MAYBE
1082.21/297.03	MAYBE
1082.21/297.03	
1082.21/297.03	We are left with following problem, upon which TcT provides the
1082.21/297.03	certificate MAYBE.
1082.21/297.03	
1082.21/297.03	Strict Trs:
1082.21/297.03	  { active(eq(X, Y)) -> mark(false())
1082.21/297.03	  , active(eq(0(), 0())) -> mark(true())
1082.21/297.03	  , active(eq(s(X), s(Y))) -> mark(eq(X, Y))
1082.21/297.03	  , active(inf(X)) -> mark(cons(X, inf(s(X))))
1082.21/297.03	  , active(inf(X)) -> inf(active(X))
1082.21/297.03	  , active(take(X1, X2)) -> take(X1, active(X2))
1082.21/297.03	  , active(take(X1, X2)) -> take(active(X1), X2)
1082.21/297.03	  , active(take(0(), X)) -> mark(nil())
1082.21/297.03	  , active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L)))
1082.21/297.03	  , active(length(X)) -> length(active(X))
1082.21/297.03	  , active(length(cons(X, L))) -> mark(s(length(L)))
1082.21/297.03	  , active(length(nil())) -> mark(0())
1082.21/297.03	  , eq(ok(X1), ok(X2)) -> ok(eq(X1, X2))
1082.21/297.03	  , s(ok(X)) -> ok(s(X))
1082.21/297.03	  , inf(mark(X)) -> mark(inf(X))
1082.21/297.03	  , inf(ok(X)) -> ok(inf(X))
1082.21/297.03	  , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
1082.21/297.03	  , take(X1, mark(X2)) -> mark(take(X1, X2))
1082.21/297.03	  , take(mark(X1), X2) -> mark(take(X1, X2))
1082.21/297.03	  , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
1082.21/297.03	  , length(mark(X)) -> mark(length(X))
1082.21/297.03	  , length(ok(X)) -> ok(length(X))
1082.21/297.03	  , proper(eq(X1, X2)) -> eq(proper(X1), proper(X2))
1082.21/297.03	  , proper(0()) -> ok(0())
1082.21/297.03	  , proper(true()) -> ok(true())
1082.21/297.03	  , proper(s(X)) -> s(proper(X))
1082.21/297.03	  , proper(false()) -> ok(false())
1082.21/297.03	  , proper(inf(X)) -> inf(proper(X))
1082.21/297.03	  , proper(cons(any(X1), X2)) ->
1082.21/297.03	    cons(any(any(proper(X1))), any(proper(X2)))
1082.21/297.03	  , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
1082.21/297.03	  , proper(nil()) -> ok(nil())
1082.21/297.03	  , proper(length(X)) -> length(proper(X))
1082.21/297.03	  , any(X) -> s(X)
1082.21/297.03	  , any(proper(X)) -> any(any(any(X)))
1082.21/297.03	  , top(mark(X)) -> top(proper(X))
1082.21/297.03	  , top(ok(X)) -> top(active(X)) }
1082.21/297.03	Obligation:
1082.21/297.03	  runtime complexity
1082.21/297.03	Answer:
1082.21/297.03	  MAYBE
1082.21/297.03	
1082.21/297.03	None of the processors succeeded.
1082.21/297.03	
1082.21/297.03	Details of failed attempt(s):
1082.21/297.03	-----------------------------
1082.21/297.03	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
1082.21/297.03	   following reason:
1082.21/297.03	   
1082.21/297.03	   Computation stopped due to timeout after 297.0 seconds.
1082.21/297.03	
1082.21/297.03	2) 'Best' failed due to the following reason:
1082.21/297.03	   
1082.21/297.03	   None of the processors succeeded.
1082.21/297.03	   
1082.21/297.03	   Details of failed attempt(s):
1082.21/297.03	   -----------------------------
1082.21/297.03	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
1082.21/297.03	      seconds)' failed due to the following reason:
1082.21/297.03	      
1082.21/297.03	      Computation stopped due to timeout after 148.0 seconds.
1082.21/297.03	   
1082.21/297.03	   2) 'Best' failed due to the following reason:
1082.21/297.03	      
1082.21/297.03	      None of the processors succeeded.
