MAYBE
698.40/297.04	MAYBE
698.40/297.04	
698.40/297.04	We are left with following problem, upon which TcT provides the
698.40/297.04	certificate MAYBE.
698.40/297.04	
698.40/297.04	Strict Trs:
698.40/297.04	  { eq(X, Y) -> false()
698.40/297.04	  , eq(n__0(), n__0()) -> true()
698.40/297.04	  , eq(n__s(X), n__s(Y)) -> eq(activate(X), activate(Y))
698.40/297.04	  , activate(X) -> X
698.40/297.04	  , activate(n__0()) -> 0()
698.40/297.04	  , activate(n__s(X)) -> s(X)
698.40/297.04	  , activate(n__inf(X)) -> inf(activate(X))
698.40/297.04	  , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
698.40/297.04	  , activate(n__length(X)) -> length(activate(X))
698.40/297.04	  , inf(X) -> cons(X, n__inf(n__s(X)))
698.40/297.04	  , inf(X) -> n__inf(X)
698.40/297.04	  , take(X1, X2) -> n__take(X1, X2)
698.40/297.04	  , take(0(), X) -> nil()
698.40/297.04	  , take(s(X), cons(Y, L)) ->
698.40/297.04	    cons(activate(Y), n__take(activate(X), activate(L)))
698.40/297.04	  , 0() -> n__0()
698.40/297.04	  , s(X) -> n__s(X)
698.40/297.04	  , length(X) -> n__length(X)
698.40/297.04	  , length(cons(X, L)) -> s(n__length(activate(L)))
698.40/297.04	  , length(nil()) -> 0() }
698.40/297.04	Obligation:
698.40/297.04	  runtime complexity
698.40/297.04	Answer:
698.40/297.04	  MAYBE
698.40/297.04	
698.40/297.04	None of the processors succeeded.
698.40/297.04	
698.40/297.04	Details of failed attempt(s):
698.40/297.04	-----------------------------
698.40/297.04	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
698.40/297.04	   following reason:
698.40/297.04	   
698.40/297.04	   Computation stopped due to timeout after 297.0 seconds.
698.40/297.04	
698.40/297.04	2) 'Best' failed due to the following reason:
698.40/297.04	   
698.40/297.04	   None of the processors succeeded.
698.40/297.04	   
698.40/297.04	   Details of failed attempt(s):
698.40/297.04	   -----------------------------
698.40/297.04	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
698.40/297.04	      seconds)' failed due to the following reason:
698.40/297.04	      
698.40/297.04	      None of the processors succeeded.
698.40/297.04	      
698.40/297.04	      Details of failed attempt(s):
698.40/297.04	      -----------------------------
698.40/297.04	      1) 'empty' failed due to the following reason:
698.40/297.04	         
698.40/297.04	         Empty strict component of the problem is NOT empty.
698.40/297.04	      
698.40/297.04	      2) 'With Problem ...' failed due to the following reason:
698.40/297.04	         
698.40/297.04	         None of the processors succeeded.
698.40/297.04	         
698.40/297.04	         Details of failed attempt(s):
698.40/297.04	         -----------------------------
698.40/297.04	         1) 'empty' failed due to the following reason:
698.40/297.04	            
698.40/297.04	            Empty strict component of the problem is NOT empty.
698.40/297.04	         
698.40/297.04	         2) 'Fastest' failed due to the following reason:
698.40/297.04	            
698.40/297.04	            None of the processors succeeded.
698.40/297.04	            
698.40/297.04	            Details of failed attempt(s):
698.40/297.04	            -----------------------------
698.40/297.04	            1) 'With Problem ...' failed due to the following reason:
698.40/297.04	               
698.40/297.04	               None of the processors succeeded.
698.40/297.04	               
698.40/297.04	               Details of failed attempt(s):
698.40/297.04	               -----------------------------
698.40/297.04	               1) 'empty' failed due to the following reason:
698.40/297.04	                  
698.40/297.04	                  Empty strict component of the problem is NOT empty.
