MAYBE
839.38/297.04	MAYBE
839.38/297.04	
839.38/297.04	We are left with following problem, upon which TcT provides the
839.38/297.04	certificate MAYBE.
839.38/297.04	
839.38/297.04	Strict Trs:
839.38/297.04	  { minus(x, 0()) -> x
839.38/297.04	  , minus(minus(x, y), z) -> minus(x, plus(y, z))
839.38/297.04	  , minus(s(x), s(y)) -> minus(x, y)
839.38/297.04	  , quot(0(), s(y)) -> 0()
839.38/297.04	  , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
839.38/297.04	  , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x))
839.38/297.04	  , plus(s(x), s(y)) ->
839.38/297.04	    s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
839.38/297.04	  , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y))))
839.38/297.04	  , plus(zero(), y) -> y
839.38/297.04	  , if(true(), x, y) -> x
839.38/297.04	  , if(false(), x, y) -> y
839.38/297.04	  , gt(s(x), s(y)) -> gt(x, y)
839.38/297.04	  , gt(s(x), zero()) -> true()
839.38/297.04	  , gt(zero(), y) -> false()
839.38/297.04	  , not(x) -> if(x, false(), true())
839.38/297.04	  , id(x) -> x }
839.38/297.04	Obligation:
839.38/297.04	  runtime complexity
839.38/297.04	Answer:
839.38/297.04	  MAYBE
839.38/297.04	
839.38/297.04	None of the processors succeeded.
839.38/297.04	
839.38/297.04	Details of failed attempt(s):
839.38/297.04	-----------------------------
839.38/297.04	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
839.38/297.04	   following reason:
839.38/297.04	   
839.38/297.04	   Computation stopped due to timeout after 297.0 seconds.
839.38/297.04	
839.38/297.04	2) 'Best' failed due to the following reason:
839.38/297.04	   
839.38/297.04	   None of the processors succeeded.
839.38/297.04	   
839.38/297.04	   Details of failed attempt(s):
839.38/297.04	   -----------------------------
839.38/297.04	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
839.38/297.04	      seconds)' failed due to the following reason:
839.38/297.04	      
839.38/297.04	      Computation stopped due to timeout after 148.0 seconds.
839.38/297.04	   
839.38/297.04	   2) 'Best' failed due to the following reason:
839.38/297.04	      
839.38/297.04	      None of the processors succeeded.
839.38/297.04	      
839.38/297.04	      Details of failed attempt(s):
839.38/297.04	      -----------------------------
839.38/297.04	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
839.38/297.04	         following reason:
839.38/297.04	         
839.38/297.04	         The processor is inapplicable, reason:
839.38/297.04	           Processor only applicable for innermost runtime complexity analysis
839.38/297.04	      
839.38/297.04	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
839.38/297.04	         to the following reason:
839.38/297.04	         
839.38/297.04	         The processor is inapplicable, reason:
839.38/297.04	           Processor only applicable for innermost runtime complexity analysis
839.38/297.04	      
839.38/297.04	   
839.38/297.04	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
839.38/297.04	      failed due to the following reason:
839.38/297.04	      
839.38/297.04	      None of the processors succeeded.
839.38/297.04	      
839.38/297.04	      Details of failed attempt(s):
839.38/297.04	      -----------------------------
839.38/297.04	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
839.38/297.04	         failed due to the following reason:
839.38/297.04	         
839.38/297.04	         match-boundness of the problem could not be verified.
839.38/297.04	      
839.38/297.04	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
839.38/297.04	         failed due to the following reason:
839.38/297.04	         
839.38/297.04	         match-boundness of the problem could not be verified.
