MAYBE
1070.94/297.04	MAYBE
1070.94/297.04	
1070.94/297.04	We are left with following problem, upon which TcT provides the
1070.94/297.04	certificate MAYBE.
1070.94/297.04	
1070.94/297.04	Strict Trs:
1070.94/297.04	  { active(eq(X, Y)) -> mark(false())
1070.94/297.04	  , active(eq(0(), 0())) -> mark(true())
1070.94/297.04	  , active(eq(s(X), s(Y))) -> mark(eq(X, Y))
1070.94/297.04	  , active(inf(X)) -> mark(cons(X, inf(s(X))))
1070.94/297.04	  , active(inf(X)) -> inf(active(X))
1070.94/297.04	  , active(take(X1, X2)) -> take(X1, active(X2))
1070.94/297.04	  , active(take(X1, X2)) -> take(active(X1), X2)
1070.94/297.04	  , active(take(0(), X)) -> mark(nil())
1070.94/297.04	  , active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L)))
1070.94/297.04	  , active(length(X)) -> length(active(X))
1070.94/297.04	  , active(length(cons(X, L))) -> mark(s(length(L)))
1070.94/297.04	  , active(length(nil())) -> mark(0())
1070.94/297.04	  , eq(ok(X1), ok(X2)) -> ok(eq(X1, X2))
1070.94/297.04	  , s(ok(X)) -> ok(s(X))
1070.94/297.04	  , inf(mark(X)) -> mark(inf(X))
1070.94/297.04	  , inf(ok(X)) -> ok(inf(X))
1070.94/297.04	  , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
1070.94/297.04	  , take(X1, mark(X2)) -> mark(take(X1, X2))
1070.94/297.04	  , take(mark(X1), X2) -> mark(take(X1, X2))
1070.94/297.04	  , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
1070.94/297.04	  , length(mark(X)) -> mark(length(X))
1070.94/297.04	  , length(ok(X)) -> ok(length(X))
1070.94/297.04	  , proper(eq(X1, X2)) -> eq(proper(X1), proper(X2))
1070.94/297.04	  , proper(0()) -> ok(0())
1070.94/297.04	  , proper(true()) -> ok(true())
1070.94/297.04	  , proper(s(X)) -> s(proper(X))
1070.94/297.04	  , proper(false()) -> ok(false())
1070.94/297.04	  , proper(inf(X)) -> inf(proper(X))
1070.94/297.04	  , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
1070.94/297.04	  , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
1070.94/297.04	  , proper(nil()) -> ok(nil())
1070.94/297.04	  , proper(length(X)) -> length(proper(X))
1070.94/297.04	  , top(mark(X)) -> top(proper(X))
1070.94/297.04	  , top(ok(X)) -> top(active(X)) }
1070.94/297.04	Obligation:
1070.94/297.04	  runtime complexity
1070.94/297.04	Answer:
1070.94/297.04	  MAYBE
1070.94/297.04	
1070.94/297.04	None of the processors succeeded.
1070.94/297.04	
1070.94/297.04	Details of failed attempt(s):
1070.94/297.04	-----------------------------
1070.94/297.04	1) 'With Problem ... (timeout of 297 seconds)' failed due to the
1070.94/297.04	   following reason:
1070.94/297.04	   
1070.94/297.04	   Computation stopped due to timeout after 297.0 seconds.
1070.94/297.04	
1070.94/297.04	2) 'Best' failed due to the following reason:
1070.94/297.04	   
1070.94/297.04	   None of the processors succeeded.
1070.94/297.04	   
1070.94/297.04	   Details of failed attempt(s):
1070.94/297.04	   -----------------------------
1070.94/297.04	   1) 'With Problem ... (timeout of 148 seconds) (timeout of 297
1070.94/297.04	      seconds)' failed due to the following reason:
1070.94/297.04	      
1070.94/297.04	      Computation stopped due to timeout after 148.0 seconds.
1070.94/297.04	   
1070.94/297.04	   2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)'
1070.94/297.04	      failed due to the following reason:
1070.94/297.04	      
1070.94/297.04	      None of the processors succeeded.
1070.94/297.04	      
1070.94/297.04	      Details of failed attempt(s):
1070.94/297.04	      -----------------------------
1070.94/297.04	      1) 'Bounds with minimal-enrichment and initial automaton 'match''
1070.94/297.04	         failed due to the following reason:
1070.94/297.04	         
1070.94/297.04	         match-boundness of the problem could not be verified.