698.40/297.04	               
698.40/297.04	               2) 'With Problem ...' failed due to the following reason:
698.40/297.04	                  
698.40/297.04	                  None of the processors succeeded.
698.40/297.04	                  
698.40/297.04	                  Details of failed attempt(s):
698.40/297.04	                  -----------------------------
698.40/297.04	                  1) 'empty' failed due to the following reason:
698.40/297.04	                     
698.40/297.04	                     Empty strict component of the problem is NOT empty.
698.40/297.04	                  
698.40/297.04	                  2) 'With Problem ...' failed due to the following reason:
698.40/297.04	                     
698.40/297.04	                     None of the processors succeeded.
698.40/297.04	                     
698.40/297.04	                     Details of failed attempt(s):
698.40/297.04	                     -----------------------------
698.40/297.04	                     1) 'empty' failed due to the following reason:
698.40/297.04	                        
698.40/297.04	                        Empty strict component of the problem is NOT empty.
698.40/297.04	                     
698.40/297.04	                     2) 'With Problem ...' failed due to the following reason:
698.40/297.04	                        
698.40/297.04	                        Empty strict component of the problem is NOT empty.
698.40/297.04	                     
698.40/297.04	                  
698.40/297.04	               
698.40/297.04	            
698.40/297.04	            2) 'With Problem ...' failed due to the following reason:
698.40/297.04	               
698.40/297.04	               None of the processors succeeded.
698.40/297.04	               
698.40/297.04	               Details of failed attempt(s):
698.40/297.04	               -----------------------------
698.40/297.04	               1) 'empty' failed due to the following reason:
698.40/297.04	                  
698.40/297.04	                  Empty strict component of the problem is NOT empty.
698.40/297.04	               
698.40/297.04	               2) 'With Problem ...' failed due to the following reason:
698.40/297.04	                  
698.40/297.04	                  Empty strict component of the problem is NOT empty.
698.40/297.04	               
698.40/297.04	            
698.40/297.04	         
698.40/297.04	      
698.40/297.04	   
698.40/297.04	   2) 'Best' failed due to the following reason:
698.40/297.04	      
698.40/297.04	      None of the processors succeeded.
698.40/297.04	      
698.40/297.04	      Details of failed attempt(s):
698.40/297.04	      -----------------------------
698.40/297.04	      1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
698.40/297.04	         to the following reason:
698.40/297.04	         
698.40/297.04	         The processor is inapplicable, reason:
698.40/297.04	           Processor only applicable for innermost runtime complexity analysis
698.40/297.04	      
698.40/297.04	      2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
698.40/297.04	         following reason:
698.40/297.04	         
698.40/297.04	         The processor is inapplicable, reason:
698.40/297.04	           Processor only applicable for innermost runtime complexity analysis
698.40/297.04	      
698.40/297.04	   
698.40/297.04	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
698.40/297.04	      failed due to the following reason:
698.40/297.04	      
698.40/297.04	      None of the processors succeeded.
698.40/297.04	      
698.40/297.04	      Details of failed attempt(s):
698.40/297.04	      -----------------------------
698.40/297.04	      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
698.40/297.04	         failed due to the following reason:
698.40/297.04	         
698.40/297.04	         match-boundness of the problem could not be verified.
698.40/297.04	      
698.40/297.04	      2) 'Bounds with minimal-enrichment and initial automaton 'match''
698.40/297.04	         failed due to the following reason:
698.40/297.04	         
698.40/297.04	         match-boundness of the problem could not be verified.