839.38/297.04	      
839.38/297.04	   
839.38/297.04	
839.38/297.04	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
839.38/297.04	   the following reason:
839.38/297.04	   
839.38/297.04	   We add the following weak dependency pairs:
839.38/297.04	   
839.38/297.04	   Strict DPs:
839.38/297.04	     { minus^#(x, 0()) -> c_1(x)
839.38/297.04	     , minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z)))
839.38/297.04	     , minus^#(s(x), s(y)) -> c_3(minus^#(x, y))
839.38/297.04	     , quot^#(0(), s(y)) -> c_4()
839.38/297.04	     , quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y)))
839.38/297.04	     , plus^#(s(x), x) -> c_6(plus^#(if(gt(x, x), id(x), id(x)), s(x)))
839.38/297.04	     , plus^#(s(x), s(y)) ->
839.38/297.04	       c_7(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))
839.38/297.04	     , plus^#(id(x), s(y)) -> c_8(plus^#(x, if(gt(s(y), y), y, s(y))))
839.38/297.04	     , plus^#(zero(), y) -> c_9(y)
839.38/297.04	     , if^#(true(), x, y) -> c_10(x)
839.38/297.04	     , if^#(false(), x, y) -> c_11(y)
839.38/297.04	     , gt^#(s(x), s(y)) -> c_12(gt^#(x, y))
839.38/297.04	     , gt^#(s(x), zero()) -> c_13()
839.38/297.04	     , gt^#(zero(), y) -> c_14()
839.38/297.04	     , not^#(x) -> c_15(if^#(x, false(), true()))
839.38/297.04	     , id^#(x) -> c_16(x) }
839.38/297.04	   
839.38/297.04	   and mark the set of starting terms.
839.38/297.04	   
839.38/297.04	   We are left with following problem, upon which TcT provides the
839.38/297.04	   certificate MAYBE.
839.38/297.04	   
839.38/297.04	   Strict DPs:
839.38/297.04	     { minus^#(x, 0()) -> c_1(x)
839.38/297.04	     , minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z)))
839.38/297.04	     , minus^#(s(x), s(y)) -> c_3(minus^#(x, y))
839.38/297.04	     , quot^#(0(), s(y)) -> c_4()
839.38/297.04	     , quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y)))
839.38/297.04	     , plus^#(s(x), x) -> c_6(plus^#(if(gt(x, x), id(x), id(x)), s(x)))
839.38/297.04	     , plus^#(s(x), s(y)) ->
839.38/297.04	       c_7(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))
839.38/297.04	     , plus^#(id(x), s(y)) -> c_8(plus^#(x, if(gt(s(y), y), y, s(y))))
839.38/297.04	     , plus^#(zero(), y) -> c_9(y)
839.38/297.04	     , if^#(true(), x, y) -> c_10(x)
839.38/297.04	     , if^#(false(), x, y) -> c_11(y)
839.38/297.04	     , gt^#(s(x), s(y)) -> c_12(gt^#(x, y))
839.38/297.04	     , gt^#(s(x), zero()) -> c_13()
839.38/297.04	     , gt^#(zero(), y) -> c_14()
839.38/297.04	     , not^#(x) -> c_15(if^#(x, false(), true()))
839.38/297.04	     , id^#(x) -> c_16(x) }
839.38/297.04	   Strict Trs:
839.38/297.04	     { minus(x, 0()) -> x
839.38/297.04	     , minus(minus(x, y), z) -> minus(x, plus(y, z))
839.38/297.04	     , minus(s(x), s(y)) -> minus(x, y)
839.38/297.04	     , quot(0(), s(y)) -> 0()
839.38/297.04	     , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
839.38/297.04	     , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x))
839.38/297.04	     , plus(s(x), s(y)) ->
839.38/297.04	       s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
839.38/297.04	     , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y))))
839.38/297.04	     , plus(zero(), y) -> y
839.38/297.04	     , if(true(), x, y) -> x
839.38/297.04	     , if(false(), x, y) -> y
839.38/297.04	     , gt(s(x), s(y)) -> gt(x, y)
839.38/297.04	     , gt(s(x), zero()) -> true()
839.38/297.04	     , gt(zero(), y) -> false()
839.38/297.04	     , not(x) -> if(x, false(), true())
839.38/297.04	     , id(x) -> x }
839.38/297.04	   Obligation:
839.38/297.04	     runtime complexity
839.38/297.04	   Answer:
839.38/297.04	     MAYBE
839.38/297.04	   
839.38/297.04	   We estimate the number of application of {4,13,14} by applications