1070.94/297.04	      
1070.94/297.04	      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
1070.94/297.04	         failed due to the following reason:
1070.94/297.04	         
1070.94/297.04	         match-boundness of the problem could not be verified.
1070.94/297.04	      
1070.94/297.04	   
1070.94/297.04	   3) 'Best' failed due to the following reason:
1070.94/297.04	      
1070.94/297.04	      None of the processors succeeded.
1070.94/297.04	      
1070.94/297.04	      Details of failed attempt(s):
1070.94/297.04	      -----------------------------
1070.94/297.04	      1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the
1070.94/297.04	         following reason:
1070.94/297.04	         
1070.94/297.04	         The processor is inapplicable, reason:
1070.94/297.04	           Processor only applicable for innermost runtime complexity analysis
1070.94/297.04	      
1070.94/297.04	      2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due
1070.94/297.04	         to the following reason:
1070.94/297.04	         
1070.94/297.04	         The processor is inapplicable, reason:
1070.94/297.04	           Processor only applicable for innermost runtime complexity analysis
1070.94/297.04	      
1070.94/297.04	   
1070.94/297.04	
1070.94/297.04	3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to
1070.94/297.04	   the following reason:
1070.94/297.04	   
1070.94/297.04	   We add the following weak dependency pairs:
1070.94/297.04	   
1070.94/297.04	   Strict DPs:
1070.94/297.04	     { active^#(eq(X, Y)) -> c_1()
1070.94/297.04	     , active^#(eq(0(), 0())) -> c_2()
1070.94/297.04	     , active^#(eq(s(X), s(Y))) -> c_3(eq^#(X, Y))
1070.94/297.04	     , active^#(inf(X)) -> c_4(cons^#(X, inf(s(X))))
1070.94/297.04	     , active^#(inf(X)) -> c_5(inf^#(active(X)))
1070.94/297.04	     , active^#(take(X1, X2)) -> c_6(take^#(X1, active(X2)))
1070.94/297.04	     , active^#(take(X1, X2)) -> c_7(take^#(active(X1), X2))
1070.94/297.04	     , active^#(take(0(), X)) -> c_8()
1070.94/297.04	     , active^#(take(s(X), cons(Y, L))) -> c_9(cons^#(Y, take(X, L)))
1070.94/297.04	     , active^#(length(X)) -> c_10(length^#(active(X)))
1070.94/297.04	     , active^#(length(cons(X, L))) -> c_11(s^#(length(L)))
1070.94/297.04	     , active^#(length(nil())) -> c_12()
1070.94/297.04	     , eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2))
1070.94/297.04	     , cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2))
1070.94/297.04	     , inf^#(mark(X)) -> c_15(inf^#(X))
1070.94/297.04	     , inf^#(ok(X)) -> c_16(inf^#(X))
1070.94/297.04	     , take^#(X1, mark(X2)) -> c_18(take^#(X1, X2))
1070.94/297.04	     , take^#(mark(X1), X2) -> c_19(take^#(X1, X2))
1070.94/297.04	     , take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2))
1070.94/297.04	     , length^#(mark(X)) -> c_21(length^#(X))
1070.94/297.04	     , length^#(ok(X)) -> c_22(length^#(X))
1070.94/297.04	     , s^#(ok(X)) -> c_14(s^#(X))
1070.94/297.04	     , proper^#(eq(X1, X2)) -> c_23(eq^#(proper(X1), proper(X2)))
1070.94/297.04	     , proper^#(0()) -> c_24()
1070.94/297.04	     , proper^#(true()) -> c_25()
1070.94/297.04	     , proper^#(s(X)) -> c_26(s^#(proper(X)))
1070.94/297.04	     , proper^#(false()) -> c_27()
1070.94/297.04	     , proper^#(inf(X)) -> c_28(inf^#(proper(X)))
1070.94/297.04	     , proper^#(cons(X1, X2)) -> c_29(cons^#(proper(X1), proper(X2)))
1070.94/297.04	     , proper^#(take(X1, X2)) -> c_30(take^#(proper(X1), proper(X2)))
1070.94/297.04	     , proper^#(nil()) -> c_31()
1070.94/297.04	     , proper^#(length(X)) -> c_32(length^#(proper(X)))
1070.94/297.04	     , top^#(mark(X)) -> c_33(top^#(proper(X)))
1070.94/297.04	     , top^#(ok(X)) -> c_34(top^#(active(X))) }
1070.94/297.04	   
1070.94/297.04	   and mark the set of starting terms.
