MAYBE
823.54/297.03	MAYBE
823.54/297.03	
823.54/297.03	We are left with following problem, upon which TcT provides the
823.54/297.03	certificate MAYBE.
823.54/297.03	
823.54/297.03	Strict Trs:
823.54/297.03	  { a(l, x, s(y), h()) -> a(l, x, y, s(h()))
823.54/297.03	  , a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z))
823.54/297.03	  , a(l, s(x), h(), z) -> a(l, x, z, z)
823.54/297.03	  , a(h(), h(), h(), x) -> s(x)
823.54/297.03	  , a(s(l), h(), h(), z) -> a(l, z, h(), z)
823.54/297.03	  , s(h()) -> 1()
823.54/297.03	  , +(x, h()) -> x
823.54/297.03	  , +(h(), x) -> x
823.54/297.03	  , +(s(x), s(y)) -> s(s(+(x, y)))
823.54/297.03	  , +(+(x, y), z) -> +(x, +(y, z))
823.54/297.03	  , app(l, nil()) -> l
823.54/297.03	  , app(nil(), k) -> k
823.54/297.03	  , app(cons(x, l), k) -> cons(x, app(l, k))
823.54/297.03	  , sum(cons(x, nil())) -> cons(x, nil())
823.54/297.03	  , sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h(), h()), l)) }
823.54/297.03	Obligation:
823.54/297.03	  runtime complexity
823.54/297.03	Answer:
823.54/297.03	  MAYBE
823.54/297.03	
823.54/297.03	None of the processors succeeded.
823.54/297.03	
823.54/297.03	Details of failed attempt(s):
823.54/297.03	-----------------------------
823.54/297.03	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
823.54/297.03	   following reason:
823.54/297.03	   
823.54/297.03	   Computation stopped due to timeout after 297.0 seconds.
823.54/297.03	
823.54/297.03	2) 'Best' failed due to the following reason:
823.54/297.03	   
823.54/297.03	   None of the processors succeeded.
823.54/297.03	   
823.54/297.03	   Details of failed attempt(s):
823.54/297.03	   -----------------------------
823.54/297.03	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
823.54/297.03	      seconds)' failed due to the following reason:
823.54/297.03	      
823.54/297.03	      Computation stopped due to timeout after 148.0 seconds.
823.54/297.03	   
823.54/297.03	   2) 'Best' failed due to the following reason:
823.54/297.03	      
823.54/297.03	      None of the processors succeeded.
823.54/297.03	      
823.54/297.03	      Details of failed attempt(s):
823.54/297.03	      -----------------------------
823.54/297.03	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
823.54/297.03	         following reason:
823.54/297.03	         
823.54/297.03	         The processor is inapplicable, reason:
823.54/297.03	           Processor only applicable for innermost runtime complexity analysis
823.54/297.03	      
823.54/297.03	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
823.54/297.03	         to the following reason:
823.54/297.03	         
823.54/297.03	         The processor is inapplicable, reason:
823.54/297.03	           Processor only applicable for innermost runtime complexity analysis
823.54/297.03	      
823.54/297.03	   
823.54/297.03	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
823.54/297.03	      failed due to the following reason:
823.54/297.03	      
823.54/297.03	      None of the processors succeeded.
823.54/297.03	      
823.54/297.03	      Details of failed attempt(s):
823.54/297.03	      -----------------------------
823.54/297.03	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
823.54/297.03	         failed due to the following reason:
823.54/297.03	         
823.54/297.03	         match-boundness of the problem could not be verified.
823.54/297.03	      
823.54/297.03	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
823.54/297.03	         failed due to the following reason:
823.54/297.03	         
823.54/297.03	         match-boundness of the problem could not be verified.
823.54/297.03	      
823.54/297.03	   
823.54/297.03	
823.54/297.03	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
823.54/297.03	   the following reason:
823.54/297.03	   
823.54/297.03	   We add the following weak dependency pairs:
823.54/297.03	   
823.54/297.03	   Strict DPs:
823.54/297.03	     { a^#(l, x, s(y), h()) -> c_1(a^#(l, x, y, s(h())))
823.54/297.03	     , a^#(l, x, s(y), s(z)) -> c_2(a^#(l, x, y, a(l, x, s(y), z)))
823.54/297.03	     , a^#(l, s(x), h(), z) -> c_3(a^#(l, x, z, z))
823.54/297.03	     , a^#(h(), h(), h(), x) -> c_4(s^#(x))
823.54/297.03	     , a^#(s(l), h(), h(), z) -> c_5(a^#(l, z, h(), z))
823.54/297.03	     , s^#(h()) -> c_6()
823.54/297.03	     , +^#(x, h()) -> c_7(x)
823.54/297.03	     , +^#(h(), x) -> c_8(x)
823.54/297.03	     , +^#(s(x), s(y)) -> c_9(s^#(s(+(x, y))))
823.54/297.03	     , +^#(+(x, y), z) -> c_10(+^#(x, +(y, z)))
823.54/297.03	     , app^#(l, nil()) -> c_11(l)
823.54/297.03	     , app^#(nil(), k) -> c_12(k)
823.54/297.03	     , app^#(cons(x, l), k) -> c_13(x, app^#(l, k))
823.54/297.03	     , sum^#(cons(x, nil())) -> c_14(x)
823.54/297.03	     , sum^#(cons(x, cons(y, l))) ->
823.54/297.03	       c_15(sum^#(cons(a(x, y, h(), h()), l))) }
823.54/297.03	   
823.54/297.03	   and mark the set of starting terms.
