MAYBE
822.85/297.04	MAYBE
822.85/297.04	
822.85/297.04	We are left with following problem, upon which TcT provides the
822.85/297.04	certificate MAYBE.
822.85/297.04	
822.85/297.04	Strict Trs:
822.85/297.04	  { eq(0(), 0()) -> true()
822.85/297.04	  , eq(0(), s(Y)) -> false()
822.85/297.04	  , eq(s(X), 0()) -> false()
822.85/297.04	  , eq(s(X), s(Y)) -> eq(X, Y)
822.85/297.04	  , le(0(), Y) -> true()
822.85/297.04	  , le(s(X), 0()) -> false()
822.85/297.04	  , le(s(X), s(Y)) -> le(X, Y)
822.85/297.04	  , min(cons(N, cons(M, L))) -> ifmin(le(N, M), cons(N, cons(M, L)))
822.85/297.04	  , min(cons(0(), nil())) -> 0()
822.85/297.04	  , min(cons(s(N), nil())) -> s(N)
822.85/297.04	  , ifmin(true(), cons(N, cons(M, L))) -> min(cons(N, L))
822.85/297.04	  , ifmin(false(), cons(N, cons(M, L))) -> min(cons(M, L))
822.85/297.04	  , replace(N, M, cons(K, L)) -> ifrepl(eq(N, K), N, M, cons(K, L))
822.85/297.04	  , replace(N, M, nil()) -> nil()
822.85/297.04	  , ifrepl(true(), N, M, cons(K, L)) -> cons(M, L)
822.85/297.04	  , ifrepl(false(), N, M, cons(K, L)) -> cons(K, replace(N, M, L))
822.85/297.04	  , selsort(cons(N, L)) ->
822.85/297.04	    ifselsort(eq(N, min(cons(N, L))), cons(N, L))
822.85/297.04	  , selsort(nil()) -> nil()
822.85/297.04	  , ifselsort(true(), cons(N, L)) -> cons(N, selsort(L))
822.85/297.04	  , ifselsort(false(), cons(N, L)) ->
822.85/297.04	    cons(min(cons(N, L)), selsort(replace(min(cons(N, L)), N, L))) }
822.85/297.04	Obligation:
822.85/297.04	  runtime complexity
822.85/297.04	Answer:
822.85/297.04	  MAYBE
822.85/297.04	
822.85/297.04	None of the processors succeeded.
822.85/297.04	
822.85/297.04	Details of failed attempt(s):
822.85/297.04	-----------------------------
822.85/297.04	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
822.85/297.04	   following reason:
822.85/297.04	   
822.85/297.04	   Computation stopped due to timeout after 297.0 seconds.
822.85/297.04	
822.85/297.04	2) 'Best' failed due to the following reason:
822.85/297.04	   
822.85/297.04	   None of the processors succeeded.
822.85/297.04	   
822.85/297.04	   Details of failed attempt(s):
822.85/297.04	   -----------------------------
822.85/297.04	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
822.85/297.04	      seconds)' failed due to the following reason:
822.85/297.04	      
822.85/297.04	      Computation stopped due to timeout after 148.0 seconds.
822.85/297.04	   
822.85/297.04	   2) 'Best' failed due to the following reason:
822.85/297.04	      
822.85/297.04	      None of the processors succeeded.
822.85/297.04	      
822.85/297.04	      Details of failed attempt(s):
822.85/297.04	      -----------------------------
822.85/297.04	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
822.85/297.04	         following reason:
822.85/297.04	         
822.85/297.04	         The processor is inapplicable, reason:
822.85/297.04	           Processor only applicable for innermost runtime complexity analysis
822.85/297.04	      
822.85/297.04	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
822.85/297.04	         to the following reason:
822.85/297.04	         
822.85/297.04	         The processor is inapplicable, reason:
822.85/297.04	           Processor only applicable for innermost runtime complexity analysis
822.85/297.04	      
822.85/297.04	   
822.85/297.04	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
822.85/297.04	      failed due to the following reason:
822.85/297.04	      
822.85/297.04	      None of the processors succeeded.