1070.94/297.04	   
1070.94/297.04	   We are left with following problem, upon which TcT provides the
1070.94/297.04	   certificate MAYBE.
1070.94/297.04	   
1070.94/297.04	   Strict DPs:
1070.94/297.04	     { active^#(eq(X, Y)) -> c_1()
1070.94/297.04	     , active^#(eq(0(), 0())) -> c_2()
1070.94/297.04	     , active^#(eq(s(X), s(Y))) -> c_3(eq^#(X, Y))
1070.94/297.04	     , active^#(inf(X)) -> c_4(cons^#(X, inf(s(X))))
1070.94/297.04	     , active^#(inf(X)) -> c_5(inf^#(active(X)))
1070.94/297.04	     , active^#(take(X1, X2)) -> c_6(take^#(X1, active(X2)))
1070.94/297.04	     , active^#(take(X1, X2)) -> c_7(take^#(active(X1), X2))
1070.94/297.04	     , active^#(take(0(), X)) -> c_8()
1070.94/297.04	     , active^#(take(s(X), cons(Y, L))) -> c_9(cons^#(Y, take(X, L)))
1070.94/297.04	     , active^#(length(X)) -> c_10(length^#(active(X)))
1070.94/297.04	     , active^#(length(cons(X, L))) -> c_11(s^#(length(L)))
1070.94/297.04	     , active^#(length(nil())) -> c_12()
1070.94/297.04	     , eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2))
1070.94/297.04	     , cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2))
1070.94/297.04	     , inf^#(mark(X)) -> c_15(inf^#(X))
1070.94/297.04	     , inf^#(ok(X)) -> c_16(inf^#(X))
1070.94/297.04	     , take^#(X1, mark(X2)) -> c_18(take^#(X1, X2))
1070.94/297.04	     , take^#(mark(X1), X2) -> c_19(take^#(X1, X2))
1070.94/297.04	     , take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2))
1070.94/297.04	     , length^#(mark(X)) -> c_21(length^#(X))
1070.94/297.04	     , length^#(ok(X)) -> c_22(length^#(X))
1070.94/297.04	     , s^#(ok(X)) -> c_14(s^#(X))
1070.94/297.04	     , proper^#(eq(X1, X2)) -> c_23(eq^#(proper(X1), proper(X2)))
1070.94/297.04	     , proper^#(0()) -> c_24()
1070.94/297.04	     , proper^#(true()) -> c_25()
1070.94/297.04	     , proper^#(s(X)) -> c_26(s^#(proper(X)))
1070.94/297.04	     , proper^#(false()) -> c_27()
1070.94/297.04	     , proper^#(inf(X)) -> c_28(inf^#(proper(X)))
1070.94/297.04	     , proper^#(cons(X1, X2)) -> c_29(cons^#(proper(X1), proper(X2)))
1070.94/297.04	     , proper^#(take(X1, X2)) -> c_30(take^#(proper(X1), proper(X2)))
1070.94/297.04	     , proper^#(nil()) -> c_31()
1070.94/297.04	     , proper^#(length(X)) -> c_32(length^#(proper(X)))
1070.94/297.04	     , top^#(mark(X)) -> c_33(top^#(proper(X)))
1070.94/297.04	     , top^#(ok(X)) -> c_34(top^#(active(X))) }
1070.94/297.04	   Strict Trs:
1070.94/297.04	     { active(eq(X, Y)) -> mark(false())
1070.94/297.04	     , active(eq(0(), 0())) -> mark(true())
1070.94/297.04	     , active(eq(s(X), s(Y))) -> mark(eq(X, Y))
1070.94/297.04	     , active(inf(X)) -> mark(cons(X, inf(s(X))))
1070.94/297.04	     , active(inf(X)) -> inf(active(X))
1070.94/297.04	     , active(take(X1, X2)) -> take(X1, active(X2))
1070.94/297.04	     , active(take(X1, X2)) -> take(active(X1), X2)
1070.94/297.04	     , active(take(0(), X)) -> mark(nil())
1070.94/297.04	     , active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L)))
1070.94/297.04	     , active(length(X)) -> length(active(X))
1070.94/297.04	     , active(length(cons(X, L))) -> mark(s(length(L)))
1070.94/297.04	     , active(length(nil())) -> mark(0())
1070.94/297.04	     , eq(ok(X1), ok(X2)) -> ok(eq(X1, X2))
1070.94/297.04	     , s(ok(X)) -> ok(s(X))