1082.21/297.03	      
1082.21/297.03	      Details of failed attempt(s):
1082.21/297.03	      -----------------------------
1082.21/297.03	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
1082.21/297.03	         following reason:
1082.21/297.03	         
1082.21/297.03	         The processor is inapplicable, reason:
1082.21/297.03	           Processor only applicable for innermost runtime complexity analysis
1082.21/297.03	      
1082.21/297.03	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
1082.21/297.03	         to the following reason:
1082.21/297.03	         
1082.21/297.03	         The processor is inapplicable, reason:
1082.21/297.03	           Processor only applicable for innermost runtime complexity analysis
1082.21/297.03	      
1082.21/297.03	   
1082.21/297.03	   3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
1082.21/297.03	      failed due to the following reason:
1082.21/297.03	      
1082.21/297.03	      None of the processors succeeded.
1082.21/297.03	      
1082.21/297.03	      Details of failed attempt(s):
1082.21/297.03	      -----------------------------
1082.21/297.03	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
1082.21/297.03	         failed due to the following reason:
1082.21/297.03	         
1082.21/297.03	         match-boundness of the problem could not be verified.
1082.21/297.03	      
1082.21/297.03	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
1082.21/297.03	         failed due to the following reason:
1082.21/297.03	         
1082.21/297.03	         match-boundness of the problem could not be verified.
1082.21/297.03	      
1082.21/297.03	   
1082.21/297.03	
1082.21/297.03	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
1082.21/297.03	   the following reason:
1082.21/297.03	   
1082.21/297.03	   We add the following weak dependency pairs:
1082.21/297.03	   
1082.21/297.03	   Strict DPs:
1082.21/297.03	     { active^#(eq(X, Y)) -> c_1()
1082.21/297.03	     , active^#(eq(0(), 0())) -> c_2()
1082.21/297.03	     , active^#(eq(s(X), s(Y))) -> c_3(eq^#(X, Y))
1082.21/297.03	     , active^#(inf(X)) -> c_4(cons^#(X, inf(s(X))))
1082.21/297.03	     , active^#(inf(X)) -> c_5(inf^#(active(X)))
1082.21/297.03	     , active^#(take(X1, X2)) -> c_6(take^#(X1, active(X2)))
1082.21/297.03	     , active^#(take(X1, X2)) -> c_7(take^#(active(X1), X2))
1082.21/297.03	     , active^#(take(0(), X)) -> c_8()
1082.21/297.03	     , active^#(take(s(X), cons(Y, L))) -> c_9(cons^#(Y, take(X, L)))
1082.21/297.03	     , active^#(length(X)) -> c_10(length^#(active(X)))
1082.21/297.03	     , active^#(length(cons(X, L))) -> c_11(s^#(length(L)))
1082.21/297.03	     , active^#(length(nil())) -> c_12()
1082.21/297.03	     , eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2))
1082.21/297.03	     , cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2))
1082.21/297.03	     , inf^#(mark(X)) -> c_15(inf^#(X))
1082.21/297.03	     , inf^#(ok(X)) -> c_16(inf^#(X))
1082.21/297.03	     , take^#(X1, mark(X2)) -> c_18(take^#(X1, X2))
1082.21/297.03	     , take^#(mark(X1), X2) -> c_19(take^#(X1, X2))
1082.21/297.03	     , take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2))
1082.21/297.03	     , length^#(mark(X)) -> c_21(length^#(X))
1082.21/297.03	     , length^#(ok(X)) -> c_22(length^#(X))
1082.21/297.03	     , s^#(ok(X)) -> c_14(s^#(X))
1082.21/297.03	     , proper^#(eq(X1, X2)) -> c_23(eq^#(proper(X1), proper(X2)))
1082.21/297.03	     , proper^#(0()) -> c_24()
1082.21/297.03	     , proper^#(true()) -> c_25()
1082.21/297.03	     , proper^#(s(X)) -> c_26(s^#(proper(X)))
1082.21/297.03	     , proper^#(false()) -> c_27()
1082.21/297.03	     , proper^#(inf(X)) -> c_28(inf^#(proper(X)))
1082.21/297.03	     , proper^#(cons(any(X1), X2)) ->
1082.21/297.03	       c_29(cons^#(any(any(proper(X1))), any(proper(X2))))
1082.21/297.03	     , proper^#(take(X1, X2)) -> c_30(take^#(proper(X1), proper(X2)))
1082.21/297.03	     , proper^#(nil()) -> c_31()
1082.21/297.03	     , proper^#(length(X)) -> c_32(length^#(proper(X)))
1082.21/297.03	     , any^#(X) -> c_33(s^#(X))
1082.21/297.03	     , any^#(proper(X)) -> c_34(any^#(any(any(X))))
1082.21/297.03	     , top^#(mark(X)) -> c_35(top^#(proper(X)))
1082.21/297.03	     , top^#(ok(X)) -> c_36(top^#(active(X))) }
1082.21/297.03	   
1082.21/297.03	   and mark the set of starting terms.
