MAYBE
341.33/192.32	MAYBE
341.33/192.32	
341.33/192.32	We are left with following problem, upon which TcT provides the
341.33/192.32	certificate MAYBE.
341.33/192.32	
341.33/192.32	Strict Trs:
341.33/192.32	  { minus(x, 0()) -> x
341.33/192.32	  , minus(minus(x, y), z) -> minus(x, plus(y, z))
341.33/192.32	  , minus(s(x), s(y)) -> minus(x, y)
341.33/192.32	  , quot(0(), s(y)) -> 0()
341.33/192.32	  , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
341.33/192.32	  , plus(0(), y) -> y
341.33/192.32	  , plus(s(x), y) -> s(plus(x, y)) }
341.33/192.32	Obligation:
341.33/192.32	  runtime complexity
341.33/192.32	Answer:
341.33/192.32	  MAYBE
341.33/192.32	
341.33/192.32	None of the processors succeeded.
341.33/192.32	
341.33/192.32	Details of failed attempt(s):
341.33/192.32	-----------------------------
341.33/192.32	1) 'Best' failed due to the following reason:
341.33/192.32	   
341.33/192.32	   None of the processors succeeded.
341.33/192.32	   
341.33/192.32	   Details of failed attempt(s):
341.33/192.32	   -----------------------------
341.33/192.32	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
341.33/192.32	      seconds)' failed due to the following reason:
341.33/192.32	      
341.33/192.32	      None of the processors succeeded.
341.33/192.32	      
341.33/192.32	      Details of failed attempt(s):
341.33/192.32	      -----------------------------
341.33/192.32	      1) 'empty' failed due to the following reason:
341.33/192.32	         
341.33/192.32	         Empty strict component of the problem is NOT empty.
341.33/192.32	      
341.33/192.32	      2) 'With Problem ...' failed due to the following reason:
341.33/192.32	         
341.33/192.32	         None of the processors succeeded.
341.33/192.32	         
341.33/192.32	         Details of failed attempt(s):
341.33/192.32	         -----------------------------
341.33/192.32	         1) 'empty' failed due to the following reason:
341.33/192.32	            
341.33/192.32	            Empty strict component of the problem is NOT empty.
341.33/192.32	         
341.33/192.32	         2) 'Fastest' failed due to the following reason:
341.33/192.32	            
341.33/192.32	            None of the processors succeeded.
341.33/192.32	            
341.33/192.32	            Details of failed attempt(s):
341.33/192.32	            -----------------------------
341.33/192.32	            1) 'With Problem ...' failed due to the following reason:
341.33/192.32	               
341.33/192.32	               None of the processors succeeded.
341.33/192.32	               
341.33/192.32	               Details of failed attempt(s):
341.33/192.32	               -----------------------------
341.33/192.32	               1) 'empty' failed due to the following reason:
341.33/192.32	                  
341.33/192.32	                  Empty strict component of the problem is NOT empty.
341.33/192.32	               
341.33/192.32	               2) 'With Problem ...' failed due to the following reason:
341.33/192.32	                  
341.33/192.32	                  Empty strict component of the problem is NOT empty.
341.33/192.32	               
341.33/192.32	            
341.33/192.32	            2) 'With Problem ...' failed due to the following reason:
341.33/192.32	               
341.33/192.32	               None of the processors succeeded.
341.33/192.32	               
341.33/192.32	               Details of failed attempt(s):
341.33/192.32	               -----------------------------
341.33/192.32	               1) 'empty' failed due to the following reason:
341.33/192.32	                  
341.33/192.32	                  Empty strict component of the problem is NOT empty.
341.33/192.32	               
341.33/192.32	               2) 'With Problem ...' failed due to the following reason:
341.33/192.32	                  
341.33/192.32	                  None of the processors succeeded.
341.33/192.32	                  
341.33/192.32	                  Details of failed attempt(s):
341.33/192.32	                  -----------------------------
341.33/192.32	                  1) 'empty' failed due to the following reason:
341.33/192.32	                     
341.33/192.32	                     Empty strict component of the problem is NOT empty.
341.33/192.32	                  
341.33/192.32	                  2) 'With Problem ...' failed due to the following reason:
341.33/192.32	                     
341.33/192.32	                     None of the processors succeeded.
341.33/192.32	                     
341.33/192.32	                     Details of failed attempt(s):
341.33/192.32	                     -----------------------------
341.33/192.32	                     1) 'empty' failed due to the following reason:
341.33/192.32	                        
341.33/192.32	                        Empty strict component of the problem is NOT empty.
341.33/192.32	                     
341.33/192.32	                     2) 'With Problem ...' failed due to the following reason:
341.33/192.32	                        
341.33/192.32	                        Empty strict component of the problem is NOT empty.
341.33/192.32	                     
341.33/192.32	                  
341.33/192.32	               
341.33/192.32	            
341.33/192.32	         
341.33/192.32	      
341.33/192.32	   
341.33/192.32	   2) 'Best' failed due to the following reason:
341.33/192.32	      
341.33/192.32	      None of the processors succeeded.
341.33/192.32	      
341.33/192.32	      Details of failed attempt(s):
341.33/192.32	      -----------------------------
341.33/192.32	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
341.33/192.32	         following reason:
341.33/192.32	         
341.33/192.32	         The processor is inapplicable, reason:
341.33/192.33	           Processor only applicable for innermost runtime complexity analysis
341.33/192.33	      
341.33/192.33	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
341.33/192.33	         to the following reason:
341.33/192.33	         
341.33/192.33	         The processor is inapplicable, reason:
341.33/192.33	           Processor only applicable for innermost runtime complexity analysis
341.33/192.33	      
341.33/192.33	   
341.33/192.33	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
341.33/192.33	      failed due to the following reason:
341.33/192.33	      
341.33/192.33	      None of the processors succeeded.