1070.94/297.04	     , inf(mark(X)) -> mark(inf(X))
1070.94/297.04	     , inf(ok(X)) -> ok(inf(X))
1070.94/297.04	     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
1070.94/297.04	     , take(X1, mark(X2)) -> mark(take(X1, X2))
1070.94/297.04	     , take(mark(X1), X2) -> mark(take(X1, X2))
1070.94/297.04	     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
1070.94/297.04	     , length(mark(X)) -> mark(length(X))
1070.94/297.04	     , length(ok(X)) -> ok(length(X))
1070.94/297.05	     , proper(eq(X1, X2)) -> eq(proper(X1), proper(X2))
1070.94/297.05	     , proper(0()) -> ok(0())
1070.94/297.05	     , proper(true()) -> ok(true())
1070.94/297.05	     , proper(s(X)) -> s(proper(X))
1070.94/297.05	     , proper(false()) -> ok(false())
1070.94/297.05	     , proper(inf(X)) -> inf(proper(X))
1070.94/297.05	     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
1070.94/297.05	     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
1070.94/297.05	     , proper(nil()) -> ok(nil())
1070.94/297.05	     , proper(length(X)) -> length(proper(X))
1070.94/297.05	     , top(mark(X)) -> top(proper(X))
1070.94/297.05	     , top(ok(X)) -> top(active(X)) }
1070.94/297.05	   Obligation:
1070.94/297.05	     runtime complexity
1070.94/297.05	   Answer:
1070.94/297.05	     MAYBE
1070.94/297.05	   
1070.94/297.05	   Consider the dependency graph:
1070.94/297.05	   
1070.94/297.05	     1: active^#(eq(X, Y)) -> c_1()
1070.94/297.05	     
1070.94/297.05	     2: active^#(eq(0(), 0())) -> c_2()
1070.94/297.05	     
1070.94/297.05	     3: active^#(eq(s(X), s(Y))) -> c_3(eq^#(X, Y))
1070.94/297.05	        -->_1 eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2)) :13
1070.94/297.05	     
1070.94/297.05	     4: active^#(inf(X)) -> c_4(cons^#(X, inf(s(X))))
1070.94/297.05	        -->_1 cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2)) :14
1070.94/297.05	     
1070.94/297.05	     5: active^#(inf(X)) -> c_5(inf^#(active(X)))
1070.94/297.05	        -->_1 inf^#(ok(X)) -> c_16(inf^#(X)) :16
1070.94/297.05	        -->_1 inf^#(mark(X)) -> c_15(inf^#(X)) :15
1070.94/297.05	     
1070.94/297.05	     6: active^#(take(X1, X2)) -> c_6(take^#(X1, active(X2)))
1070.94/297.05	        -->_1 take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2)) :19
1070.94/297.05	        -->_1 take^#(mark(X1), X2) -> c_19(take^#(X1, X2)) :18
1070.94/297.05	        -->_1 take^#(X1, mark(X2)) -> c_18(take^#(X1, X2)) :17
1070.94/297.05	     
1070.94/297.05	     7: active^#(take(X1, X2)) -> c_7(take^#(active(X1), X2))
1070.94/297.05	        -->_1 take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2)) :19
1070.94/297.05	        -->_1 take^#(mark(X1), X2) -> c_19(take^#(X1, X2)) :18
1070.94/297.05	        -->_1 take^#(X1, mark(X2)) -> c_18(take^#(X1, X2)) :17
1070.94/297.05	     
1070.94/297.05	     8: active^#(take(0(), X)) -> c_8()
1070.94/297.05	     
1070.94/297.05	     9: active^#(take(s(X), cons(Y, L))) -> c_9(cons^#(Y, take(X, L)))
1070.94/297.05	        -->_1 cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2)) :14
1070.94/297.05	     
1070.94/297.05	     10: active^#(length(X)) -> c_10(length^#(active(X)))
1070.94/297.05	        -->_1 length^#(ok(X)) -> c_22(length^#(X)) :21
1070.94/297.05	        -->_1 length^#(mark(X)) -> c_21(length^#(X)) :20
