MAYBE
802.83/297.04	MAYBE
802.83/297.04	
802.83/297.04	We are left with following problem, upon which TcT provides the
802.83/297.04	certificate MAYBE.
802.83/297.04	
802.83/297.04	Strict Trs:
802.83/297.04	  { le(0(), y) -> true()
802.83/297.04	  , le(s(x), 0()) -> false()
802.83/297.04	  , le(s(x), s(y)) -> le(x, y)
802.83/297.04	  , eq(0(), 0()) -> true()
802.83/297.04	  , eq(0(), s(y)) -> false()
802.83/297.04	  , eq(s(x), 0()) -> false()
802.83/297.04	  , eq(s(x), s(y)) -> eq(x, y)
802.83/297.04	  , if1(true(), x, y, xs) -> min(x, xs)
802.83/297.04	  , if1(false(), x, y, xs) -> min(y, xs)
802.83/297.04	  , min(x, cons(y, z)) -> if1(le(x, y), x, y, z)
802.83/297.04	  , min(x, nil()) -> x
802.83/297.04	  , if2(true(), x, y, xs) -> xs
802.83/297.04	  , if2(false(), x, y, xs) -> cons(y, del(x, xs))
802.83/297.04	  , del(x, cons(y, z)) -> if2(eq(x, y), x, y, z)
802.83/297.04	  , del(x, nil()) -> nil()
802.83/297.04	  , minsort(cons(x, y)) ->
802.83/297.04	    cons(min(x, y), minsort(del(min(x, y), cons(x, y))))
802.83/297.04	  , minsort(nil()) -> nil() }
802.83/297.04	Obligation:
802.83/297.04	  runtime complexity
802.83/297.04	Answer:
802.83/297.04	  MAYBE
802.83/297.04	
802.83/297.04	None of the processors succeeded.
802.83/297.04	
802.83/297.04	Details of failed attempt(s):
802.83/297.04	-----------------------------
802.83/297.04	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
802.83/297.04	   following reason:
802.83/297.04	   
802.83/297.04	   Computation stopped due to timeout after 297.0 seconds.
802.83/297.04	
802.83/297.04	2) 'Best' failed due to the following reason:
802.83/297.04	   
802.83/297.04	   None of the processors succeeded.
802.83/297.04	   
802.83/297.04	   Details of failed attempt(s):
802.83/297.04	   -----------------------------
802.83/297.04	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
802.83/297.04	      seconds)' failed due to the following reason:
802.83/297.04	      
802.83/297.04	      Computation stopped due to timeout after 148.0 seconds.
802.83/297.04	   
802.83/297.04	   2) 'Best' failed due to the following reason:
802.83/297.04	      
802.83/297.04	      None of the processors succeeded.
802.83/297.04	      
802.83/297.04	      Details of failed attempt(s):
802.83/297.04	      -----------------------------
802.83/297.04	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
802.83/297.04	         following reason:
802.83/297.04	         
802.83/297.04	         The processor is inapplicable, reason:
802.83/297.04	           Processor only applicable for innermost runtime complexity analysis
802.83/297.04	      
802.83/297.04	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
802.83/297.04	         to the following reason:
802.83/297.04	         
802.83/297.04	         The processor is inapplicable, reason:
802.83/297.04	           Processor only applicable for innermost runtime complexity analysis
802.83/297.04	      
802.83/297.04	   
802.83/297.04	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
802.83/297.04	      failed due to the following reason:
802.83/297.04	      
802.83/297.04	      None of the processors succeeded.
802.83/297.04	      
802.83/297.04	      Details of failed attempt(s):
802.83/297.04	      -----------------------------
802.83/297.04	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
802.83/297.04	         failed due to the following reason:
802.83/297.04	         
802.83/297.04	         match-boundness of the problem could not be verified.
802.83/297.04	      
802.83/297.04	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
802.83/297.04	         failed due to the following reason:
802.83/297.04	         
802.83/297.04	         match-boundness of the problem could not be verified.
802.83/297.04	      
802.83/297.04	   
802.83/297.04	
802.83/297.04	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
802.83/297.04	   the following reason:
802.83/297.04	   
802.83/297.04	   We add the following weak dependency pairs:
802.83/297.04	   
802.83/297.04	   Strict DPs:
802.83/297.04	     { le^#(0(), y) -> c_1()
802.83/297.04	     , le^#(s(x), 0()) -> c_2()
802.83/297.04	     , le^#(s(x), s(y)) -> c_3(le^#(x, y))
802.83/297.04	     , eq^#(0(), 0()) -> c_4()
802.83/297.04	     , eq^#(0(), s(y)) -> c_5()
802.83/297.04	     , eq^#(s(x), 0()) -> c_6()
802.83/297.04	     , eq^#(s(x), s(y)) -> c_7(eq^#(x, y))
802.83/297.04	     , if1^#(true(), x, y, xs) -> c_8(min^#(x, xs))
802.83/297.04	     , if1^#(false(), x, y, xs) -> c_9(min^#(y, xs))
802.83/297.04	     , min^#(x, cons(y, z)) -> c_10(if1^#(le(x, y), x, y, z))
802.83/297.04	     , min^#(x, nil()) -> c_11(x)
802.83/297.04	     , if2^#(true(), x, y, xs) -> c_12(xs)
802.83/297.04	     , if2^#(false(), x, y, xs) -> c_13(y, del^#(x, xs))
802.83/297.04	     , del^#(x, cons(y, z)) -> c_14(if2^#(eq(x, y), x, y, z))
802.83/297.04	     , del^#(x, nil()) -> c_15()
802.83/297.04	     , minsort^#(cons(x, y)) ->
802.83/297.04	       c_16(min^#(x, y), minsort^#(del(min(x, y), cons(x, y))))
802.83/297.04	     , minsort^#(nil()) -> c_17() }
802.83/297.04	   
802.83/297.04	   and mark the set of starting terms.
