))) }
1072.85/297.03	   Strict Trs:
1072.85/297.03	     { active(f(X1, X2, X3)) -> f(X1, X2, active(X3))
1072.85/297.03	     , active(f(a(), b(), X)) -> mark(f(X, X, X))
1072.85/297.03	     , active(c()) -> mark(a())
1072.85/297.03	     , active(c()) -> mark(b())
1072.85/297.03	     , f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3))
1072.85/297.03	     , f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3))
1072.85/297.03	     , proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3))
1072.85/297.03	     , proper(a()) -> ok(a())
1072.85/297.03	     , proper(b()) -> ok(b())
1072.85/297.03	     , proper(c()) -> ok(c())
1072.85/297.03	     , top(mark(X)) -> top(proper(X))
1072.85/297.03	     , top(ok(X)) -> top(active(X)) }
1072.85/297.03	   Weak DPs:
1072.85/297.03	     { active^#(c()) -> c_3()
1072.85/297.03	     , active^#(c()) -> c_4()
1072.85/297.03	     , proper^#(a()) -> c_8()
1072.85/297.03	     , proper^#(b()) -> c_9()
1072.85/297.03	     , proper^#(c()) -> c_10() }
1072.85/297.03	   Obligation:
1072.85/297.03	     runtime complexity
1072.85/297.03	   Answer:
1072.85/297.03	     MAYBE
1072.85/297.03	   
1072.85/297.03	   Empty strict component of the problem is NOT empty.
1072.85/297.03	
1072.85/297.03	
1072.85/297.03	Arrrr..
1073.09/297.20	EOF