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