1082.21/297.03	   
1082.21/297.03	   We are left with following problem, upon which TcT provides the
1082.21/297.03	   certificate MAYBE.
1082.21/297.03	   
1082.21/297.03	   Strict DPs:
1082.21/297.03	     { active^#(eq(X, Y)) -> c_1()
1082.21/297.03	     , active^#(eq(0(), 0())) -> c_2()
1082.21/297.03	     , active^#(eq(s(X), s(Y))) -> c_3(eq^#(X, Y))
1082.21/297.03	     , active^#(inf(X)) -> c_4(cons^#(X, inf(s(X))))
1082.21/297.03	     , active^#(inf(X)) -> c_5(inf^#(active(X)))
1082.21/297.03	     , active^#(take(X1, X2)) -> c_6(take^#(X1, active(X2)))
1082.21/297.03	     , active^#(take(X1, X2)) -> c_7(take^#(active(X1), X2))
1082.21/297.03	     , active^#(take(0(), X)) -> c_8()
1082.21/297.03	     , active^#(take(s(X), cons(Y, L))) -> c_9(cons^#(Y, take(X, L)))
1082.21/297.03	     , active^#(length(X)) -> c_10(length^#(active(X)))
1082.21/297.03	     , active^#(length(cons(X, L))) -> c_11(s^#(length(L)))
1082.21/297.03	     , active^#(length(nil())) -> c_12()
1082.21/297.03	     , eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2))
1082.21/297.03	     , cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2))
1082.21/297.03	     , inf^#(mark(X)) -> c_15(inf^#(X))
1082.21/297.03	     , inf^#(ok(X)) -> c_16(inf^#(X))
1082.21/297.03	     , take^#(X1, mark(X2)) -> c_18(take^#(X1, X2))
1082.21/297.03	     , take^#(mark(X1), X2) -> c_19(take^#(X1, X2))
1082.21/297.03	     , take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2))
1082.21/297.03	     , length^#(mark(X)) -> c_21(length^#(X))
1082.21/297.03	     , length^#(ok(X)) -> c_22(length^#(X))
1082.21/297.03	     , s^#(ok(X)) -> c_14(s^#(X))
1082.21/297.03	     , proper^#(eq(X1, X2)) -> c_23(eq^#(proper(X1), proper(X2)))
1082.21/297.03	     , proper^#(0()) -> c_24()
1082.21/297.03	     , proper^#(true()) -> c_25()
1082.21/297.03	     , proper^#(s(X)) -> c_26(s^#(proper(X)))
1082.21/297.03	     , proper^#(false()) -> c_27()
1082.21/297.03	     , proper^#(inf(X)) -> c_28(inf^#(proper(X)))
1082.21/297.03	     , proper^#(cons(any(X1), X2)) ->
1082.21/297.03	       c_29(cons^#(any(any(proper(X1))), any(proper(X2))))
1082.21/297.03	     , proper^#(take(X1, X2)) -> c_30(take^#(proper(X1), proper(X2)))
1082.21/297.03	     , proper^#(nil()) -> c_31()
1082.21/297.03	     , proper^#(length(X)) -> c_32(length^#(proper(X)))
1082.21/297.03	     , any^#(X) -> c_33(s^#(X))
1082.21/297.03	     , any^#(proper(X)) -> c_34(any^#(any(any(X))))
1082.21/297.03	     , top^#(mark(X)) -> c_35(top^#(proper(X)))
1082.21/297.03	     , top^#(ok(X)) -> c_36(top^#(active(X))) }
1082.21/297.03	   Strict Trs:
1082.21/297.03	     { active(eq(X, Y)) -> mark(false())
1082.21/297.03	     , active(eq(0(), 0())) -> mark(true())
1082.21/297.03	     , active(eq(s(X), s(Y))) -> mark(eq(X, Y))
1082.21/297.03	     , active(inf(X)) -> mark(cons(X, inf(s(X))))
1082.21/297.03	     , active(inf(X)) -> inf(active(X))
1082.21/297.03	     , active(take(X1, X2)) -> take(X1, active(X2))
1082.21/297.03	     , active(take(X1, X2)) -> take(active(X1), X2)
1082.21/297.03	     , active(take(0(), X)) -> mark(nil())
1082.21/297.03	     , active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L)))
1082.21/297.03	     , active(length(X)) -> length(active(X))
1082.21/297.03	     , active(length(cons(X, L))) -> mark(s(length(L)))
1082.21/297.03	     , active(length(nil())) -> mark(0())
1082.21/297.03	     , eq(ok(X1), ok(X2)) -> ok(eq(X1, X2))
1082.21/297.03	     , s(ok(X)) -> ok(s(X))