822.85/297.04	      
822.85/297.04	      Details of failed attempt(s):
822.85/297.04	      -----------------------------
822.85/297.04	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
822.85/297.04	         failed due to the following reason:
822.85/297.04	         
822.85/297.04	         match-boundness of the problem could not be verified.
822.85/297.04	      
822.85/297.04	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
822.85/297.04	         failed due to the following reason:
822.85/297.04	         
822.85/297.04	         match-boundness of the problem could not be verified.
822.85/297.04	      
822.85/297.04	   
822.85/297.04	
822.85/297.04	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
822.85/297.04	   the following reason:
822.85/297.04	   
822.85/297.04	   We add the following weak dependency pairs:
822.85/297.04	   
822.85/297.04	   Strict DPs:
822.85/297.04	     { eq^#(0(), 0()) -> c_1()
822.85/297.04	     , eq^#(0(), s(Y)) -> c_2()
822.85/297.04	     , eq^#(s(X), 0()) -> c_3()
822.85/297.04	     , eq^#(s(X), s(Y)) -> c_4(eq^#(X, Y))
822.85/297.04	     , le^#(0(), Y) -> c_5()
822.85/297.04	     , le^#(s(X), 0()) -> c_6()
822.85/297.04	     , le^#(s(X), s(Y)) -> c_7(le^#(X, Y))
822.85/297.04	     , min^#(cons(N, cons(M, L))) ->
822.85/297.04	       c_8(ifmin^#(le(N, M), cons(N, cons(M, L))))
822.85/297.04	     , min^#(cons(0(), nil())) -> c_9()
822.85/297.04	     , min^#(cons(s(N), nil())) -> c_10(N)
822.85/297.04	     , ifmin^#(true(), cons(N, cons(M, L))) -> c_11(min^#(cons(N, L)))
822.85/297.04	     , ifmin^#(false(), cons(N, cons(M, L))) -> c_12(min^#(cons(M, L)))
822.85/297.04	     , replace^#(N, M, cons(K, L)) ->
822.85/297.04	       c_13(ifrepl^#(eq(N, K), N, M, cons(K, L)))
822.85/297.04	     , replace^#(N, M, nil()) -> c_14()
822.85/297.04	     , ifrepl^#(true(), N, M, cons(K, L)) -> c_15(M, L)
822.85/297.04	     , ifrepl^#(false(), N, M, cons(K, L)) ->
822.85/297.04	       c_16(K, replace^#(N, M, L))
822.85/297.04	     , selsort^#(cons(N, L)) ->
822.85/297.04	       c_17(ifselsort^#(eq(N, min(cons(N, L))), cons(N, L)))
822.85/297.04	     , selsort^#(nil()) -> c_18()
822.85/297.04	     , ifselsort^#(true(), cons(N, L)) -> c_19(N, selsort^#(L))
822.85/297.04	     , ifselsort^#(false(), cons(N, L)) ->
822.85/297.04	       c_20(min^#(cons(N, L)),
822.85/297.04	            selsort^#(replace(min(cons(N, L)), N, L))) }
822.85/297.04	   
822.85/297.04	   and mark the set of starting terms.
822.85/297.04	   
822.85/297.04	   We are left with following problem, upon which TcT provides the
822.85/297.04	   certificate MAYBE.