698.40/297.04	      
698.40/297.04	   
698.40/297.04	
698.40/297.04	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
698.40/297.04	   the following reason:
698.40/297.04	   
698.40/297.04	   We add the following weak dependency pairs:
698.40/297.04	   
698.40/297.04	   Strict DPs:
698.40/297.04	     { eq^#(X, Y) -> c_1()
698.40/297.04	     , eq^#(n__0(), n__0()) -> c_2()
698.40/297.04	     , eq^#(n__s(X), n__s(Y)) -> c_3(eq^#(activate(X), activate(Y)))
698.40/297.04	     , activate^#(X) -> c_4(X)
698.40/297.04	     , activate^#(n__0()) -> c_5(0^#())
698.40/297.04	     , activate^#(n__s(X)) -> c_6(s^#(X))
698.40/297.04	     , activate^#(n__inf(X)) -> c_7(inf^#(activate(X)))
698.40/297.04	     , activate^#(n__take(X1, X2)) ->
698.40/297.04	       c_8(take^#(activate(X1), activate(X2)))
698.40/297.04	     , activate^#(n__length(X)) -> c_9(length^#(activate(X)))
698.40/297.04	     , 0^#() -> c_15()
698.40/297.04	     , s^#(X) -> c_16(X)
698.40/297.04	     , inf^#(X) -> c_10(X, X)
698.40/297.04	     , inf^#(X) -> c_11(X)
698.40/297.04	     , take^#(X1, X2) -> c_12(X1, X2)
698.40/297.04	     , take^#(0(), X) -> c_13()
698.40/297.04	     , take^#(s(X), cons(Y, L)) ->
698.40/297.04	       c_14(activate^#(Y), activate^#(X), activate^#(L))
698.40/297.04	     , length^#(X) -> c_17(X)
698.40/297.04	     , length^#(cons(X, L)) -> c_18(s^#(n__length(activate(L))))
698.40/297.04	     , length^#(nil()) -> c_19(0^#()) }
698.40/297.04	   
698.40/297.04	   and mark the set of starting terms.
698.40/297.04	   
698.40/297.04	   We are left with following problem, upon which TcT provides the
698.40/297.04	   certificate MAYBE.
698.40/297.04	   
698.40/297.04	   Strict DPs:
698.40/297.04	     { eq^#(X, Y) -> c_1()
698.40/297.04	     , eq^#(n__0(), n__0()) -> c_2()
698.40/297.04	     , eq^#(n__s(X), n__s(Y)) -> c_3(eq^#(activate(X), activate(Y)))
698.40/297.04	     , activate^#(X) -> c_4(X)
698.40/297.04	     , activate^#(n__0()) -> c_5(0^#())
698.40/297.04	     , activate^#(n__s(X)) -> c_6(s^#(X))
698.40/297.04	     , activate^#(n__inf(X)) -> c_7(inf^#(activate(X)))
698.40/297.04	     , activate^#(n__take(X1, X2)) ->
698.40/297.04	       c_8(take^#(activate(X1), activate(X2)))
698.40/297.04	     , activate^#(n__length(X)) -> c_9(length^#(activate(X)))
698.40/297.04	     , 0^#() -> c_15()
698.40/297.04	     , s^#(X) -> c_16(X)
698.40/297.04	     , inf^#(X) -> c_10(X, X)
698.40/297.04	     , inf^#(X) -> c_11(X)
698.40/297.04	     , take^#(X1, X2) -> c_12(X1, X2)
698.40/297.04	     , take^#(0(), X) -> c_13()
698.40/297.04	     , take^#(s(X), cons(Y, L)) ->
698.40/297.04	       c_14(activate^#(Y), activate^#(X), activate^#(L))
698.40/297.04	     , length^#(X) -> c_17(X)
698.40/297.04	     , length^#(cons(X, L)) -> c_18(s^#(n__length(activate(L))))
698.40/297.04	     , length^#(nil()) -> c_19(0^#()) }
698.40/297.04	   Strict Trs:
698.40/297.04	     { eq(X, Y) -> false()
698.40/297.04	     , eq(n__0(), n__0()) -> true()
698.40/297.04	     , eq(n__s(X), n__s(Y)) -> eq(activate(X), activate(Y))
698.40/297.04	     , activate(X) -> X
698.40/297.04	     , activate(n__0()) -> 0()
698.40/297.04	     , activate(n__s(X)) -> s(X)
698.40/297.04	     , activate(n__inf(X)) -> inf(activate(X))
698.40/297.04	     , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
698.40/297.04	     , activate(n__length(X)) -> length(activate(X))
698.40/297.04	     , inf(X) -> cons(X, n__inf(n__s(X)))
698.40/297.04	     , inf(X) -> n__inf(X)
698.40/297.04	     , take(X1, X2) -> n__take(X1, X2)
698.40/297.04	     , take(0(), X) -> nil()
698.40/297.04	     , take(s(X), cons(Y, L)) ->
698.40/297.04	       cons(activate(Y), n__take(activate(X), activate(L)))
698.40/297.04	     , 0() -> n__0()
698.40/297.04	     , s(X) -> n__s(X)
698.40/297.04	     , length(X) -> n__length(X)
698.40/297.04	     , length(cons(X, L)) -> s(n__length(activate(L)))
698.40/297.04	     , length(nil()) -> 0() }
698.40/297.04	   Obligation:
698.40/297.04	     runtime complexity
698.40/297.04	   Answer:
698.40/297.04	     MAYBE
698.40/297.04	   
698.40/297.04	   We estimate the number of application of {1,2,10,15} by
698.40/297.04	   applications of Pre({1,2,10,15}) = {3,4,5,8,11,12,13,14,17,19}.
