MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { double(0()) -> 0() , double(s(x)) -> s(s(double(x))) , del(x, nil()) -> nil() , del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs) , if(true(), x, y, xs) -> xs , if(false(), x, y, xs) -> cons(y, del(x, xs)) , eq(0(), 0()) -> true() , eq(0(), s(y)) -> false() , eq(s(x), 0()) -> false() , eq(s(x), s(y)) -> eq(x, y) , first(nil()) -> 0() , first(cons(x, xs)) -> x , doublelist(nil()) -> nil() , doublelist(cons(x, xs)) -> cons(double(x), doublelist(del(first(cons(x, xs)), cons(x, xs)))) } 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: Computation stopped due to timeout after 30.0 seconds. 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: { double^#(0()) -> c_1() , double^#(s(x)) -> c_2(double^#(x)) , del^#(x, nil()) -> c_3() , del^#(x, cons(y, xs)) -> c_4(if^#(eq(x, y), x, y, xs)) , if^#(true(), x, y, xs) -> c_5(xs) , if^#(false(), x, y, xs) -> c_6(y, del^#(x, xs)) , eq^#(0(), 0()) -> c_7() , eq^#(0(), s(y)) -> c_8() , eq^#(s(x), 0()) -> c_9() , eq^#(s(x), s(y)) -> c_10(eq^#(x, y)) , first^#(nil()) -> c_11() , first^#(cons(x, xs)) -> c_12(x) , doublelist^#(nil()) -> c_13() , doublelist^#(cons(x, xs)) -> c_14(double^#(x), doublelist^#(del(first(cons(x, xs)), cons(x, xs)))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { double^#(0()) -> c_1() , double^#(s(x)) -> c_2(double^#(x)) , del^#(x, nil()) -> c_3() , del^#(x, cons(y, xs)) -> c_4(if^#(eq(x, y), x, y, xs)) , if^#(true(), x, y, xs) -> c_5(xs) , if^#(false(), x, y, xs) -> c_6(y, del^#(x, xs)) , eq^#(0(), 0()) -> c_7() , eq^#(0(), s(y)) -> c_8() , eq^#(s(x), 0()) -> c_9() , eq^#(s(x), s(y)) -> c_10(eq^#(x, y)) , first^#(nil()) -> c_11() , first^#(cons(x, xs)) -> c_12(x) , doublelist^#(nil()) -> c_13() , doublelist^#(cons(x, xs)) -> c_14(double^#(x), doublelist^#(del(first(cons(x, xs)), cons(x, xs)))) } Strict Trs: { double(0()) -> 0() , double(s(x)) -> s(s(double(x))) , del(x, nil()) -> nil() , del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs) , if(true(), x, y, xs) -> xs , if(false(), x, y, xs) -> cons(y, del(x, xs)) , eq(0(), 0()) -> true() , eq(0(), s(y)) -> false() , eq(s(x), 0()) -> false() , eq(s(x), s(y)) -> eq(x, y) , first(nil()) -> 0() , first(cons(x, xs)) -> x , doublelist(nil()) -> nil() , doublelist(cons(x, xs)) -> cons(double(x), doublelist(del(first(cons(x, xs)), cons(x, xs)))) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {1,3,7,8,9,11,13} by applications of Pre({1,3,7,8,9,11,13}) = {2,5,6,10,12,14}. Here rules are labeled as follows: DPs: { 1: double^#(0()) -> c_1() , 2: double^#(s(x)) -> c_2(double^#(x)) , 3: del^#(x, nil()) -> c_3() , 4: del^#(x, cons(y, xs)) -> c_4(if^#(eq(x, y), x, y, xs)) , 5: if^#(true(), x, y, xs) -> c_5(xs) , 6: if^#(false(), x, y, xs) -> c_6(y, del^#(x, xs)) , 7: eq^#(0(), 0()) -> c_7() , 8: eq^#(0(), s(y)) -> c_8() , 9: eq^#(s(x), 0()) -> c_9() , 10: eq^#(s(x), s(y)) -> c_10(eq^#(x, y)) , 11: first^#(nil()) -> c_11() , 12: first^#(cons(x, xs)) -> c_12(x) , 13: doublelist^#(nil()) -> c_13() , 14: doublelist^#(cons(x, xs)) -> c_14(double^#(x), doublelist^#(del(first(cons(x, xs)), cons(x, xs)))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { double^#(s(x)) -> c_2(double^#(x)) , del^#(x, cons(y, xs)) -> c_4(if^#(eq(x, y), x, y, xs)) , if^#(true(), x, y, xs) -> c_5(xs) , if^#(false(), x, y, xs) -> c_6(y, del^#(x, xs)) , eq^#(s(x), s(y)) -> c_10(eq^#(x, y)) , first^#(cons(x, xs)) -> c_12(x) , doublelist^#(cons(x, xs)) -> c_14(double^#(x), doublelist^#(del(first(cons(x, xs)), cons(x, xs)))) } Strict Trs: { double(0()) -> 0() , double(s(x)) -> s(s(double(x))) , del(x, nil()) -> nil() , del(x, cons(y, xs)) -> if(eq(x, y), x, y, xs) , if(true(), x, y, xs) -> xs , if(false(), x, y, xs) -> cons(y, del(x, xs)) , eq(0(), 0()) -> true() , eq(0(), s(y)) -> false() , eq(s(x), 0()) -> false() , eq(s(x), s(y)) -> eq(x, y) , first(nil()) -> 0() , first(cons(x, xs)) -> x , doublelist(nil()) -> nil() , doublelist(cons(x, xs)) -> cons(double(x), doublelist(del(first(cons(x, xs)), cons(x, xs)))) } Weak DPs: { double^#(0()) -> c_1() , del^#(x, nil()) -> c_3() , eq^#(0(), 0()) -> c_7() , eq^#(0(), s(y)) -> c_8() , eq^#(s(x), 0()) -> c_9() , first^#(nil()) -> c_11() , doublelist^#(nil()) -> c_13() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..