1070.94/297.05	     
1070.94/297.05	     11: active^#(length(cons(X, L))) -> c_11(s^#(length(L)))
1070.94/297.05	        -->_1 s^#(ok(X)) -> c_14(s^#(X)) :22
1070.94/297.05	     
1070.94/297.05	     12: active^#(length(nil())) -> c_12()
1070.94/297.05	     
1070.94/297.05	     13: eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2))
1070.94/297.05	        -->_1 eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2)) :13
1070.94/297.05	     
1070.94/297.05	     14: cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2))
1070.94/297.05	        -->_1 cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2)) :14
1070.94/297.05	     
1070.94/297.05	     15: inf^#(mark(X)) -> c_15(inf^#(X))
1070.94/297.05	        -->_1 inf^#(ok(X)) -> c_16(inf^#(X)) :16
1070.94/297.05	        -->_1 inf^#(mark(X)) -> c_15(inf^#(X)) :15
1070.94/297.05	     
1070.94/297.05	     16: inf^#(ok(X)) -> c_16(inf^#(X))
1070.94/297.05	        -->_1 inf^#(ok(X)) -> c_16(inf^#(X)) :16
1070.94/297.05	        -->_1 inf^#(mark(X)) -> c_15(inf^#(X)) :15
1070.94/297.05	     
1070.94/297.05	     17: take^#(X1, mark(X2)) -> c_18(take^#(X1, X2))
1070.94/297.05	        -->_1 take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2)) :19
1070.94/297.05	        -->_1 take^#(mark(X1), X2) -> c_19(take^#(X1, X2)) :18
1070.94/297.05	        -->_1 take^#(X1, mark(X2)) -> c_18(take^#(X1, X2)) :17
1070.94/297.05	     
1070.94/297.05	     18: take^#(mark(X1), X2) -> c_19(take^#(X1, X2))
1070.94/297.05	        -->_1 take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2)) :19
1070.94/297.05	        -->_1 take^#(mark(X1), X2) -> c_19(take^#(X1, X2)) :18
1070.94/297.05	        -->_1 take^#(X1, mark(X2)) -> c_18(take^#(X1, X2)) :17
1070.94/297.05	     
1070.94/297.05	     19: take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2))
1070.94/297.05	        -->_1 take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2)) :19
1070.94/297.05	        -->_1 take^#(mark(X1), X2) -> c_19(take^#(X1, X2)) :18
1070.94/297.05	        -->_1 take^#(X1, mark(X2)) -> c_18(take^#(X1, X2)) :17
1070.94/297.05	     
1070.94/297.05	     20: length^#(mark(X)) -> c_21(length^#(X))
1070.94/297.05	        -->_1 length^#(ok(X)) -> c_22(length^#(X)) :21
1070.94/297.05	        -->_1 length^#(mark(X)) -> c_21(length^#(X)) :20
1070.94/297.05	     
1070.94/297.05	     21: length^#(ok(X)) -> c_22(length^#(X))
1070.94/297.05	        -->_1 length^#(ok(X)) -> c_22(length^#(X)) :21
1070.94/297.05	        -->_1 length^#(mark(X)) -> c_21(length^#(X)) :20
1070.94/297.05	     
1070.94/297.05	     22: s^#(ok(X)) -> c_14(s^#(X)) -->_1 s^#(ok(X)) -> c_14(s^#(X)) :22
1070.94/297.05	     
1070.94/297.05	     23: proper^#(eq(X1, X2)) -> c_23(eq^#(proper(X1), proper(X2)))
1070.94/297.05	        -->_1 eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2)) :13
1070.94/297.05	     
1070.94/297.05	     24: proper^#(0()) -> c_24()
1070.94/297.05	     
1070.94/297.05	     25: proper^#(true()) -> c_25()
1070.94/297.05	     
1070.94/297.05	     26: proper^#(s(X)) -> c_26(s^#(proper(X)))
1070.94/297.05	        -->_1 s^#(ok(X)) -> c_14(s^#(X)) :22
1070.94/297.05	     
1070.94/297.05	     27: proper^#(false()) -> c_27()
1070.94/297.05	     
1070.94/297.05	     28: proper^#(inf(X)) -> c_28(inf^#(proper(X)))