839.38/297.04	   of Pre({4,13,14}) = {1,5,9,10,11,12,16}. Here rules are labeled as
839.38/297.04	   follows:
839.38/297.04	   
839.38/297.04	     DPs:
839.38/297.04	       { 1: minus^#(x, 0()) -> c_1(x)
839.38/297.04	       , 2: minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z)))
839.38/297.04	       , 3: minus^#(s(x), s(y)) -> c_3(minus^#(x, y))
839.38/297.04	       , 4: quot^#(0(), s(y)) -> c_4()
839.38/297.04	       , 5: quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y)))
839.38/297.04	       , 6: plus^#(s(x), x) ->
839.38/297.04	            c_6(plus^#(if(gt(x, x), id(x), id(x)), s(x)))
839.38/297.04	       , 7: plus^#(s(x), s(y)) ->
839.38/297.04	            c_7(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))
839.38/297.04	       , 8: plus^#(id(x), s(y)) ->
839.38/297.04	            c_8(plus^#(x, if(gt(s(y), y), y, s(y))))
839.38/297.04	       , 9: plus^#(zero(), y) -> c_9(y)
839.38/297.04	       , 10: if^#(true(), x, y) -> c_10(x)
839.38/297.04	       , 11: if^#(false(), x, y) -> c_11(y)
839.38/297.04	       , 12: gt^#(s(x), s(y)) -> c_12(gt^#(x, y))
839.38/297.04	       , 13: gt^#(s(x), zero()) -> c_13()
839.38/297.04	       , 14: gt^#(zero(), y) -> c_14()
839.38/297.04	       , 15: not^#(x) -> c_15(if^#(x, false(), true()))
839.38/297.04	       , 16: id^#(x) -> c_16(x) }
839.38/297.04	   
839.38/297.04	   We are left with following problem, upon which TcT provides the
839.38/297.04	   certificate MAYBE.
839.38/297.04	   
839.38/297.04	   Strict DPs:
839.38/297.04	     { minus^#(x, 0()) -> c_1(x)
839.38/297.04	     , minus^#(minus(x, y), z) -> c_2(minus^#(x, plus(y, z)))
839.38/297.04	     , minus^#(s(x), s(y)) -> c_3(minus^#(x, y))
839.38/297.04	     , quot^#(s(x), s(y)) -> c_5(quot^#(minus(x, y), s(y)))
839.38/297.04	     , plus^#(s(x), x) -> c_6(plus^#(if(gt(x, x), id(x), id(x)), s(x)))
839.38/297.04	     , plus^#(s(x), s(y)) ->
839.38/297.04	       c_7(plus^#(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y))))
839.38/297.04	     , plus^#(id(x), s(y)) -> c_8(plus^#(x, if(gt(s(y), y), y, s(y))))
839.38/297.04	     , plus^#(zero(), y) -> c_9(y)
839.38/297.04	     , if^#(true(), x, y) -> c_10(x)
839.38/297.04	     , if^#(false(), x, y) -> c_11(y)
839.38/297.04	     , gt^#(s(x), s(y)) -> c_12(gt^#(x, y))
839.38/297.04	     , not^#(x) -> c_15(if^#(x, false(), true()))
839.38/297.04	     , id^#(x) -> c_16(x) }
839.38/297.04	   Strict Trs:
839.38/297.04	     { minus(x, 0()) -> x
839.38/297.04	     , minus(minus(x, y), z) -> minus(x, plus(y, z))
839.38/297.04	     , minus(s(x), s(y)) -> minus(x, y)
839.38/297.04	     , quot(0(), s(y)) -> 0()
839.38/297.04	     , quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
839.38/297.04	     , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x))
839.38/297.04	     , plus(s(x), s(y)) ->
839.38/297.04	       s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
839.38/297.04	     , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y))))
839.38/297.04	     , plus(zero(), y) -> y
839.38/297.04	     , if(true(), x, y) -> x
839.38/297.04	     , if(false(), x, y) -> y
839.38/297.04	     , gt(s(x), s(y)) -> gt(x, y)
839.38/297.04	     , gt(s(x), zero()) -> true()
839.38/297.04	     , gt(zero(), y) -> false()
839.38/297.04	     , not(x) -> if(x, false(), true())
839.38/297.04	     , id(x) -> x }
839.38/297.04	   Weak DPs:
839.38/297.04	     { quot^#(0(), s(y)) -> c_4()
839.38/297.04	     , gt^#(s(x), zero()) -> c_13()
839.38/297.04	     , gt^#(zero(), y) -> c_14() }
839.38/297.04	   Obligation:
839.38/297.04	     runtime complexity
839.38/297.04	   Answer:
839.38/297.04	     MAYBE
839.38/297.04	   
839.38/297.04	   Empty strict component of the problem is NOT empty.
839.38/297.04	
839.38/297.04	
839.38/297.04	Arrrr..
839.60/297.27	EOF