802.83/297.04	   
802.83/297.04	   We are left with following problem, upon which TcT provides the
802.83/297.04	   certificate MAYBE.
802.83/297.04	   
802.83/297.04	   Strict DPs:
802.83/297.04	     { le^#(0(), y) -> c_1()
802.83/297.04	     , le^#(s(x), 0()) -> c_2()
802.83/297.04	     , le^#(s(x), s(y)) -> c_3(le^#(x, y))
802.83/297.04	     , eq^#(0(), 0()) -> c_4()
802.83/297.04	     , eq^#(0(), s(y)) -> c_5()
802.83/297.04	     , eq^#(s(x), 0()) -> c_6()
802.83/297.04	     , eq^#(s(x), s(y)) -> c_7(eq^#(x, y))
802.83/297.04	     , if1^#(true(), x, y, xs) -> c_8(min^#(x, xs))
802.83/297.04	     , if1^#(false(), x, y, xs) -> c_9(min^#(y, xs))
802.83/297.04	     , min^#(x, cons(y, z)) -> c_10(if1^#(le(x, y), x, y, z))
802.83/297.04	     , min^#(x, nil()) -> c_11(x)
802.83/297.04	     , if2^#(true(), x, y, xs) -> c_12(xs)
802.83/297.04	     , if2^#(false(), x, y, xs) -> c_13(y, del^#(x, xs))
802.83/297.04	     , del^#(x, cons(y, z)) -> c_14(if2^#(eq(x, y), x, y, z))
802.83/297.04	     , del^#(x, nil()) -> c_15()
802.83/297.04	     , minsort^#(cons(x, y)) ->
802.83/297.04	       c_16(min^#(x, y), minsort^#(del(min(x, y), cons(x, y))))
802.83/297.04	     , minsort^#(nil()) -> c_17() }
802.83/297.04	   Strict Trs:
802.83/297.04	     { le(0(), y) -> true()
802.83/297.04	     , le(s(x), 0()) -> false()
802.83/297.04	     , le(s(x), s(y)) -> le(x, y)
802.83/297.04	     , eq(0(), 0()) -> true()
802.83/297.04	     , eq(0(), s(y)) -> false()
802.83/297.04	     , eq(s(x), 0()) -> false()
802.83/297.04	     , eq(s(x), s(y)) -> eq(x, y)
802.83/297.04	     , if1(true(), x, y, xs) -> min(x, xs)
802.83/297.04	     , if1(false(), x, y, xs) -> min(y, xs)
802.83/297.04	     , min(x, cons(y, z)) -> if1(le(x, y), x, y, z)
802.83/297.04	     , min(x, nil()) -> x
802.83/297.04	     , if2(true(), x, y, xs) -> xs
802.83/297.04	     , if2(false(), x, y, xs) -> cons(y, del(x, xs))
802.83/297.04	     , del(x, cons(y, z)) -> if2(eq(x, y), x, y, z)
802.83/297.04	     , del(x, nil()) -> nil()
802.83/297.04	     , minsort(cons(x, y)) ->
802.83/297.04	       cons(min(x, y), minsort(del(min(x, y), cons(x, y))))
802.83/297.04	     , minsort(nil()) -> nil() }
802.83/297.04	   Obligation:
802.83/297.04	     runtime complexity
802.83/297.04	   Answer:
802.83/297.04	     MAYBE
802.83/297.04	   
802.83/297.04	   We estimate the number of application of {1,2,4,5,6,15,17} by
802.83/297.04	   applications of Pre({1,2,4,5,6,15,17}) = {3,7,11,12,13,16}. Here
802.83/297.04	   rules are labeled as follows:
802.83/297.04	   
802.83/297.04	     DPs:
802.83/297.04	       { 1: le^#(0(), y) -> c_1()
802.83/297.04	       , 2: le^#(s(x), 0()) -> c_2()
802.83/297.04	       , 3: le^#(s(x), s(y)) -> c_3(le^#(x, y))
802.83/297.04	       , 4: eq^#(0(), 0()) -> c_4()
802.83/297.04	       , 5: eq^#(0(), s(y)) -> c_5()
802.83/297.04	       , 6: eq^#(s(x), 0()) -> c_6()
802.83/297.04	       , 7: eq^#(s(x), s(y)) -> c_7(eq^#(x, y))
802.83/297.04	       , 8: if1^#(true(), x, y, xs) -> c_8(min^#(x, xs))
802.83/297.04	       , 9: if1^#(false(), x, y, xs) -> c_9(min^#(y, xs))