1070.94/297.05	        -->_1 inf^#(ok(X)) -> c_16(inf^#(X)) :16
1070.94/297.05	        -->_1 inf^#(mark(X)) -> c_15(inf^#(X)) :15
1070.94/297.05	     
1070.94/297.05	     29: proper^#(cons(X1, X2)) -> c_29(cons^#(proper(X1), proper(X2)))
1070.94/297.05	        -->_1 cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2)) :14
1070.94/297.05	     
1070.94/297.05	     30: proper^#(take(X1, X2)) -> c_30(take^#(proper(X1), proper(X2)))
1070.94/297.05	        -->_1 take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2)) :19
1070.94/297.05	        -->_1 take^#(mark(X1), X2) -> c_19(take^#(X1, X2)) :18
1070.94/297.05	        -->_1 take^#(X1, mark(X2)) -> c_18(take^#(X1, X2)) :17
1070.94/297.05	     
1070.94/297.05	     31: proper^#(nil()) -> c_31()
1070.94/297.05	     
1070.94/297.05	     32: proper^#(length(X)) -> c_32(length^#(proper(X)))
1070.94/297.05	        -->_1 length^#(ok(X)) -> c_22(length^#(X)) :21
1070.94/297.05	        -->_1 length^#(mark(X)) -> c_21(length^#(X)) :20
1070.94/297.05	     
1070.94/297.05	     33: top^#(mark(X)) -> c_33(top^#(proper(X)))
1070.94/297.05	        -->_1 top^#(ok(X)) -> c_34(top^#(active(X))) :34
1070.94/297.05	        -->_1 top^#(mark(X)) -> c_33(top^#(proper(X))) :33
1070.94/297.05	     
1070.94/297.05	     34: top^#(ok(X)) -> c_34(top^#(active(X)))
1070.94/297.05	        -->_1 top^#(ok(X)) -> c_34(top^#(active(X))) :34
1070.94/297.05	        -->_1 top^#(mark(X)) -> c_33(top^#(proper(X))) :33
1070.94/297.05	     
1070.94/297.05	   
1070.94/297.05	   Only the nodes {13,14,15,16,17,19,18,20,21,22,24,25,27,31,33,34}
1070.94/297.05	   are reachable from nodes
1070.94/297.05	   {13,14,15,16,17,18,19,20,21,22,24,25,27,31,33,34} that start
1070.94/297.05	   derivation from marked basic terms. The nodes not reachable are
1070.94/297.05	   removed from the problem.
1070.94/297.05	   
1070.94/297.05	   We are left with following problem, upon which TcT provides the
1070.94/297.05	   certificate MAYBE.
1070.94/297.05	   
1070.94/297.05	   Strict DPs:
1070.94/297.05	     { eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2))
1070.94/297.05	     , cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2))
1070.94/297.05	     , inf^#(mark(X)) -> c_15(inf^#(X))
1070.94/297.05	     , inf^#(ok(X)) -> c_16(inf^#(X))
1070.94/297.05	     , take^#(X1, mark(X2)) -> c_18(take^#(X1, X2))
1070.94/297.05	     , take^#(mark(X1), X2) -> c_19(take^#(X1, X2))
1070.94/297.05	     , take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2))
1070.94/297.05	     , length^#(mark(X)) -> c_21(length^#(X))
1070.94/297.05	     , length^#(ok(X)) -> c_22(length^#(X))
1070.94/297.05	     , s^#(ok(X)) -> c_14(s^#(X))
1070.94/297.05	     , proper^#(0()) -> c_24()
1070.94/297.05	     , proper^#(true()) -> c_25()
1070.94/297.05	     , proper^#(false()) -> c_27()
1070.94/297.05	     , proper^#(nil()) -> c_31()
1070.94/297.05	     , top^#(mark(X)) -> c_33(top^#(proper(X)))
1070.94/297.05	     , top^#(ok(X)) -> c_34(top^#(active(X))) }
1070.94/297.05	   Strict Trs:
1070.94/297.05	     { active(eq(X, Y)) -> mark(false())
1070.94/297.05	     , active(eq(0(), 0())) -> mark(true())
1070.94/297.05	     , active(eq(s(X), s(Y))) -> mark(eq(X, Y))
1070.94/297.05	     , active(inf(X)) -> mark(cons(X, inf(s(X))))
1070.94/297.05	     , active(inf(X)) -> inf(active(X))