823.54/297.03	   
823.54/297.03	   We are left with following problem, upon which TcT provides the
823.54/297.03	   certificate MAYBE.
823.54/297.03	   
823.54/297.03	   Strict DPs:
823.54/297.03	     { a^#(l, x, s(y), h()) -> c_1(a^#(l, x, y, s(h())))
823.54/297.03	     , a^#(l, x, s(y), s(z)) -> c_2(a^#(l, x, y, a(l, x, s(y), z)))
823.54/297.03	     , a^#(l, s(x), h(), z) -> c_3(a^#(l, x, z, z))
823.54/297.03	     , a^#(h(), h(), h(), x) -> c_4(s^#(x))
823.54/297.03	     , a^#(s(l), h(), h(), z) -> c_5(a^#(l, z, h(), z))
823.54/297.03	     , s^#(h()) -> c_6()
823.54/297.03	     , +^#(x, h()) -> c_7(x)
823.54/297.03	     , +^#(h(), x) -> c_8(x)
823.54/297.03	     , +^#(s(x), s(y)) -> c_9(s^#(s(+(x, y))))
823.54/297.03	     , +^#(+(x, y), z) -> c_10(+^#(x, +(y, z)))
823.54/297.03	     , app^#(l, nil()) -> c_11(l)
823.54/297.03	     , app^#(nil(), k) -> c_12(k)
823.54/297.03	     , app^#(cons(x, l), k) -> c_13(x, app^#(l, k))
823.54/297.03	     , sum^#(cons(x, nil())) -> c_14(x)
823.54/297.03	     , sum^#(cons(x, cons(y, l))) ->
823.54/297.03	       c_15(sum^#(cons(a(x, y, h(), h()), l))) }
823.54/297.03	   Strict Trs:
823.54/297.03	     { a(l, x, s(y), h()) -> a(l, x, y, s(h()))
823.54/297.03	     , a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z))
823.54/297.03	     , a(l, s(x), h(), z) -> a(l, x, z, z)
823.54/297.03	     , a(h(), h(), h(), x) -> s(x)
823.54/297.03	     , a(s(l), h(), h(), z) -> a(l, z, h(), z)
823.54/297.03	     , s(h()) -> 1()
823.54/297.03	     , +(x, h()) -> x
823.54/297.03	     , +(h(), x) -> x
823.54/297.03	     , +(s(x), s(y)) -> s(s(+(x, y)))
823.54/297.03	     , +(+(x, y), z) -> +(x, +(y, z))
823.54/297.03	     , app(l, nil()) -> l
823.54/297.03	     , app(nil(), k) -> k
823.54/297.03	     , app(cons(x, l), k) -> cons(x, app(l, k))
823.54/297.03	     , sum(cons(x, nil())) -> cons(x, nil())
823.54/297.03	     , sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h(), h()), l)) }
823.54/297.03	   Obligation:
823.54/297.03	     runtime complexity
823.54/297.03	   Answer:
823.54/297.03	     MAYBE
823.54/297.03	   
823.54/297.03	   We estimate the number of application of {6} by applications of
823.54/297.03	   Pre({6}) = {4,7,8,9,11,12,13,14}. Here rules are labeled as
823.54/297.03	   follows:
823.54/297.03	   
823.54/297.03	     DPs:
823.54/297.03	       { 1: a^#(l, x, s(y), h()) -> c_1(a^#(l, x, y, s(h())))
823.54/297.03	       , 2: a^#(l, x, s(y), s(z)) -> c_2(a^#(l, x, y, a(l, x, s(y), z)))
823.54/297.03	       , 3: a^#(l, s(x), h(), z) -> c_3(a^#(l, x, z, z))
823.54/297.03	       , 4: a^#(h(), h(), h(), x) -> c_4(s^#(x))
823.54/297.03	       , 5: a^#(s(l), h(), h(), z) -> c_5(a^#(l, z, h(), z))
823.54/297.03	       , 6: s^#(h()) -> c_6()
823.54/297.03	       , 7: +^#(x, h()) -> c_7(x)
823.54/297.03	       , 8: +^#(h(), x) -> c_8(x)
823.54/297.03	       , 9: +^#(s(x), s(y)) -> c_9(s^#(s(+(x, y))))
823.54/297.03	       , 10: +^#(+(x, y), z) -> c_10(+^#(x, +(y, z)))
823.54/297.03	       , 11: app^#(l, nil()) -> c_11(l)
823.54/297.03	       , 12: app^#(nil(), k) -> c_12(k)
823.54/297.03	       , 13: app^#(cons(x, l), k) -> c_13(x, app^#(l, k))
823.54/297.03	       , 14: sum^#(cons(x, nil())) -> c_14(x)
823.54/297.03	       , 15: sum^#(cons(x, cons(y, l))) ->
823.54/297.03	             c_15(sum^#(cons(a(x, y, h(), h()), l))) }
823.54/297.03	   
823.54/297.03	   We are left with following problem, upon which TcT provides the
823.54/297.03	   certificate MAYBE.