1082.21/297.03	     , inf(mark(X)) -> mark(inf(X))
1082.21/297.03	     , inf(ok(X)) -> ok(inf(X))
1082.21/297.03	     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
1082.21/297.03	     , take(X1, mark(X2)) -> mark(take(X1, X2))
1082.21/297.03	     , take(mark(X1), X2) -> mark(take(X1, X2))
1082.21/297.03	     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
1082.21/297.03	     , length(mark(X)) -> mark(length(X))
1082.21/297.03	     , length(ok(X)) -> ok(length(X))
1082.21/297.03	     , proper(eq(X1, X2)) -> eq(proper(X1), proper(X2))
1082.21/297.03	     , proper(0()) -> ok(0())
1082.21/297.03	     , proper(true()) -> ok(true())
1082.21/297.03	     , proper(s(X)) -> s(proper(X))
1082.21/297.03	     , proper(false()) -> ok(false())
1082.21/297.03	     , proper(inf(X)) -> inf(proper(X))
1082.21/297.03	     , proper(cons(any(X1), X2)) ->
1082.21/297.03	       cons(any(any(proper(X1))), any(proper(X2)))
1082.21/297.03	     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
1082.21/297.03	     , proper(nil()) -> ok(nil())
1082.21/297.03	     , proper(length(X)) -> length(proper(X))
1082.21/297.03	     , any(X) -> s(X)
1082.21/297.03	     , any(proper(X)) -> any(any(any(X)))
1082.21/297.03	     , top(mark(X)) -> top(proper(X))
1082.21/297.03	     , top(ok(X)) -> top(active(X)) }
1082.21/297.03	   Obligation:
1082.21/297.03	     runtime complexity
1082.21/297.03	   Answer:
1082.21/297.03	     MAYBE
1082.21/297.03	   
1082.21/297.03	   Consider the dependency graph:
1082.21/297.03	   
1082.21/297.03	     1: active^#(eq(X, Y)) -> c_1()
1082.21/297.03	     
1082.21/297.03	     2: active^#(eq(0(), 0())) -> c_2()
1082.21/297.03	     
1082.21/297.03	     3: active^#(eq(s(X), s(Y))) -> c_3(eq^#(X, Y))
1082.21/297.03	        -->_1 eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2)) :13
1082.21/297.03	     
1082.21/297.03	     4: active^#(inf(X)) -> c_4(cons^#(X, inf(s(X))))
1082.21/297.03	        -->_1 cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2)) :14
1082.21/297.03	     
1082.21/297.03	     5: active^#(inf(X)) -> c_5(inf^#(active(X)))
1082.21/297.03	        -->_1 inf^#(ok(X)) -> c_16(inf^#(X)) :16
1082.21/297.03	        -->_1 inf^#(mark(X)) -> c_15(inf^#(X)) :15
1082.21/297.03	     
1082.21/297.03	     6: active^#(take(X1, X2)) -> c_6(take^#(X1, active(X2)))
1082.21/297.03	        -->_1 take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2)) :19
1082.21/297.03	        -->_1 take^#(mark(X1), X2) -> c_19(take^#(X1, X2)) :18
1082.21/297.03	        -->_1 take^#(X1, mark(X2)) -> c_18(take^#(X1, X2)) :17
1082.21/297.03	     
1082.21/297.03	     7: active^#(take(X1, X2)) -> c_7(take^#(active(X1), X2))
1082.21/297.03	        -->_1 take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2)) :19
1082.21/297.03	        -->_1 take^#(mark(X1), X2) -> c_19(take^#(X1, X2)) :18
1082.21/297.03	        -->_1 take^#(X1, mark(X2)) -> c_18(take^#(X1, X2)) :17
1082.21/297.03	     
1082.21/297.03	     8: active^#(take(0(), X)) -> c_8()
1082.21/297.03	     
1082.21/297.03	     9: active^#(take(s(X), cons(Y, L))) -> c_9(cons^#(Y, take(X, L)))
1082.21/297.03	        -->_1 cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2)) :14
1082.21/297.03	     
1082.21/297.03	     10: active^#(length(X)) -> c_10(length^#(active(X)))
1082.21/297.03	        -->_1 length^#(ok(X)) -> c_22(length^#(X)) :21
1082.21/297.03	        -->_1 length^#(mark(X)) -> c_21(length^#(X)) :20
1082.21/297.03	     