1070.94/297.05	     , active(take(X1, X2)) -> take(X1, active(X2))
1070.94/297.05	     , active(take(X1, X2)) -> take(active(X1), X2)
1070.94/297.05	     , active(take(0(), X)) -> mark(nil())
1070.94/297.05	     , active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L)))
1070.94/297.05	     , active(length(X)) -> length(active(X))
1070.94/297.05	     , active(length(cons(X, L))) -> mark(s(length(L)))
1070.94/297.05	     , active(length(nil())) -> mark(0())
1070.94/297.05	     , eq(ok(X1), ok(X2)) -> ok(eq(X1, X2))
1070.94/297.05	     , s(ok(X)) -> ok(s(X))
1070.94/297.05	     , inf(mark(X)) -> mark(inf(X))
1070.94/297.05	     , inf(ok(X)) -> ok(inf(X))
1070.94/297.05	     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
1070.94/297.05	     , take(X1, mark(X2)) -> mark(take(X1, X2))
1070.94/297.05	     , take(mark(X1), X2) -> mark(take(X1, X2))
1070.94/297.05	     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
1070.94/297.05	     , length(mark(X)) -> mark(length(X))
1070.94/297.05	     , length(ok(X)) -> ok(length(X))
1070.94/297.05	     , proper(eq(X1, X2)) -> eq(proper(X1), proper(X2))
1070.94/297.05	     , proper(0()) -> ok(0())
1070.94/297.05	     , proper(true()) -> ok(true())
1070.94/297.05	     , proper(s(X)) -> s(proper(X))
1070.94/297.05	     , proper(false()) -> ok(false())
1070.94/297.05	     , proper(inf(X)) -> inf(proper(X))
1070.94/297.05	     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
1070.94/297.05	     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
1070.94/297.05	     , proper(nil()) -> ok(nil())
1070.94/297.05	     , proper(length(X)) -> length(proper(X))
1070.94/297.05	     , top(mark(X)) -> top(proper(X))
1070.94/297.05	     , top(ok(X)) -> top(active(X)) }
1070.94/297.05	   Obligation:
1070.94/297.05	     runtime complexity
1070.94/297.05	   Answer:
1070.94/297.05	     MAYBE
1070.94/297.05	   
1070.94/297.05	   We estimate the number of application of {11,12,13,14} by
1070.94/297.05	   applications of Pre({11,12,13,14}) = {}. Here rules are labeled as
1070.94/297.05	   follows:
1070.94/297.05	   
1070.94/297.05	     DPs:
1070.94/297.05	       { 1: eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2))
1070.94/297.05	       , 2: cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2))
1070.94/297.05	       , 3: inf^#(mark(X)) -> c_15(inf^#(X))
1070.94/297.05	       , 4: inf^#(ok(X)) -> c_16(inf^#(X))
1070.94/297.05	       , 5: take^#(X1, mark(X2)) -> c_18(take^#(X1, X2))
1070.94/297.05	       , 6: take^#(mark(X1), X2) -> c_19(take^#(X1, X2))
1070.94/297.05	       , 7: take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2))
1070.94/297.05	       , 8: length^#(mark(X)) -> c_21(length^#(X))
1070.94/297.05	       , 9: length^#(ok(X)) -> c_22(length^#(X))
1070.94/297.05	       , 10: s^#(ok(X)) -> c_14(s^#(X))
1070.94/297.05	       , 11: proper^#(0()) -> c_24()
1070.94/297.05	       , 12: proper^#(true()) -> c_25()
1070.94/297.05	       , 13: proper^#(false()) -> c_27()
1070.94/297.05	       , 14: proper^#(nil()) -> c_31()
1070.94/297.05	       , 15: top^#(mark(X)) -> c_33(top^#(proper(X)))
1070.94/297.05	       , 16: top^#(ok(X)) -> c_34(top^#(active(X))) }
1070.94/297.05	   
1070.94/297.05	   We are left with following problem, upon which TcT provides the
1070.94/297.05	   certificate MAYBE.
