MAYBE
354.84/193.81	MAYBE
354.84/193.81	
354.84/193.81	We are left with following problem, upon which TcT provides the
354.84/193.81	certificate MAYBE.
354.84/193.81	
354.84/193.81	Strict Trs:
354.84/193.81	  { le(0(), y) -> true()
354.84/193.81	  , le(s(x), 0()) -> false()
354.84/193.81	  , le(s(x), s(y)) -> le(x, y)
354.84/193.81	  , minus(x, x) -> 0()
354.84/193.81	  , minus(x, 0()) -> x
354.84/193.81	  , minus(0(), x) -> 0()
354.84/193.81	  , minus(s(x), s(y)) -> minus(x, y)
354.84/193.81	  , isZero(0()) -> true()
354.84/193.81	  , isZero(s(x)) -> false()
354.84/193.81	  , mod(x, y) -> if_mod(isZero(y), le(y, x), x, y, minus(x, y))
354.84/193.81	  , if_mod(true(), b, x, y, z) -> divByZeroError()
354.84/193.81	  , if_mod(false(), true(), x, y, z) -> mod(z, y)
354.84/193.81	  , if_mod(false(), false(), x, y, z) -> x }
354.84/193.81	Obligation:
354.84/193.81	  runtime complexity
354.84/193.81	Answer:
354.84/193.81	  MAYBE
354.84/193.81	
354.84/193.81	None of the processors succeeded.
354.84/193.81	
354.84/193.81	Details of failed attempt(s):
354.84/193.81	-----------------------------
354.84/193.81	1) 'Best' failed due to the following reason:
354.84/193.81	   
354.84/193.81	   None of the processors succeeded.
354.84/193.81	   
354.84/193.81	   Details of failed attempt(s):
354.84/193.81	   -----------------------------
354.84/193.81	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
354.84/193.81	      seconds)' failed due to the following reason:
354.84/193.81	      
354.84/193.81	      None of the processors succeeded.
354.84/193.81	      
354.84/193.81	      Details of failed attempt(s):
354.84/193.81	      -----------------------------
354.84/193.81	      1) 'empty' failed due to the following reason:
354.84/193.81	         
354.84/193.81	         Empty strict component of the problem is NOT empty.
354.84/193.81	      
354.84/193.81	      2) 'With Problem ...' failed due to the following reason:
354.84/193.81	         
354.84/193.81	         None of the processors succeeded.
354.84/193.81	         
354.84/193.81	         Details of failed attempt(s):
354.84/193.81	         -----------------------------
354.84/193.81	         1) 'empty' failed due to the following reason:
354.84/193.81	            
354.84/193.81	            Empty strict component of the problem is NOT empty.
354.84/193.81	         
354.84/193.81	         2) 'Fastest' failed due to the following reason:
354.84/193.81	            
354.84/193.81	            None of the processors succeeded.
354.84/193.81	            
354.84/193.81	            Details of failed attempt(s):
354.84/193.81	            -----------------------------
354.84/193.81	            1) 'With Problem ...' failed due to the following reason:
354.84/193.81	               
354.84/193.81	               None of the processors succeeded.
354.84/193.81	               
354.84/193.81	               Details of failed attempt(s):
354.84/193.81	               -----------------------------
354.84/193.81	               1) 'empty' failed due to the following reason:
354.84/193.81	                  
354.84/193.81	                  Empty strict component of the problem is NOT empty.
354.84/193.81	               
354.84/193.81	               2) 'With Problem ...' failed due to the following reason:
354.84/193.81	                  
354.84/193.81	                  Empty strict component of the problem is NOT empty.
354.84/193.81	               
354.84/193.81	            
354.84/193.81	            2) 'With Problem ...' failed due to the following reason:
354.84/193.81	               
354.84/193.81	               None of the processors succeeded.
354.84/193.81	               
354.84/193.81	               Details of failed attempt(s):
354.84/193.81	               -----------------------------
354.84/193.81	               1) 'empty' failed due to the following reason:
354.84/193.81	                  
354.84/193.81	                  Empty strict component of the problem is NOT empty.
354.84/193.81	               
354.84/193.81	               2) 'With Problem ...' failed due to the following reason:
354.84/193.81	                  
354.84/193.81	                  None of the processors succeeded.
354.84/193.81	                  
354.84/193.81	                  Details of failed attempt(s):
354.84/193.81	                  -----------------------------
354.84/193.81	                  1) 'empty' failed due to the following reason:
354.84/193.81	                     
354.84/193.81	                     Empty strict component of the problem is NOT empty.
354.84/193.81	                  
354.84/193.81	                  2) 'With Problem ...' failed due to the following reason:
354.84/193.81	                     
354.84/193.81	                     None of the processors succeeded.
354.84/193.81	                     
354.84/193.81	                     Details of failed attempt(s):
354.84/193.81	                     -----------------------------
354.84/193.81	                     1) 'empty' failed due to the following reason:
354.84/193.81	                        
354.84/193.81	                        Empty strict component of the problem is NOT empty.