1082.21/297.03	     11: active^#(length(cons(X, L))) -> c_11(s^#(length(L)))
1082.21/297.03	        -->_1 s^#(ok(X)) -> c_14(s^#(X)) :22
1082.21/297.03	     
1082.21/297.03	     12: active^#(length(nil())) -> c_12()
1082.21/297.03	     
1082.21/297.03	     13: eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2))
1082.21/297.03	        -->_1 eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2)) :13
1082.21/297.03	     
1082.21/297.03	     14: cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2))
1082.21/297.03	        -->_1 cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2)) :14
1082.21/297.03	     
1082.21/297.03	     15: inf^#(mark(X)) -> c_15(inf^#(X))
1082.21/297.03	        -->_1 inf^#(ok(X)) -> c_16(inf^#(X)) :16
1082.21/297.03	        -->_1 inf^#(mark(X)) -> c_15(inf^#(X)) :15
1082.21/297.03	     
1082.21/297.03	     16: inf^#(ok(X)) -> c_16(inf^#(X))
1082.21/297.03	        -->_1 inf^#(ok(X)) -> c_16(inf^#(X)) :16
1082.21/297.03	        -->_1 inf^#(mark(X)) -> c_15(inf^#(X)) :15
1082.21/297.03	     
1082.21/297.03	     17: take^#(X1, mark(X2)) -> c_18(take^#(X1, X2))
1082.21/297.03	        -->_1 take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2)) :19
1082.21/297.03	        -->_1 take^#(mark(X1), X2) -> c_19(take^#(X1, X2)) :18
1082.21/297.03	        -->_1 take^#(X1, mark(X2)) -> c_18(take^#(X1, X2)) :17
1082.21/297.03	     
1082.21/297.03	     18: take^#(mark(X1), X2) -> c_19(take^#(X1, X2))
1082.21/297.03	        -->_1 take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2)) :19
1082.21/297.03	        -->_1 take^#(mark(X1), X2) -> c_19(take^#(X1, X2)) :18
1082.21/297.03	        -->_1 take^#(X1, mark(X2)) -> c_18(take^#(X1, X2)) :17
1082.21/297.03	     
1082.21/297.03	     19: take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2))
1082.21/297.03	        -->_1 take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2)) :19
1082.21/297.03	        -->_1 take^#(mark(X1), X2) -> c_19(take^#(X1, X2)) :18
1082.21/297.03	        -->_1 take^#(X1, mark(X2)) -> c_18(take^#(X1, X2)) :17
1082.21/297.03	     
1082.21/297.03	     20: length^#(mark(X)) -> c_21(length^#(X))
1082.21/297.03	        -->_1 length^#(ok(X)) -> c_22(length^#(X)) :21
1082.21/297.03	        -->_1 length^#(mark(X)) -> c_21(length^#(X)) :20
1082.21/297.03	     
1082.21/297.03	     21: length^#(ok(X)) -> c_22(length^#(X))
1082.21/297.03	        -->_1 length^#(ok(X)) -> c_22(length^#(X)) :21
1082.21/297.03	        -->_1 length^#(mark(X)) -> c_21(length^#(X)) :20
1082.21/297.03	     
1082.21/297.03	     22: s^#(ok(X)) -> c_14(s^#(X)) -->_1 s^#(ok(X)) -> c_14(s^#(X)) :22
1082.21/297.03	     
1082.21/297.03	     23: proper^#(eq(X1, X2)) -> c_23(eq^#(proper(X1), proper(X2)))
1082.21/297.03	        -->_1 eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2)) :13
1082.21/297.03	     
1082.21/297.03	     24: proper^#(0()) -> c_24()
1082.21/297.03	     
1082.21/297.03	     25: proper^#(true()) -> c_25()
1082.21/297.03	     
1082.21/297.03	     26: proper^#(s(X)) -> c_26(s^#(proper(X)))
1082.21/297.03	        -->_1 s^#(ok(X)) -> c_14(s^#(X)) :22
1082.21/297.03	     
1082.21/297.03	     27: proper^#(false()) -> c_27()
1082.21/297.03	     
1082.21/297.03	     28: proper^#(inf(X)) -> c_28(inf^#(proper(X)))
1082.21/297.03	        -->_1 inf^#(ok(X)) -> c_16(inf^#(X)) :16
1082.21/297.03	        -->_1 inf^#(mark(X)) -> c_15(inf^#(X)) :15
1082.21/297.03	     
1082.21/297.03	     29: proper^#(cons(any(X1), X2)) ->