698.40/297.04	   Here rules are labeled as follows:
698.40/297.04	   
698.40/297.04	     DPs:
698.40/297.04	       { 1: eq^#(X, Y) -> c_1()
698.40/297.04	       , 2: eq^#(n__0(), n__0()) -> c_2()
698.40/297.04	       , 3: eq^#(n__s(X), n__s(Y)) -> c_3(eq^#(activate(X), activate(Y)))
698.40/297.04	       , 4: activate^#(X) -> c_4(X)
698.40/297.04	       , 5: activate^#(n__0()) -> c_5(0^#())
698.40/297.04	       , 6: activate^#(n__s(X)) -> c_6(s^#(X))
698.40/297.04	       , 7: activate^#(n__inf(X)) -> c_7(inf^#(activate(X)))
698.40/297.04	       , 8: activate^#(n__take(X1, X2)) ->
698.40/297.04	            c_8(take^#(activate(X1), activate(X2)))
698.40/297.04	       , 9: activate^#(n__length(X)) -> c_9(length^#(activate(X)))
698.40/297.04	       , 10: 0^#() -> c_15()
698.40/297.04	       , 11: s^#(X) -> c_16(X)
698.40/297.04	       , 12: inf^#(X) -> c_10(X, X)
698.40/297.04	       , 13: inf^#(X) -> c_11(X)
698.40/297.04	       , 14: take^#(X1, X2) -> c_12(X1, X2)
698.40/297.04	       , 15: take^#(0(), X) -> c_13()
698.40/297.04	       , 16: take^#(s(X), cons(Y, L)) ->
698.40/297.04	             c_14(activate^#(Y), activate^#(X), activate^#(L))
698.40/297.04	       , 17: length^#(X) -> c_17(X)
698.40/297.04	       , 18: length^#(cons(X, L)) -> c_18(s^#(n__length(activate(L))))
698.40/297.04	       , 19: length^#(nil()) -> c_19(0^#()) }
698.40/297.04	   
698.40/297.04	   We are left with following problem, upon which TcT provides the
698.40/297.04	   certificate MAYBE.