822.85/297.04	   
822.85/297.04	   Strict DPs:
822.85/297.04	     { eq^#(0(), 0()) -> c_1()
822.85/297.04	     , eq^#(0(), s(Y)) -> c_2()
822.85/297.04	     , eq^#(s(X), 0()) -> c_3()
822.85/297.04	     , eq^#(s(X), s(Y)) -> c_4(eq^#(X, Y))
822.85/297.04	     , le^#(0(), Y) -> c_5()
822.85/297.04	     , le^#(s(X), 0()) -> c_6()
822.85/297.04	     , le^#(s(X), s(Y)) -> c_7(le^#(X, Y))
822.85/297.04	     , min^#(cons(N, cons(M, L))) ->
822.85/297.04	       c_8(ifmin^#(le(N, M), cons(N, cons(M, L))))
822.85/297.04	     , min^#(cons(0(), nil())) -> c_9()
822.85/297.04	     , min^#(cons(s(N), nil())) -> c_10(N)
822.85/297.04	     , ifmin^#(true(), cons(N, cons(M, L))) -> c_11(min^#(cons(N, L)))
822.85/297.04	     , ifmin^#(false(), cons(N, cons(M, L))) -> c_12(min^#(cons(M, L)))
822.85/297.04	     , replace^#(N, M, cons(K, L)) ->
822.85/297.04	       c_13(ifrepl^#(eq(N, K), N, M, cons(K, L)))
822.85/297.04	     , replace^#(N, M, nil()) -> c_14()
822.85/297.04	     , ifrepl^#(true(), N, M, cons(K, L)) -> c_15(M, L)
822.85/297.04	     , ifrepl^#(false(), N, M, cons(K, L)) ->
822.85/297.04	       c_16(K, replace^#(N, M, L))
822.85/297.04	     , selsort^#(cons(N, L)) ->
822.85/297.04	       c_17(ifselsort^#(eq(N, min(cons(N, L))), cons(N, L)))
822.85/297.04	     , selsort^#(nil()) -> c_18()
822.85/297.04	     , ifselsort^#(true(), cons(N, L)) -> c_19(N, selsort^#(L))
822.85/297.04	     , ifselsort^#(false(), cons(N, L)) ->
822.85/297.04	       c_20(min^#(cons(N, L)),
822.85/297.04	            selsort^#(replace(min(cons(N, L)), N, L))) }
822.85/297.04	   Strict Trs:
822.85/297.04	     { eq(0(), 0()) -> true()
822.85/297.04	     , eq(0(), s(Y)) -> false()
822.85/297.04	     , eq(s(X), 0()) -> false()
822.85/297.04	     , eq(s(X), s(Y)) -> eq(X, Y)
822.85/297.04	     , le(0(), Y) -> true()
822.85/297.04	     , le(s(X), 0()) -> false()
822.85/297.04	     , le(s(X), s(Y)) -> le(X, Y)
822.85/297.04	     , min(cons(N, cons(M, L))) -> ifmin(le(N, M), cons(N, cons(M, L)))
822.85/297.04	     , min(cons(0(), nil())) -> 0()
822.85/297.04	     , min(cons(s(N), nil())) -> s(N)
822.85/297.04	     , ifmin(true(), cons(N, cons(M, L))) -> min(cons(N, L))
822.85/297.04	     , ifmin(false(), cons(N, cons(M, L))) -> min(cons(M, L))
822.85/297.04	     , replace(N, M, cons(K, L)) -> ifrepl(eq(N, K), N, M, cons(K, L))
822.85/297.04	     , replace(N, M, nil()) -> nil()
822.85/297.04	     , ifrepl(true(), N, M, cons(K, L)) -> cons(M, L)
822.85/297.04	     , ifrepl(false(), N, M, cons(K, L)) -> cons(K, replace(N, M, L))
822.85/297.04	     , selsort(cons(N, L)) ->
