MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { dbl(0()) -> 0() , dbl(s(X)) -> s(s(dbl(X))) , dbls(nil()) -> nil() , dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y)) , sel(0(), cons(X, Y)) -> X , sel(s(X), cons(Y, Z)) -> sel(X, Z) , indx(nil(), X) -> nil() , indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z)) , from(X) -> cons(X, from(s(X))) , dbl1(0()) -> 01() , dbl1(s(X)) -> s1(s1(dbl1(X))) , sel1(0(), cons(X, Y)) -> X , sel1(s(X), cons(Y, Z)) -> sel1(X, Z) , quote(dbl(X)) -> dbl1(X) , quote(0()) -> 01() , quote(s(X)) -> s1(quote(X)) , quote(sel(X, Y)) -> sel1(X, Y) } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 60.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Fastest' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { dbl^#(0()) -> c_1() , dbl^#(s(X)) -> c_2(dbl^#(X)) , dbls^#(nil()) -> c_3() , dbls^#(cons(X, Y)) -> c_4(dbl^#(X), dbls^#(Y)) , sel^#(0(), cons(X, Y)) -> c_5(X) , sel^#(s(X), cons(Y, Z)) -> c_6(sel^#(X, Z)) , indx^#(nil(), X) -> c_7() , indx^#(cons(X, Y), Z) -> c_8(sel^#(X, Z), indx^#(Y, Z)) , from^#(X) -> c_9(X, from^#(s(X))) , dbl1^#(0()) -> c_10() , dbl1^#(s(X)) -> c_11(dbl1^#(X)) , sel1^#(0(), cons(X, Y)) -> c_12(X) , sel1^#(s(X), cons(Y, Z)) -> c_13(sel1^#(X, Z)) , quote^#(dbl(X)) -> c_14(dbl1^#(X)) , quote^#(0()) -> c_15() , quote^#(s(X)) -> c_16(quote^#(X)) , quote^#(sel(X, Y)) -> c_17(sel1^#(X, Y)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { dbl^#(0()) -> c_1() , dbl^#(s(X)) -> c_2(dbl^#(X)) , dbls^#(nil()) -> c_3() , dbls^#(cons(X, Y)) -> c_4(dbl^#(X), dbls^#(Y)) , sel^#(0(), cons(X, Y)) -> c_5(X) , sel^#(s(X), cons(Y, Z)) -> c_6(sel^#(X, Z)) , indx^#(nil(), X) -> c_7() , indx^#(cons(X, Y), Z) -> c_8(sel^#(X, Z), indx^#(Y, Z)) , from^#(X) -> c_9(X, from^#(s(X))) , dbl1^#(0()) -> c_10() , dbl1^#(s(X)) -> c_11(dbl1^#(X)) , sel1^#(0(), cons(X, Y)) -> c_12(X) , sel1^#(s(X), cons(Y, Z)) -> c_13(sel1^#(X, Z)) , quote^#(dbl(X)) -> c_14(dbl1^#(X)) , quote^#(0()) -> c_15() , quote^#(s(X)) -> c_16(quote^#(X)) , quote^#(sel(X, Y)) -> c_17(sel1^#(X, Y)) } Strict Trs: { dbl(0()) -> 0() , dbl(s(X)) -> s(s(dbl(X))) , dbls(nil()) -> nil() , dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y)) , sel(0(), cons(X, Y)) -> X , sel(s(X), cons(Y, Z)) -> sel(X, Z) , indx(nil(), X) -> nil() , indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z)) , from(X) -> cons(X, from(s(X))) , dbl1(0()) -> 01() , dbl1(s(X)) -> s1(s1(dbl1(X))) , sel1(0(), cons(X, Y)) -> X , sel1(s(X), cons(Y, Z)) -> sel1(X, Z) , quote(dbl(X)) -> dbl1(X) , quote(0()) -> 01() , quote(s(X)) -> s1(quote(X)) , quote(sel(X, Y)) -> sel1(X, Y) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {1,3,7,10,15} by applications of Pre({1,3,7,10,15}) = {2,4,5,8,9,11,12,14,16}. Here rules are labeled as follows: DPs: { 1: dbl^#(0()) -> c_1() , 2: dbl^#(s(X)) -> c_2(dbl^#(X)) , 3: dbls^#(nil()) -> c_3() , 4: dbls^#(cons(X, Y)) -> c_4(dbl^#(X), dbls^#(Y)) , 5: sel^#(0(), cons(X, Y)) -> c_5(X) , 6: sel^#(s(X), cons(Y, Z)) -> c_6(sel^#(X, Z)) , 7: indx^#(nil(), X) -> c_7() , 8: indx^#(cons(X, Y), Z) -> c_8(sel^#(X, Z), indx^#(Y, Z)) , 9: from^#(X) -> c_9(X, from^#(s(X))) , 10: dbl1^#(0()) -> c_10() , 11: dbl1^#(s(X)) -> c_11(dbl1^#(X)) , 12: sel1^#(0(), cons(X, Y)) -> c_12(X) , 13: sel1^#(s(X), cons(Y, Z)) -> c_13(sel1^#(X, Z)) , 14: quote^#(dbl(X)) -> c_14(dbl1^#(X)) , 15: quote^#(0()) -> c_15() , 16: quote^#(s(X)) -> c_16(quote^#(X)) , 17: quote^#(sel(X, Y)) -> c_17(sel1^#(X, Y)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { dbl^#(s(X)) -> c_2(dbl^#(X)) , dbls^#(cons(X, Y)) -> c_4(dbl^#(X), dbls^#(Y)) , sel^#(0(), cons(X, Y)) -> c_5(X) , sel^#(s(X), cons(Y, Z)) -> c_6(sel^#(X, Z)) , indx^#(cons(X, Y), Z) -> c_8(sel^#(X, Z), indx^#(Y, Z)) , from^#(X) -> c_9(X, from^#(s(X))) , dbl1^#(s(X)) -> c_11(dbl1^#(X)) , sel1^#(0(), cons(X, Y)) -> c_12(X) , sel1^#(s(X), cons(Y, Z)) -> c_13(sel1^#(X, Z)) , quote^#(dbl(X)) -> c_14(dbl1^#(X)) , quote^#(s(X)) -> c_16(quote^#(X)) , quote^#(sel(X, Y)) -> c_17(sel1^#(X, Y)) } Strict Trs: { dbl(0()) -> 0() , dbl(s(X)) -> s(s(dbl(X))) , dbls(nil()) -> nil() , dbls(cons(X, Y)) -> cons(dbl(X), dbls(Y)) , sel(0(), cons(X, Y)) -> X , sel(s(X), cons(Y, Z)) -> sel(X, Z) , indx(nil(), X) -> nil() , indx(cons(X, Y), Z) -> cons(sel(X, Z), indx(Y, Z)) , from(X) -> cons(X, from(s(X))) , dbl1(0()) -> 01() , dbl1(s(X)) -> s1(s1(dbl1(X))) , sel1(0(), cons(X, Y)) -> X , sel1(s(X), cons(Y, Z)) -> sel1(X, Z) , quote(dbl(X)) -> dbl1(X) , quote(0()) -> 01() , quote(s(X)) -> s1(quote(X)) , quote(sel(X, Y)) -> sel1(X, Y) } Weak DPs: { dbl^#(0()) -> c_1() , dbls^#(nil()) -> c_3() , indx^#(nil(), X) -> c_7() , dbl1^#(0()) -> c_10() , quote^#(0()) -> c_15() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..