1082.21/297.03	         c_29(cons^#(any(any(proper(X1))), any(proper(X2))))
1082.21/297.03	        -->_1 cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2)) :14
1082.21/297.03	     
1082.21/297.03	     30: proper^#(take(X1, X2)) -> c_30(take^#(proper(X1), proper(X2)))
1082.21/297.03	        -->_1 take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2)) :19
1082.21/297.03	        -->_1 take^#(mark(X1), X2) -> c_19(take^#(X1, X2)) :18
1082.21/297.03	        -->_1 take^#(X1, mark(X2)) -> c_18(take^#(X1, X2)) :17
1082.21/297.03	     
1082.21/297.03	     31: proper^#(nil()) -> c_31()
1082.21/297.03	     
1082.21/297.03	     32: proper^#(length(X)) -> c_32(length^#(proper(X)))
1082.21/297.03	        -->_1 length^#(ok(X)) -> c_22(length^#(X)) :21
1082.21/297.03	        -->_1 length^#(mark(X)) -> c_21(length^#(X)) :20
1082.21/297.03	     
1082.21/297.03	     33: any^#(X) -> c_33(s^#(X)) -->_1 s^#(ok(X)) -> c_14(s^#(X)) :22
1082.21/297.03	     
1082.21/297.03	     34: any^#(proper(X)) -> c_34(any^#(any(any(X))))
1082.21/297.03	        -->_1 any^#(X) -> c_33(s^#(X)) :33
1082.21/297.03	     
1082.21/297.03	     35: top^#(mark(X)) -> c_35(top^#(proper(X)))
1082.21/297.03	        -->_1 top^#(ok(X)) -> c_36(top^#(active(X))) :36
1082.21/297.03	        -->_1 top^#(mark(X)) -> c_35(top^#(proper(X))) :35
1082.21/297.03	     
1082.21/297.03	     36: top^#(ok(X)) -> c_36(top^#(active(X)))
1082.21/297.03	        -->_1 top^#(ok(X)) -> c_36(top^#(active(X))) :36
1082.21/297.03	        -->_1 top^#(mark(X)) -> c_35(top^#(proper(X))) :35
1082.21/297.03	     
1082.21/297.03	   
1082.21/297.03	   Only the nodes {13,14,15,16,17,19,18,20,21,22,24,25,27,31,33,35,36}
1082.21/297.03	   are reachable from nodes
1082.21/297.03	   {13,14,15,16,17,18,19,20,21,22,24,25,27,31,33,35,36} that start
1082.21/297.03	   derivation from marked basic terms. The nodes not reachable are
1082.21/297.03	   removed from the problem.
1082.21/297.03	   
1082.21/297.03	   We are left with following problem, upon which TcT provides the
1082.21/297.03	   certificate MAYBE.
1082.21/297.03	   
1082.21/297.03	   Strict DPs:
1082.21/297.03	     { eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2))
1082.21/297.03	     , cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2))
1082.21/297.03	     , inf^#(mark(X)) -> c_15(inf^#(X))
1082.21/297.03	     , inf^#(ok(X)) -> c_16(inf^#(X))
1082.21/297.03	     , take^#(X1, mark(X2)) -> c_18(take^#(X1, X2))
1082.21/297.03	     , take^#(mark(X1), X2) -> c_19(take^#(X1, X2))
1082.21/297.03	     , take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2))
1082.21/297.03	     , length^#(mark(X)) -> c_21(length^#(X))
1082.21/297.03	     , length^#(ok(X)) -> c_22(length^#(X))
1082.21/297.03	     , s^#(ok(X)) -> c_14(s^#(X))
1082.21/297.03	     , proper^#(0()) -> c_24()
1082.21/297.03	     , proper^#(true()) -> c_25()
1082.21/297.03	     , proper^#(false()) -> c_27()
1082.21/297.03	     , proper^#(nil()) -> c_31()
1082.21/297.03	     , any^#(X) -> c_33(s^#(X))
1082.21/297.03	     , top^#(mark(X)) -> c_35(top^#(proper(X)))
1082.21/297.03	     , top^#(ok(X)) -> c_36(top^#(active(X))) }
1082.21/297.03	   Strict Trs:
1082.21/297.03	     { active(eq(X, Y)) -> mark(false())
1082.21/297.03	     , active(eq(0(), 0())) -> mark(true())
1082.21/297.03	     , active(eq(s(X), s(Y))) -> mark(eq(X, Y))
1082.21/297.03	     , active(inf(X)) -> mark(cons(X, inf(s(X))))
1082.21/297.03	     , active(inf(X)) -> inf(active(X))
1082.21/297.03	     , active(take(X1, X2)) -> take(X1, active(X2))