822.85/297.04	       ifselsort(eq(N, min(cons(N, L))), cons(N, L))
822.85/297.04	     , selsort(nil()) -> nil()
822.85/297.04	     , ifselsort(true(), cons(N, L)) -> cons(N, selsort(L))
822.85/297.04	     , ifselsort(false(), cons(N, L)) ->
822.85/297.04	       cons(min(cons(N, L)), selsort(replace(min(cons(N, L)), N, L))) }
822.85/297.04	   Obligation:
822.85/297.04	     runtime complexity
822.85/297.04	   Answer:
822.85/297.04	     MAYBE
822.85/297.04	   
822.85/297.04	   We estimate the number of application of {1,2,3,5,6,9,14,18} by
822.85/297.04	   applications of Pre({1,2,3,5,6,9,14,18}) =
822.85/297.04	   {4,7,10,11,12,15,16,19,20}. Here rules are labeled as follows:
822.85/297.04	   
822.85/297.04	     DPs:
822.85/297.04	       { 1: eq^#(0(), 0()) -> c_1()
822.85/297.04	       , 2: eq^#(0(), s(Y)) -> c_2()
822.85/297.04	       , 3: eq^#(s(X), 0()) -> c_3()
822.85/297.04	       , 4: eq^#(s(X), s(Y)) -> c_4(eq^#(X, Y))
822.85/297.04	       , 5: le^#(0(), Y) -> c_5()
822.85/297.04	       , 6: le^#(s(X), 0()) -> c_6()
822.85/297.04	       , 7: le^#(s(X), s(Y)) -> c_7(le^#(X, Y))
822.85/297.04	       , 8: min^#(cons(N, cons(M, L))) ->
822.85/297.04	            c_8(ifmin^#(le(N, M), cons(N, cons(M, L))))
822.85/297.04	       , 9: min^#(cons(0(), nil())) -> c_9()
822.85/297.04	       , 10: min^#(cons(s(N), nil())) -> c_10(N)
822.85/297.04	       , 11: ifmin^#(true(), cons(N, cons(M, L))) ->
822.85/297.04	             c_11(min^#(cons(N, L)))
822.85/297.04	       , 12: ifmin^#(false(), cons(N, cons(M, L))) ->
822.85/297.04	             c_12(min^#(cons(M, L)))
822.85/297.04	       , 13: replace^#(N, M, cons(K, L)) ->
822.85/297.04	             c_13(ifrepl^#(eq(N, K), N, M, cons(K, L)))
822.85/297.04	       , 14: replace^#(N, M, nil()) -> c_14()
822.85/297.04	       , 15: ifrepl^#(true(), N, M, cons(K, L)) -> c_15(M, L)
822.85/297.04	       , 16: ifrepl^#(false(), N, M, cons(K, L)) ->
822.85/297.04	             c_16(K, replace^#(N, M, L))
822.85/297.04	       , 17: selsort^#(cons(N, L)) ->
822.85/297.04	             c_17(ifselsort^#(eq(N, min(cons(N, L))), cons(N, L)))
822.85/297.04	       , 18: selsort^#(nil()) -> c_18()
822.85/297.04	       , 19: ifselsort^#(true(), cons(N, L)) -> c_19(N, selsort^#(L))
822.85/297.04	       , 20: ifselsort^#(false(), cons(N, L)) ->
822.85/297.04	             c_20(min^#(cons(N, L)),
822.85/297.04	                  selsort^#(replace(min(cons(N, L)), N, L))) }
822.85/297.04	   
822.85/297.04	   We are left with following problem, upon which TcT provides the
822.85/297.04	   certificate MAYBE.