698.40/297.04	   
698.40/297.04	   Strict DPs:
698.40/297.04	     { eq^#(n__s(X), n__s(Y)) -> c_3(eq^#(activate(X), activate(Y)))
698.40/297.04	     , activate^#(X) -> c_4(X)
698.40/297.04	     , activate^#(n__0()) -> c_5(0^#())
698.40/297.04	     , activate^#(n__s(X)) -> c_6(s^#(X))
698.40/297.04	     , activate^#(n__inf(X)) -> c_7(inf^#(activate(X)))
698.40/297.04	     , activate^#(n__take(X1, X2)) ->
698.40/297.04	       c_8(take^#(activate(X1), activate(X2)))
698.40/297.04	     , activate^#(n__length(X)) -> c_9(length^#(activate(X)))
698.40/297.04	     , s^#(X) -> c_16(X)
698.40/297.04	     , inf^#(X) -> c_10(X, X)
698.40/297.04	     , inf^#(X) -> c_11(X)
698.40/297.04	     , take^#(X1, X2) -> c_12(X1, X2)
698.40/297.04	     , take^#(s(X), cons(Y, L)) ->
698.40/297.04	       c_14(activate^#(Y), activate^#(X), activate^#(L))
698.40/297.04	     , length^#(X) -> c_17(X)
698.40/297.04	     , length^#(cons(X, L)) -> c_18(s^#(n__length(activate(L))))
698.40/297.04	     , length^#(nil()) -> c_19(0^#()) }
698.40/297.04	   Strict Trs:
698.40/297.04	     { eq(X, Y) -> false()
698.40/297.04	     , eq(n__0(), n__0()) -> true()
698.40/297.04	     , eq(n__s(X), n__s(Y)) -> eq(activate(X), activate(Y))
698.40/297.04	     , activate(X) -> X
698.40/297.04	     , activate(n__0()) -> 0()
698.40/297.04	     , activate(n__s(X)) -> s(X)
698.40/297.04	     , activate(n__inf(X)) -> inf(activate(X))
698.40/297.04	     , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
698.40/297.04	     , activate(n__length(X)) -> length(activate(X))
698.40/297.04	     , inf(X) -> cons(X, n__inf(n__s(X)))
698.40/297.04	     , inf(X) -> n__inf(X)
698.40/297.04	     , take(X1, X2) -> n__take(X1, X2)
698.40/297.04	     , take(0(), X) -> nil()
698.40/297.04	     , take(s(X), cons(Y, L)) ->
698.40/297.04	       cons(activate(Y), n__take(activate(X), activate(L)))
698.40/297.04	     , 0() -> n__0()
698.40/297.04	     , s(X) -> n__s(X)
698.40/297.04	     , length(X) -> n__length(X)
698.40/297.04	     , length(cons(X, L)) -> s(n__length(activate(L)))
698.40/297.04	     , length(nil()) -> 0() }
698.40/297.04	   Weak DPs:
698.40/297.04	     { eq^#(X, Y) -> c_1()
698.40/297.04	     , eq^#(n__0(), n__0()) -> c_2()
698.40/297.04	     , 0^#() -> c_15()
698.40/297.04	     , take^#(0(), X) -> c_13() }
698.40/297.04	   Obligation:
698.40/297.04	     runtime complexity
698.40/297.04	   Answer:
698.40/297.04	     MAYBE
698.40/297.04	   
698.40/297.04	   We estimate the number of application of {3,15} by applications of
698.40/297.04	   Pre({3,15}) = {2,7,8,9,10,11,12,13}. Here rules are labeled as
698.40/297.04	   follows:
698.40/297.04	   
698.40/297.04	     DPs:
698.40/297.04	       { 1: eq^#(n__s(X), n__s(Y)) -> c_3(eq^#(activate(X), activate(Y)))
698.40/297.04	       , 2: activate^#(X) -> c_4(X)
698.40/297.04	       , 3: activate^#(n__0()) -> c_5(0^#())
698.40/297.04	       , 4: activate^#(n__s(X)) -> c_6(s^#(X))
698.40/297.04	       , 5: activate^#(n__inf(X)) -> c_7(inf^#(activate(X)))
698.40/297.04	       , 6: activate^#(n__take(X1, X2)) ->
698.40/297.04	            c_8(take^#(activate(X1), activate(X2)))
698.40/297.04	       , 7: activate^#(n__length(X)) -> c_9(length^#(activate(X)))
698.40/297.04	       , 8: s^#(X) -> c_16(X)
698.40/297.04	       , 9: inf^#(X) -> c_10(X, X)
698.40/297.04	       , 10: inf^#(X) -> c_11(X)
698.40/297.04	       , 11: take^#(X1, X2) -> c_12(X1, X2)
698.40/297.04	       , 12: take^#(s(X), cons(Y, L)) ->
698.40/297.04	             c_14(activate^#(Y), activate^#(X), activate^#(L))
698.40/297.04	       , 13: length^#(X) -> c_17(X)
698.40/297.04	       , 14: length^#(cons(X, L)) -> c_18(s^#(n__length(activate(L))))
698.40/297.04	       , 15: length^#(nil()) -> c_19(0^#())
698.40/297.04	       , 16: eq^#(X, Y) -> c_1()
698.40/297.04	       , 17: eq^#(n__0(), n__0()) -> c_2()
698.40/297.04	       , 18: 0^#() -> c_15()
698.40/297.04	       , 19: take^#(0(), X) -> c_13() }
698.40/297.04	   
698.40/297.04	   We are left with following problem, upon which TcT provides the
698.40/297.04	   certificate MAYBE.