354.84/193.81	                     
354.84/193.81	                     2) 'With Problem ...' failed due to the following reason:
354.84/193.81	                        
354.84/193.81	                        Empty strict component of the problem is NOT empty.
354.84/193.81	                     
354.84/193.81	                  
354.84/193.81	               
354.84/193.81	            
354.84/193.81	         
354.84/193.81	      
354.84/193.81	   
354.84/193.81	   2) 'Best' failed due to the following reason:
354.84/193.81	      
354.84/193.81	      None of the processors succeeded.
354.84/193.81	      
354.84/193.81	      Details of failed attempt(s):
354.84/193.81	      -----------------------------
354.84/193.81	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
354.84/193.81	         following reason:
354.84/193.81	         
354.84/193.81	         The processor is inapplicable, reason:
354.84/193.81	           Processor only applicable for innermost runtime complexity analysis
354.84/193.81	      
354.84/193.81	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
354.84/193.81	         to the following reason:
354.84/193.81	         
354.84/193.81	         The processor is inapplicable, reason:
354.84/193.81	           Processor only applicable for innermost runtime complexity analysis
354.84/193.81	      
354.84/193.81	   
354.84/193.81	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
354.84/193.81	      failed due to the following reason:
354.84/193.81	      
354.84/193.81	      None of the processors succeeded.
354.84/193.81	      
354.84/193.81	      Details of failed attempt(s):
354.84/193.81	      -----------------------------
354.84/193.81	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
354.84/193.81	         failed due to the following reason:
354.84/193.81	         
354.84/193.81	         match-boundness of the problem could not be verified.
354.84/193.81	      
354.84/193.81	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
354.84/193.81	         failed due to the following reason:
354.84/193.81	         
354.84/193.81	         match-boundness of the problem could not be verified.
354.84/193.81	      
354.84/193.81	   
354.84/193.81	
354.84/193.81	2) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
354.84/193.81	   the following reason:
354.84/193.81	   
354.84/193.81	   We add the following weak dependency pairs:
354.84/193.81	   
354.84/193.81	   Strict DPs:
354.84/193.81	     { le^#(0(), y) -> c_1()
354.84/193.81	     , le^#(s(x), 0()) -> c_2()
354.84/193.81	     , le^#(s(x), s(y)) -> c_3(le^#(x, y))
354.84/193.81	     , minus^#(x, x) -> c_4()
354.84/193.81	     , minus^#(x, 0()) -> c_5(x)
354.84/193.81	     , minus^#(0(), x) -> c_6()
354.84/193.81	     , minus^#(s(x), s(y)) -> c_7(minus^#(x, y))
354.84/193.81	     , isZero^#(0()) -> c_8()
354.84/193.81	     , isZero^#(s(x)) -> c_9()
354.84/193.81	     , mod^#(x, y) ->
354.84/193.81	       c_10(if_mod^#(isZero(y), le(y, x), x, y, minus(x, y)))
354.84/193.81	     , if_mod^#(true(), b, x, y, z) -> c_11()
354.84/193.81	     , if_mod^#(false(), true(), x, y, z) -> c_12(mod^#(z, y))
354.84/193.81	     , if_mod^#(false(), false(), x, y, z) -> c_13(x) }
354.84/193.81	   
354.84/193.81	   and mark the set of starting terms.
354.84/193.81	   
354.84/193.81	   We are left with following problem, upon which TcT provides the
354.84/193.81	   certificate MAYBE.
354.84/193.81	   
354.84/193.81	   Strict DPs:
354.84/193.81	     { le^#(0(), y) -> c_1()
354.84/193.81	     , le^#(s(x), 0()) -> c_2()
354.84/193.81	     , le^#(s(x), s(y)) -> c_3(le^#(x, y))
354.84/193.81	     , minus^#(x, x) -> c_4()
354.84/193.81	     , minus^#(x, 0()) -> c_5(x)
354.84/193.81	     , minus^#(0(), x) -> c_6()
354.84/193.81	     , minus^#(s(x), s(y)) -> c_7(minus^#(x, y))
354.84/193.81	     , isZero^#(0()) -> c_8()
354.84/193.81	     , isZero^#(s(x)) -> c_9()
354.84/193.81	     , mod^#(x, y) ->
354.84/193.81	       c_10(if_mod^#(isZero(y), le(y, x), x, y, minus(x, y)))
354.84/193.81	     , if_mod^#(true(), b, x, y, z) -> c_11()