802.83/297.04	       , 10: min^#(x, cons(y, z)) -> c_10(if1^#(le(x, y), x, y, z))
802.83/297.04	       , 11: min^#(x, nil()) -> c_11(x)
802.83/297.04	       , 12: if2^#(true(), x, y, xs) -> c_12(xs)
802.83/297.04	       , 13: if2^#(false(), x, y, xs) -> c_13(y, del^#(x, xs))
802.83/297.04	       , 14: del^#(x, cons(y, z)) -> c_14(if2^#(eq(x, y), x, y, z))
802.83/297.04	       , 15: del^#(x, nil()) -> c_15()
802.83/297.04	       , 16: minsort^#(cons(x, y)) ->
802.83/297.04	             c_16(min^#(x, y), minsort^#(del(min(x, y), cons(x, y))))
802.83/297.04	       , 17: minsort^#(nil()) -> c_17() }
802.83/297.04	   
802.83/297.04	   We are left with following problem, upon which TcT provides the
802.83/297.04	   certificate MAYBE.
802.83/297.04	   
802.83/297.04	   Strict DPs:
802.83/297.04	     { le^#(s(x), s(y)) -> c_3(le^#(x, y))
802.83/297.04	     , eq^#(s(x), s(y)) -> c_7(eq^#(x, y))
802.83/297.04	     , if1^#(true(), x, y, xs) -> c_8(min^#(x, xs))
802.83/297.04	     , if1^#(false(), x, y, xs) -> c_9(min^#(y, xs))
802.83/297.04	     , min^#(x, cons(y, z)) -> c_10(if1^#(le(x, y), x, y, z))
802.83/297.04	     , min^#(x, nil()) -> c_11(x)
802.83/297.04	     , if2^#(true(), x, y, xs) -> c_12(xs)
802.83/297.04	     , if2^#(false(), x, y, xs) -> c_13(y, del^#(x, xs))
802.83/297.04	     , del^#(x, cons(y, z)) -> c_14(if2^#(eq(x, y), x, y, z))
802.83/297.04	     , minsort^#(cons(x, y)) ->
802.83/297.04	       c_16(min^#(x, y), minsort^#(del(min(x, y), cons(x, y)))) }
802.83/297.04	   Strict Trs:
802.83/297.04	     { le(0(), y) -> true()
802.83/297.04	     , le(s(x), 0()) -> false()
802.83/297.04	     , le(s(x), s(y)) -> le(x, y)
802.83/297.04	     , eq(0(), 0()) -> true()
802.83/297.04	     , eq(0(), s(y)) -> false()
802.83/297.04	     , eq(s(x), 0()) -> false()
802.83/297.04	     , eq(s(x), s(y)) -> eq(x, y)
802.83/297.04	     , if1(true(), x, y, xs) -> min(x, xs)
802.83/297.04	     , if1(false(), x, y, xs) -> min(y, xs)
802.83/297.04	     , min(x, cons(y, z)) -> if1(le(x, y), x, y, z)
802.83/297.04	     , min(x, nil()) -> x
802.83/297.04	     , if2(true(), x, y, xs) -> xs
802.83/297.04	     , if2(false(), x, y, xs) -> cons(y, del(x, xs))
802.83/297.04	     , del(x, cons(y, z)) -> if2(eq(x, y), x, y, z)
802.83/297.04	     , del(x, nil()) -> nil()
802.83/297.04	     , minsort(cons(x, y)) ->
802.83/297.04	       cons(min(x, y), minsort(del(min(x, y), cons(x, y))))
802.83/297.04	     , minsort(nil()) -> nil() }
802.83/297.04	   Weak DPs:
802.83/297.04	     { le^#(0(), y) -> c_1()
802.83/297.04	     , le^#(s(x), 0()) -> c_2()
802.83/297.04	     , eq^#(0(), 0()) -> c_4()
802.83/297.04	     , eq^#(0(), s(y)) -> c_5()
802.83/297.04	     , eq^#(s(x), 0()) -> c_6()
802.83/297.04	     , del^#(x, nil()) -> c_15()
802.83/297.04	     , minsort^#(nil()) -> c_17() }
802.83/297.04	   Obligation:
802.83/297.04	     runtime complexity
802.83/297.04	   Answer:
802.83/297.04	     MAYBE
802.83/297.04	   
802.83/297.04	   Empty strict component of the problem is NOT empty.
802.83/297.04	
802.83/297.04	
802.83/297.04	Arrrr..
803.06/297.27	EOF