341.33/192.33	      
341.33/192.33	      Details of failed attempt(s):
341.33/192.33	      -----------------------------
341.33/192.33	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
341.33/192.33	         failed due to the following reason:
341.33/192.33	         
341.33/192.33	         match-boundness of the problem could not be verified.
341.33/192.33	      
341.33/192.33	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
341.33/192.33	         failed due to the following reason:
341.33/192.33	         
341.33/192.33	         match-boundness of the problem could not be verified.
341.33/192.33	      
341.33/192.33	   
341.33/192.33	
341.33/192.33	2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
341.33/192.33	   the following reason:
341.33/192.33	   
341.33/192.33	   We add the following weak dependency pairs:
341.33/192.33	   
341.33/192.33	   Strict DPs:
341.33/192.33	     { minus^#(x, 0()) -> c_1(x)
341.33/192.33	     , minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z)))
341.33/192.33	     , minus^#(s(x), s(y)) -> c_3(minus^#(x, y))
341.33/192.33	     , quot^#(0(), s(y)) -> c_4()
341.33/192.33	     , quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y)))
341.33/192.33	     , plus^#(0(), y) -> c_6(y)
341.33/192.33	     , plus^#(s(x), y) -> c_7(plus^#(x, y)) }
341.33/192.33	   
341.33/192.33	   and mark the set of starting terms.
341.33/192.33	   
341.33/192.33	   We are left with following problem, upon which TcT provides the
341.33/192.33	   certificate MAYBE.
341.33/192.33	   
341.33/192.33	   Strict DPs:
341.33/192.33	     { minus^#(x, 0()) -> c_1(x)
341.33/192.33	     , minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z)))
341.33/192.33	     , minus^#(s(x), s(y)) -> c_3(minus^#(x, y))
341.33/192.33	     , quot^#(0(), s(y)) -> c_4()
341.33/192.33	     , quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y)))
341.33/192.33	     , plus^#(0(), y) -> c_6(y)
341.33/192.33	     , plus^#(s(x), y) -> c_7(plus^#(x, y)) }
341.33/192.33	   Strict Trs:
341.33/192.33	     { minus(x, 0()) -> x
341.33/192.33	     , minus(minus(x, y), z) -> minus(x, plus(y, z))
341.33/192.33	     , minus(s(x), s(y)) -> minus(x, y)
341.33/192.33	     , quot(0(), s(y)) -> 0()
341.33/192.33	     , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
341.33/192.33	     , plus(0(), y) -> y
341.33/192.33	     , plus(s(x), y) -> s(plus(x, y)) }
341.33/192.33	   Obligation:
341.33/192.33	     runtime complexity
341.33/192.33	   Answer:
341.33/192.33	     MAYBE
341.33/192.33	   
341.33/192.33	   We estimate the number of application of {4} by applications of
341.33/192.33	   Pre({4}) = {1,5,6}. Here rules are labeled as follows:
341.33/192.33	   
341.33/192.33	     DPs:
341.33/192.33	       { 1: minus^#(x, 0()) -> c_1(x)
341.33/192.33	       , 2: minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z)))
341.33/192.33	       , 3: minus^#(s(x), s(y)) -> c_3(minus^#(x, y))
341.33/192.33	       , 4: quot^#(0(), s(y)) -> c_4()
341.33/192.33	       , 5: quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y)))
341.33/192.33	       , 6: plus^#(0(), y) -> c_6(y)
341.33/192.33	       , 7: plus^#(s(x), y) -> c_7(plus^#(x, y)) }
341.33/192.33	   
341.33/192.33	   We are left with following problem, upon which TcT provides the
341.33/192.33	   certificate MAYBE.
341.33/192.33	   
341.33/192.33	   Strict DPs:
341.33/192.33	     { minus^#(x, 0()) -> c_1(x)
341.33/192.33	     , minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z)))
341.33/192.33	     , minus^#(s(x), s(y)) -> c_3(minus^#(x, y))
341.33/192.33	     , quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y)))
341.33/192.33	     , plus^#(0(), y) -> c_6(y)
341.33/192.33	     , plus^#(s(x), y) -> c_7(plus^#(x, y)) }
341.33/192.33	   Strict Trs:
341.33/192.33	     { minus(x, 0()) -> x
341.33/192.33	     , minus(minus(x, y), z) -> minus(x, plus(y, z))
341.33/192.33	     , minus(s(x), s(y)) -> minus(x, y)
341.33/192.33	     , quot(0(), s(y)) -> 0()
341.33/192.33	     , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
341.33/192.33	     , plus(0(), y) -> y
341.33/192.33	     , plus(s(x), y) -> s(plus(x, y)) }
341.33/192.33	   Weak DPs: { quot^#(0(), s(y)) -> c_4() }
341.33/192.33	   Obligation:
341.33/192.33	     runtime complexity
341.33/192.33	   Answer:
341.33/192.33	     MAYBE
341.33/192.33	   
341.33/192.33	   Empty strict component of the problem is NOT empty.
341.33/192.33	
341.33/192.33	
341.33/192.33	Arrrr..
341.55/192.55	EOF