354.84/193.81	     , if_mod^#(false(), true(), x, y, z) -> c_12(mod^#(z, y))
354.84/193.81	     , if_mod^#(false(), false(), x, y, z) -> c_13(x) }
354.84/193.81	   Strict Trs:
354.84/193.81	     { le(0(), y) -> true()
354.84/193.81	     , le(s(x), 0()) -> false()
354.84/193.81	     , le(s(x), s(y)) -> le(x, y)
354.84/193.81	     , minus(x, x) -> 0()
354.84/193.81	     , minus(x, 0()) -> x
354.84/193.81	     , minus(0(), x) -> 0()
354.84/193.81	     , minus(s(x), s(y)) -> minus(x, y)
354.84/193.81	     , isZero(0()) -> true()
354.84/193.81	     , isZero(s(x)) -> false()
354.84/193.81	     , mod(x, y) -> if_mod(isZero(y), le(y, x), x, y, minus(x, y))
354.84/193.81	     , if_mod(true(), b, x, y, z) -> divByZeroError()
354.84/193.81	     , if_mod(false(), true(), x, y, z) -> mod(z, y)
354.84/193.81	     , if_mod(false(), false(), x, y, z) -> x }
354.84/193.81	   Obligation:
354.84/193.81	     runtime complexity
354.84/193.81	   Answer:
354.84/193.81	     MAYBE
354.84/193.81	   
354.84/193.81	   We estimate the number of application of {1,2,4,6,8,9,11} by
354.84/193.81	   applications of Pre({1,2,4,6,8,9,11}) = {3,5,7,10,13}. Here rules
354.84/193.81	   are labeled as follows:
354.84/193.81	   
354.84/193.81	     DPs:
354.84/193.81	       { 1: le^#(0(), y) -> c_1()
354.84/193.81	       , 2: le^#(s(x), 0()) -> c_2()
354.84/193.81	       , 3: le^#(s(x), s(y)) -> c_3(le^#(x, y))
354.84/193.81	       , 4: minus^#(x, x) -> c_4()
354.84/193.81	       , 5: minus^#(x, 0()) -> c_5(x)
354.84/193.81	       , 6: minus^#(0(), x) -> c_6()
354.84/193.81	       , 7: minus^#(s(x), s(y)) -> c_7(minus^#(x, y))
354.84/193.81	       , 8: isZero^#(0()) -> c_8()
354.84/193.81	       , 9: isZero^#(s(x)) -> c_9()
354.84/193.81	       , 10: mod^#(x, y) ->
354.84/193.81	             c_10(if_mod^#(isZero(y), le(y, x), x, y, minus(x, y)))
354.84/193.81	       , 11: if_mod^#(true(), b, x, y, z) -> c_11()
354.84/193.81	       , 12: if_mod^#(false(), true(), x, y, z) -> c_12(mod^#(z, y))
354.84/193.81	       , 13: if_mod^#(false(), false(), x, y, z) -> c_13(x) }
354.84/193.81	   
354.84/193.81	   We are left with following problem, upon which TcT provides the
354.84/193.81	   certificate MAYBE.
354.84/193.81	   
354.84/193.81	   Strict DPs:
354.84/193.81	     { le^#(s(x), s(y)) -> c_3(le^#(x, y))
354.84/193.81	     , minus^#(x, 0()) -> c_5(x)
354.84/193.81	     , minus^#(s(x), s(y)) -> c_7(minus^#(x, y))
354.84/193.81	     , mod^#(x, y) ->
354.84/193.81	       c_10(if_mod^#(isZero(y), le(y, x), x, y, minus(x, y)))
354.84/193.81	     , if_mod^#(false(), true(), x, y, z) -> c_12(mod^#(z, y))
354.84/193.81	     , if_mod^#(false(), false(), x, y, z) -> c_13(x) }
354.84/193.81	   Strict Trs:
354.84/193.81	     { le(0(), y) -> true()
354.84/193.81	     , le(s(x), 0()) -> false()
354.84/193.81	     , le(s(x), s(y)) -> le(x, y)
354.84/193.81	     , minus(x, x) -> 0()
354.84/193.81	     , minus(x, 0()) -> x
354.84/193.81	     , minus(0(), x) -> 0()
354.84/193.81	     , minus(s(x), s(y)) -> minus(x, y)
354.84/193.81	     , isZero(0()) -> true()
354.84/193.81	     , isZero(s(x)) -> false()
354.84/193.81	     , mod(x, y) -> if_mod(isZero(y), le(y, x), x, y, minus(x, y))
354.84/193.81	     , if_mod(true(), b, x, y, z) -> divByZeroError()
354.84/193.81	     , if_mod(false(), true(), x, y, z) -> mod(z, y)
354.84/193.81	     , if_mod(false(), false(), x, y, z) -> x }
354.84/193.81	   Weak DPs:
354.84/193.81	     { le^#(0(), y) -> c_1()
354.84/193.81	     , le^#(s(x), 0()) -> c_2()
354.84/193.81	     , minus^#(x, x) -> c_4()
354.84/193.81	     , minus^#(0(), x) -> c_6()
354.84/193.81	     , isZero^#(0()) -> c_8()
354.84/193.81	     , isZero^#(s(x)) -> c_9()
354.84/193.81	     , if_mod^#(true(), b, x, y, z) -> c_11() }
354.84/193.81	   Obligation:
354.84/193.81	     runtime complexity
354.84/193.81	   Answer:
354.84/193.81	     MAYBE
354.84/193.81	   
354.84/193.81	   Empty strict component of the problem is NOT empty.
354.84/193.81	
354.84/193.81	
354.84/193.81	Arrrr..
355.05/194.05	EOF