1070.94/297.05	   
1070.94/297.05	   Strict DPs:
1070.94/297.05	     { eq^#(ok(X1), ok(X2)) -> c_13(eq^#(X1, X2))
1070.94/297.05	     , cons^#(ok(X1), ok(X2)) -> c_17(cons^#(X1, X2))
1070.94/297.05	     , inf^#(mark(X)) -> c_15(inf^#(X))
1070.94/297.05	     , inf^#(ok(X)) -> c_16(inf^#(X))
1070.94/297.05	     , take^#(X1, mark(X2)) -> c_18(take^#(X1, X2))
1070.94/297.05	     , take^#(mark(X1), X2) -> c_19(take^#(X1, X2))
1070.94/297.05	     , take^#(ok(X1), ok(X2)) -> c_20(take^#(X1, X2))
1070.94/297.05	     , length^#(mark(X)) -> c_21(length^#(X))
1070.94/297.05	     , length^#(ok(X)) -> c_22(length^#(X))
1070.94/297.05	     , s^#(ok(X)) -> c_14(s^#(X))
1070.94/297.05	     , top^#(mark(X)) -> c_33(top^#(proper(X)))
1070.94/297.05	     , top^#(ok(X)) -> c_34(top^#(active(X))) }
1070.94/297.05	   Strict Trs:
1070.94/297.05	     { active(eq(X, Y)) -> mark(false())
1070.94/297.05	     , active(eq(0(), 0())) -> mark(true())
1070.94/297.05	     , active(eq(s(X), s(Y))) -> mark(eq(X, Y))
1070.94/297.05	     , active(inf(X)) -> mark(cons(X, inf(s(X))))
1070.94/297.05	     , active(inf(X)) -> inf(active(X))
1070.94/297.05	     , active(take(X1, X2)) -> take(X1, active(X2))
1070.94/297.05	     , active(take(X1, X2)) -> take(active(X1), X2)
1070.94/297.05	     , active(take(0(), X)) -> mark(nil())
1070.94/297.05	     , active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L)))
1070.94/297.05	     , active(length(X)) -> length(active(X))
1070.94/297.05	     , active(length(cons(X, L))) -> mark(s(length(L)))
1070.94/297.05	     , active(length(nil())) -> mark(0())
1070.94/297.05	     , eq(ok(X1), ok(X2)) -> ok(eq(X1, X2))
1070.94/297.05	     , s(ok(X)) -> ok(s(X))
1070.94/297.05	     , inf(mark(X)) -> mark(inf(X))
1070.94/297.05	     , inf(ok(X)) -> ok(inf(X))
1070.94/297.05	     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
1070.94/297.05	     , take(X1, mark(X2)) -> mark(take(X1, X2))
1070.94/297.05	     , take(mark(X1), X2) -> mark(take(X1, X2))
1070.94/297.05	     , take(ok(X1), ok(X2)) -> ok(take(X1, X2))
1070.94/297.05	     , length(mark(X)) -> mark(length(X))
1070.94/297.05	     , length(ok(X)) -> ok(length(X))
1070.94/297.05	     , proper(eq(X1, X2)) -> eq(proper(X1), proper(X2))
1070.94/297.05	     , proper(0()) -> ok(0())
1070.94/297.05	     , proper(true()) -> ok(true())
1070.94/297.05	     , proper(s(X)) -> s(proper(X))
1070.94/297.05	     , proper(false()) -> ok(false())
1070.94/297.05	     , proper(inf(X)) -> inf(proper(X))
1070.94/297.05	     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
1070.94/297.05	     , proper(take(X1, X2)) -> take(proper(X1), proper(X2))
1070.94/297.05	     , proper(nil()) -> ok(nil())
1070.94/297.05	     , proper(length(X)) -> length(proper(X))
1070.94/297.05	     , top(mark(X)) -> top(proper(X))
1070.94/297.05	     , top(ok(X)) -> top(active(X)) }
1070.94/297.05	   Weak DPs:
1070.94/297.05	     { proper^#(0()) -> c_24()
1070.94/297.05	     , proper^#(true()) -> c_25()
1070.94/297.05	     , proper^#(false()) -> c_27()
1070.94/297.05	     , proper^#(nil()) -> c_31() }
1070.94/297.05	   Obligation:
1070.94/297.05	     runtime complexity
1070.94/297.05	   Answer:
1070.94/297.05	     MAYBE
1070.94/297.05	   
1070.94/297.05	   Empty strict component of the problem is NOT empty.
1070.94/297.05	
1070.94/297.05	
1070.94/297.05	Arrrr..
1071.30/297.36	EOF