1082.21/297.03	     , active(take(X1, X2)) -> take(active(X1), X2)
1082.21/297.03	     , active(take(0(), X)) -> mark(nil())
1082.21/297.03	     , active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L)))
1082.21/297.03	     , active(length(X)) -> length(active(X))
1082.21/297.03	     , active(length(cons(X, L))) -> mark(s(length(L)))
1082.21/297.03	     , active(length(nil())) -> mark(0())
1082.21/297.03	     , eq(ok(X1), ok(X2)) -> ok(eq(X1, X2))
1082.21/297.03	     , s(ok(X)) -> ok(s(X))
1082.21/297.03	     , inf(mark(X)) -> mark(inf(X))
1082.21/297.03	     , inf(ok(X)) -> ok(inf(X))
1082.21/297.03	     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
1082.21/297.03	     , take(X1, mark(X2)) -> mark(take(X1, X2))
1082.21/297.03	     , take(mark(X1), X2) -> mark(take(X1, X2))
1082.21/297.03	     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
1082.21/297.03	     , length(mark(X)) -> mark(length(X))
1082.21/297.03	     , length(ok(X)) -> ok(length(X))
1082.21/297.03	     , proper(eq(X1, X2)) -> eq(proper(X1), proper(X2))
1082.21/297.03	     , proper(0()) -> ok(0())
1082.21/297.03	     , proper(true()) -> ok(true())
1082.21/297.03	     , proper(s(X)) -> s(proper(X))
1082.21/297.03	     , proper(false()) -> ok(false())
1082.21/297.03	     , proper(inf(X)) -> inf(proper(X))
1082.21/297.03	     , proper(cons(any(X1), X2)) ->
1082.21/297.03	       cons(any(any(proper(X1))), any(proper(X2)))
1082.21/297.03	     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
1082.21/297.03	     , proper(nil()) -> ok(nil())
1082.21/297.03	     , proper(length(X)) -> length(proper(X))
1082.21/297.03	     , any(X) -> s(X)
1082.21/297.03	     , any(proper(X)) -> any(any(any(X)))
1082.21/297.03	     , top(mark(X)) -> top(proper(X))
1082.21/297.03	     , top(ok(X)) -> top(active(X)) }
1082.21/297.03	   Obligation:
1082.21/297.03	     runtime complexity
1082.21/297.03	   Answer:
1082.21/297.03	     MAYBE
1082.21/297.03	   
1082.21/297.03	   We estimate the number of application of {11,12,13,14} by
1082.21/297.03	   applications of Pre({11,12,13,14}) = {}. Here rules are labeled as
1082.21/297.03	   follows:
1082.21/297.03	   
1082.21/297.03	     DPs:
1082.21/297.03	       { 1: eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2))
1082.21/297.03	       , 2: cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2))
1082.21/297.03	       , 3: inf^#(mark(X)) -> c_15(inf^#(X))
1082.21/297.03	       , 4: inf^#(ok(X)) -> c_16(inf^#(X))
1082.21/297.03	       , 5: take^#(X1, mark(X2)) -> c_18(take^#(X1, X2))
1082.21/297.03	       , 6: take^#(mark(X1), X2) -> c_19(take^#(X1, X2))
1082.21/297.03	       , 7: take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2))
1082.21/297.03	       , 8: length^#(mark(X)) -> c_21(length^#(X))
1082.21/297.03	       , 9: length^#(ok(X)) -> c_22(length^#(X))
1082.21/297.03	       , 10: s^#(ok(X)) -> c_14(s^#(X))
1082.21/297.03	       , 11: proper^#(0()) -> c_24()
1082.21/297.03	       , 12: proper^#(true()) -> c_25()
1082.21/297.03	       , 13: proper^#(false()) -> c_27()
1082.21/297.03	       , 14: proper^#(nil()) -> c_31()
1082.21/297.03	       , 15: any^#(X) -> c_33(s^#(X))
1082.21/297.03	       , 16: top^#(mark(X)) -> c_35(top^#(proper(X)))
1082.21/297.03	       , 17: top^#(ok(X)) -> c_36(top^#(active(X))) }
1082.21/297.03	   
1082.21/297.03	   We are left with following problem, upon which TcT provides the
1082.21/297.03	   certificate MAYBE.