822.85/297.04	   
822.85/297.04	   Strict DPs:
822.85/297.04	     { eq^#(s(X), s(Y)) -> c_4(eq^#(X, Y))
822.85/297.04	     , le^#(s(X), s(Y)) -> c_7(le^#(X, Y))
822.85/297.04	     , min^#(cons(N, cons(M, L))) ->
822.85/297.04	       c_8(ifmin^#(le(N, M), cons(N, cons(M, L))))
822.85/297.04	     , min^#(cons(s(N), nil())) -> c_10(N)
822.85/297.04	     , ifmin^#(true(), cons(N, cons(M, L))) -> c_11(min^#(cons(N, L)))
822.85/297.04	     , ifmin^#(false(), cons(N, cons(M, L))) -> c_12(min^#(cons(M, L)))
822.85/297.04	     , replace^#(N, M, cons(K, L)) ->
822.85/297.04	       c_13(ifrepl^#(eq(N, K), N, M, cons(K, L)))
822.85/297.04	     , ifrepl^#(true(), N, M, cons(K, L)) -> c_15(M, L)
822.85/297.04	     , ifrepl^#(false(), N, M, cons(K, L)) ->
822.85/297.04	       c_16(K, replace^#(N, M, L))
822.85/297.04	     , selsort^#(cons(N, L)) ->
822.85/297.04	       c_17(ifselsort^#(eq(N, min(cons(N, L))), cons(N, L)))
822.85/297.04	     , ifselsort^#(true(), cons(N, L)) -> c_19(N, selsort^#(L))
822.85/297.04	     , ifselsort^#(false(), cons(N, L)) ->
822.85/297.04	       c_20(min^#(cons(N, L)),
822.85/297.04	            selsort^#(replace(min(cons(N, L)), N, L))) }
822.85/297.04	   Strict Trs:
822.85/297.04	     { eq(0(), 0()) -> true()
822.85/297.04	     , eq(0(), s(Y)) -> false()
822.85/297.04	     , eq(s(X), 0()) -> false()
822.85/297.04	     , eq(s(X), s(Y)) -> eq(X, Y)
822.85/297.04	     , le(0(), Y) -> true()
822.85/297.04	     , le(s(X), 0()) -> false()
822.85/297.04	     , le(s(X), s(Y)) -> le(X, Y)
822.85/297.04	     , min(cons(N, cons(M, L))) -> ifmin(le(N, M), cons(N, cons(M, L)))
822.85/297.04	     , min(cons(0(), nil())) -> 0()
822.85/297.04	     , min(cons(s(N), nil())) -> s(N)
822.85/297.04	     , ifmin(true(), cons(N, cons(M, L))) -> min(cons(N, L))
822.85/297.04	     , ifmin(false(), cons(N, cons(M, L))) -> min(cons(M, L))
822.85/297.04	     , replace(N, M, cons(K, L)) -> ifrepl(eq(N, K), N, M, cons(K, L))
822.85/297.04	     , replace(N, M, nil()) -> nil()
822.85/297.04	     , ifrepl(true(), N, M, cons(K, L)) -> cons(M, L)
822.85/297.04	     , ifrepl(false(), N, M, cons(K, L)) -> cons(K, replace(N, M, L))
822.85/297.04	     , selsort(cons(N, L)) ->
822.85/297.04	       ifselsort(eq(N, min(cons(N, L))), cons(N, L))
822.85/297.04	     , selsort(nil()) -> nil()
822.85/297.04	     , ifselsort(true(), cons(N, L)) -> cons(N, selsort(L))
822.85/297.04	     , ifselsort(false(), cons(N, L)) ->
822.85/297.04	       cons(min(cons(N, L)), selsort(replace(min(cons(N, L)), N, L))) }
822.85/297.04	   Weak DPs:
822.85/297.04	     { eq^#(0(), 0()) -> c_1()
822.85/297.04	     , eq^#(0(), s(Y)) -> c_2()
822.85/297.04	     , eq^#(s(X), 0()) -> c_3()
822.85/297.04	     , le^#(0(), Y) -> c_5()
822.85/297.04	     , le^#(s(X), 0()) -> c_6()
822.85/297.04	     , min^#(cons(0(), nil())) -> c_9()
822.85/297.04	     , replace^#(N, M, nil()) -> c_14()
822.85/297.04	     , selsort^#(nil()) -> c_18() }
822.85/297.04	   Obligation:
822.85/297.04	     runtime complexity
822.85/297.04	   Answer:
822.85/297.04	     MAYBE
822.85/297.04	   
822.85/297.04	   Empty strict component of the problem is NOT empty.
822.85/297.04	
822.85/297.04	
822.85/297.04	Arrrr..
823.07/297.21	EOF