698.40/297.04	   
698.40/297.04	   Strict DPs:
698.40/297.04	     { eq^#(n__s(X), n__s(Y)) -> c_3(eq^#(activate(X), activate(Y)))
698.40/297.04	     , activate^#(X) -> c_4(X)
698.40/297.04	     , activate^#(n__s(X)) -> c_6(s^#(X))
698.40/297.04	     , activate^#(n__inf(X)) -> c_7(inf^#(activate(X)))
698.40/297.04	     , activate^#(n__take(X1, X2)) ->
698.40/297.04	       c_8(take^#(activate(X1), activate(X2)))
698.40/297.04	     , activate^#(n__length(X)) -> c_9(length^#(activate(X)))
698.40/297.04	     , s^#(X) -> c_16(X)
698.40/297.04	     , inf^#(X) -> c_10(X, X)
698.40/297.04	     , inf^#(X) -> c_11(X)
698.40/297.04	     , take^#(X1, X2) -> c_12(X1, X2)
698.40/297.04	     , take^#(s(X), cons(Y, L)) ->
698.40/297.04	       c_14(activate^#(Y), activate^#(X), activate^#(L))
698.40/297.04	     , length^#(X) -> c_17(X)
698.40/297.04	     , length^#(cons(X, L)) -> c_18(s^#(n__length(activate(L)))) }
698.40/297.04	   Strict Trs:
698.40/297.04	     { eq(X, Y) -> false()
698.40/297.04	     , eq(n__0(), n__0()) -> true()
698.40/297.04	     , eq(n__s(X), n__s(Y)) -> eq(activate(X), activate(Y))
698.40/297.04	     , activate(X) -> X
698.40/297.04	     , activate(n__0()) -> 0()
698.40/297.04	     , activate(n__s(X)) -> s(X)
698.40/297.04	     , activate(n__inf(X)) -> inf(activate(X))
698.40/297.04	     , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
698.40/297.04	     , activate(n__length(X)) -> length(activate(X))
698.40/297.04	     , inf(X) -> cons(X, n__inf(n__s(X)))
698.40/297.04	     , inf(X) -> n__inf(X)
698.40/297.04	     , take(X1, X2) -> n__take(X1, X2)
698.40/297.04	     , take(0(), X) -> nil()
698.40/297.04	     , take(s(X), cons(Y, L)) ->
698.40/297.04	       cons(activate(Y), n__take(activate(X), activate(L)))
698.40/297.04	     , 0() -> n__0()
698.40/297.04	     , s(X) -> n__s(X)
698.40/297.04	     , length(X) -> n__length(X)
698.40/297.04	     , length(cons(X, L)) -> s(n__length(activate(L)))
698.40/297.04	     , length(nil()) -> 0() }
698.40/297.04	   Weak DPs:
698.40/297.04	     { eq^#(X, Y) -> c_1()
698.40/297.04	     , eq^#(n__0(), n__0()) -> c_2()
698.40/297.04	     , activate^#(n__0()) -> c_5(0^#())
698.40/297.04	     , 0^#() -> c_15()
698.40/297.04	     , take^#(0(), X) -> c_13()
698.40/297.04	     , length^#(nil()) -> c_19(0^#()) }
698.40/297.04	   Obligation:
698.40/297.04	     runtime complexity
698.40/297.04	   Answer:
698.40/297.04	     MAYBE
698.40/297.04	   
698.40/297.04	   Empty strict component of the problem is NOT empty.
698.40/297.04	
698.40/297.04	
698.40/297.04	Arrrr..
698.64/297.22	EOF