1082.21/297.03	   
1082.21/297.03	   Strict DPs:
1082.21/297.03	     { eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2))
1082.21/297.03	     , cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2))
1082.21/297.03	     , inf^#(mark(X)) -> c_15(inf^#(X))
1082.21/297.03	     , inf^#(ok(X)) -> c_16(inf^#(X))
1082.21/297.03	     , take^#(X1, mark(X2)) -> c_18(take^#(X1, X2))
1082.21/297.03	     , take^#(mark(X1), X2) -> c_19(take^#(X1, X2))
1082.21/297.03	     , take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2))
1082.21/297.03	     , length^#(mark(X)) -> c_21(length^#(X))
1082.21/297.03	     , length^#(ok(X)) -> c_22(length^#(X))
1082.21/297.03	     , s^#(ok(X)) -> c_14(s^#(X))
1082.21/297.03	     , any^#(X) -> c_33(s^#(X))
1082.21/297.03	     , top^#(mark(X)) -> c_35(top^#(proper(X)))
1082.21/297.03	     , top^#(ok(X)) -> c_36(top^#(active(X))) }
1082.21/297.03	   Strict Trs:
1082.21/297.03	     { active(eq(X, Y)) -> mark(false())
1082.21/297.03	     , active(eq(0(), 0())) -> mark(true())
1082.21/297.03	     , active(eq(s(X), s(Y))) -> mark(eq(X, Y))
1082.21/297.03	     , active(inf(X)) -> mark(cons(X, inf(s(X))))
1082.21/297.03	     , active(inf(X)) -> inf(active(X))
1082.21/297.03	     , active(take(X1, X2)) -> take(X1, active(X2))
1082.21/297.03	     , active(take(X1, X2)) -> take(active(X1), X2)
1082.21/297.03	     , active(take(0(), X)) -> mark(nil())
1082.21/297.03	     , active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L)))
1082.21/297.03	     , active(length(X)) -> length(active(X))
1082.21/297.03	     , active(length(cons(X, L))) -> mark(s(length(L)))
1082.21/297.03	     , active(length(nil())) -> mark(0())
1082.21/297.03	     , eq(ok(X1), ok(X2)) -> ok(eq(X1, X2))
1082.21/297.03	     , s(ok(X)) -> ok(s(X))
1082.21/297.03	     , inf(mark(X)) -> mark(inf(X))
1082.21/297.03	     , inf(ok(X)) -> ok(inf(X))
1082.21/297.03	     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
1082.21/297.03	     , take(X1, mark(X2)) -> mark(take(X1, X2))
1082.21/297.03	     , take(mark(X1), X2) -> mark(take(X1, X2))
1082.21/297.03	     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
1082.21/297.03	     , length(mark(X)) -> mark(length(X))
1082.21/297.03	     , length(ok(X)) -> ok(length(X))
1082.21/297.03	     , proper(eq(X1, X2)) -> eq(proper(X1), proper(X2))
1082.21/297.03	     , proper(0()) -> ok(0())
1082.21/297.03	     , proper(true()) -> ok(true())
1082.21/297.03	     , proper(s(X)) -> s(proper(X))
1082.21/297.03	     , proper(false()) -> ok(false())
1082.21/297.03	     , proper(inf(X)) -> inf(proper(X))
1082.21/297.03	     , proper(cons(any(X1), X2)) ->
1082.21/297.03	       cons(any(any(proper(X1))), any(proper(X2)))
1082.21/297.03	     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
1082.21/297.03	     , proper(nil()) -> ok(nil())
1082.21/297.03	     , proper(length(X)) -> length(proper(X))
1082.21/297.03	     , any(X) -> s(X)
1082.21/297.03	     , any(proper(X)) -> any(any(any(X)))
1082.21/297.03	     , top(mark(X)) -> top(proper(X))
1082.21/297.03	     , top(ok(X)) -> top(active(X)) }
1082.21/297.03	   Weak DPs:
1082.21/297.03	     { proper^#(0()) -> c_24()
1082.21/297.03	     , proper^#(true()) -> c_25()
1082.21/297.03	     , proper^#(false()) -> c_27()
1082.21/297.03	     , proper^#(nil()) -> c_31() }
1082.21/297.03	   Obligation:
1082.21/297.03	     runtime complexity
1082.21/297.03	   Answer:
1082.21/297.03	     MAYBE
1082.21/297.03	   
1082.21/297.03	   Empty strict component of the problem is NOT empty.
1082.21/297.03	
1082.21/297.03	
1082.21/297.03	Arrrr..
1082.58/297.37	EOF