823.54/297.03	   
823.54/297.03	   Strict DPs:
823.54/297.03	     { a^#(l, x, s(y), h()) -> c_1(a^#(l, x, y, s(h())))
823.54/297.03	     , a^#(l, x, s(y), s(z)) -> c_2(a^#(l, x, y, a(l, x, s(y), z)))
823.54/297.03	     , a^#(l, s(x), h(), z) -> c_3(a^#(l, x, z, z))
823.54/297.03	     , a^#(h(), h(), h(), x) -> c_4(s^#(x))
823.54/297.03	     , a^#(s(l), h(), h(), z) -> c_5(a^#(l, z, h(), z))
823.54/297.03	     , +^#(x, h()) -> c_7(x)
823.54/297.03	     , +^#(h(), x) -> c_8(x)
823.54/297.03	     , +^#(s(x), s(y)) -> c_9(s^#(s(+(x, y))))
823.54/297.03	     , +^#(+(x, y), z) -> c_10(+^#(x, +(y, z)))
823.54/297.03	     , app^#(l, nil()) -> c_11(l)
823.54/297.03	     , app^#(nil(), k) -> c_12(k)
823.54/297.03	     , app^#(cons(x, l), k) -> c_13(x, app^#(l, k))
823.54/297.03	     , sum^#(cons(x, nil())) -> c_14(x)
823.54/297.03	     , sum^#(cons(x, cons(y, l))) ->
823.54/297.03	       c_15(sum^#(cons(a(x, y, h(), h()), l))) }
823.54/297.03	   Strict Trs:
823.54/297.03	     { a(l, x, s(y), h()) -> a(l, x, y, s(h()))
823.54/297.03	     , a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z))
823.54/297.03	     , a(l, s(x), h(), z) -> a(l, x, z, z)
823.54/297.03	     , a(h(), h(), h(), x) -> s(x)
823.54/297.03	     , a(s(l), h(), h(), z) -> a(l, z, h(), z)
823.54/297.03	     , s(h()) -> 1()
823.54/297.03	     , +(x, h()) -> x
823.54/297.03	     , +(h(), x) -> x
823.54/297.03	     , +(s(x), s(y)) -> s(s(+(x, y)))
823.54/297.03	     , +(+(x, y), z) -> +(x, +(y, z))
823.54/297.03	     , app(l, nil()) -> l
823.54/297.03	     , app(nil(), k) -> k
823.54/297.03	     , app(cons(x, l), k) -> cons(x, app(l, k))
823.54/297.03	     , sum(cons(x, nil())) -> cons(x, nil())
823.54/297.03	     , sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h(), h()), l)) }
823.54/297.03	   Weak DPs: { s^#(h()) -> c_6() }
823.54/297.03	   Obligation:
823.54/297.03	     runtime complexity
823.54/297.03	   Answer:
823.54/297.03	     MAYBE
823.54/297.03	   
823.54/297.03	   We estimate the number of application of {4,8} by applications of
823.54/297.03	   Pre({4,8}) = {1,2,3,5,6,7,9,10,11,12,13}. Here rules are labeled as
823.54/297.03	   follows:
823.54/297.03	   
823.54/297.03	     DPs:
823.54/297.03	       { 1: a^#(l, x, s(y), h()) -> c_1(a^#(l, x, y, s(h())))
823.54/297.03	       , 2: a^#(l, x, s(y), s(z)) -> c_2(a^#(l, x, y, a(l, x, s(y), z)))
823.54/297.03	       , 3: a^#(l, s(x), h(), z) -> c_3(a^#(l, x, z, z))
823.54/297.03	       , 4: a^#(h(), h(), h(), x) -> c_4(s^#(x))
823.54/297.03	       , 5: a^#(s(l), h(), h(), z) -> c_5(a^#(l, z, h(), z))
823.54/297.03	       , 6: +^#(x, h()) -> c_7(x)
823.54/297.03	       , 7: +^#(h(), x) -> c_8(x)
823.54/297.03	       , 8: +^#(s(x), s(y)) -> c_9(s^#(s(+(x, y))))
823.54/297.03	       , 9: +^#(+(x, y), z) -> c_10(+^#(x, +(y, z)))
823.54/297.03	       , 10: app^#(l, nil()) -> c_11(l)
823.54/297.03	       , 11: app^#(nil(), k) -> c_12(k)
823.54/297.03	       , 12: app^#(cons(x, l), k) -> c_13(x, app^#(l, k))
823.54/297.03	       , 13: sum^#(cons(x, nil())) -> c_14(x)
823.54/297.03	       , 14: sum^#(cons(x, cons(y, l))) ->
823.54/297.03	             c_15(sum^#(cons(a(x, y, h(), h()), l)))
823.54/297.03	       , 15: s^#(h()) -> c_6() }
823.54/297.03	   
823.54/297.03	   We are left with following problem, upon which TcT provides the
823.54/297.03	   certificate MAYBE.
823.54/297.03	   
823.54/297.03	   Strict DPs:
823.54/297.03	     { a^#(l, x, s(y), h()) -> c_1(a^#(l, x, y, s(h())))
823.54/297.03	     , a^#(l, x, s(y), s(z)) -> c_2(a^#(l, x, y, a(l, x, s(y), z)))
823.54/297.03	     , a^#(l, s(x), h(), z) -> c_3(a^#(l, x, z, z))
823.54/297.03	     , a^#(s(l), h(), h(), z) -> c_5(a^#(l, z, h(), z))
823.54/297.03	     , +^#(x, h()) -> c_7(x)
823.54/297.03	     , +^#(h(), x) -> c_8(x)
823.54/297.03	     , +^#(+(x, y), z) -> c_10(+^#(x, +(y, z)))
823.54/297.03	     , app^#(l, nil()) -> c_11(l)
823.54/297.03	     , app^#(nil(), k) -> c_12(k)
823.54/297.03	     , app^#(cons(x, l), k) -> c_13(x, app^#(l, k))
823.54/297.03	     , sum^#(cons(x, nil())) -> c_14(x)
823.54/297.03	     , sum^#(cons(x, cons(y, l))) ->
823.54/297.03	       c_15(sum^#(cons(a(x, y, h(), h()), l))) }
823.54/297.03	   Strict Trs:
823.54/297.03	     { a(l, x, s(y), h()) -> a(l, x, y, s(h()))
823.54/297.03	     , a(l, x, s(y), s(z)) -> a(l, x, y, a(l, x, s(y), z))
823.54/297.03	     , a(l, s(x), h(), z) -> a(l, x, z, z)
823.54/297.03	     , a(h(), h(), h(), x) -> s(x)
823.54/297.03	     , a(s(l), h(), h(), z) -> a(l, z, h(), z)
823.54/297.03	     , s(h()) -> 1()
823.54/297.03	     , +(x, h()) -> x
823.54/297.03	     , +(h(), x) -> x
823.54/297.03	     , +(s(x), s(y)) -> s(s(+(x, y)))
823.54/297.03	     , +(+(x, y), z) -> +(x, +(y, z))
823.54/297.03	     , app(l, nil()) -> l
823.54/297.03	     , app(nil(), k) -> k
823.54/297.03	     , app(cons(x, l), k) -> cons(x, app(l, k))
823.54/297.03	     , sum(cons(x, nil())) -> cons(x, nil())
823.54/297.03	     , sum(cons(x, cons(y, l))) -> sum(cons(a(x, y, h(), h()), l)) }
823.54/297.03	   Weak DPs:
823.54/297.03	     { a^#(h(), h(), h(), x) -> c_4(s^#(x))
823.54/297.03	     , s^#(h()) -> c_6()
823.54/297.03	     , +^#(s(x), s(y)) -> c_9(s^#(s(+(x, y)))) }
823.54/297.03	   Obligation:
823.54/297.03	     runtime complexity
823.54/297.03	   Answer:
823.54/297.03	     MAYBE
823.54/297.03	   
823.54/297.03	   Empty strict component of the problem is NOT empty.
823.54/297.03	
823.54/297.03	
823.54/297.03	Arrrr..
823.76/297.21	EOF