MAYBE 821.50/297.06 MAYBE 821.50/297.06 821.50/297.06 We are left with following problem, upon which TcT provides the 821.50/297.06 certificate MAYBE. 821.50/297.06 821.50/297.06 Strict Trs: 821.50/297.06 { max(nil()) -> 0() 821.50/297.06 , max(cons(x, nil())) -> x 821.50/297.06 , max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs) 821.50/297.06 , if1(true(), x, y, xs) -> max(cons(x, xs)) 821.50/297.06 , if1(false(), x, y, xs) -> max(cons(y, xs)) 821.50/297.06 , ge(x, 0()) -> true() 821.50/297.06 , ge(0(), s(x)) -> false() 821.50/297.06 , ge(s(x), s(y)) -> ge(x, y) 821.50/297.06 , del(x, nil()) -> nil() 821.50/297.06 , del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) 821.50/297.06 , if2(true(), x, y, xs) -> xs 821.50/297.06 , if2(false(), x, y, xs) -> cons(y, del(x, xs)) 821.50/297.06 , eq(0(), 0()) -> true() 821.50/297.06 , eq(0(), s(y)) -> false() 821.50/297.06 , eq(s(x), 0()) -> false() 821.50/297.06 , eq(s(x), s(y)) -> eq(x, y) 821.50/297.06 , sort(nil()) -> nil() 821.50/297.06 , sort(cons(x, xs)) -> 821.50/297.06 cons(max(cons(x, xs)), sort(del(max(cons(x, xs)), cons(x, xs)))) } 821.50/297.06 Obligation: 821.50/297.06 runtime complexity 821.50/297.06 Answer: 821.50/297.06 MAYBE 821.50/297.06 821.50/297.06 None of the processors succeeded. 821.50/297.06 821.50/297.06 Details of failed attempt(s): 821.50/297.06 ----------------------------- 821.50/297.06 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 821.50/297.06 following reason: 821.50/297.06 821.50/297.06 Computation stopped due to timeout after 297.0 seconds. 821.50/297.06 821.50/297.06 2) 'Best' failed due to the following reason: 821.50/297.06 821.50/297.06 None of the processors succeeded. 821.50/297.06 821.50/297.06 Details of failed attempt(s): 821.50/297.06 ----------------------------- 821.50/297.06 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 821.50/297.06 seconds)' failed due to the following reason: 821.50/297.06 821.50/297.06 Computation stopped due to timeout after 148.0 seconds. 821.50/297.06 821.50/297.06 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 821.50/297.06 failed due to the following reason: 821.50/297.06 821.50/297.06 None of the processors succeeded. 821.50/297.06 821.50/297.06 Details of failed attempt(s): 821.50/297.06 ----------------------------- 821.50/297.06 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 821.50/297.06 failed due to the following reason: 821.50/297.06 821.50/297.06 match-boundness of the problem could not be verified. 821.50/297.06 821.50/297.06 2) 'Bounds with minimal-enrichment and initial automaton 'match'' 821.50/297.06 failed due to the following reason: 821.50/297.06 821.50/297.06 match-boundness of the problem could not be verified. 821.50/297.06 821.50/297.06 821.50/297.06 3) 'Best' failed due to the following reason: 821.50/297.06 821.50/297.06 None of the processors succeeded. 821.50/297.06 821.50/297.06 Details of failed attempt(s): 821.50/297.06 ----------------------------- 821.50/297.06 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 821.50/297.06 to the following reason: 821.50/297.06 821.50/297.06 The processor is inapplicable, reason: 821.50/297.06 Processor only applicable for innermost runtime complexity analysis 821.50/297.06 821.50/297.06 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 821.50/297.06 following reason: 821.50/297.06 821.50/297.06 The processor is inapplicable, reason: 821.50/297.06 Processor only applicable for innermost runtime complexity analysis 821.50/297.06 821.50/297.06 821.50/297.06 821.50/297.06 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 821.50/297.06 the following reason: 821.50/297.06 821.50/297.06 We add the following weak dependency pairs: 821.50/297.06 821.50/297.06 Strict DPs: 821.50/297.06 { max^#(nil()) -> c_1() 821.50/297.06 , max^#(cons(x, nil())) -> c_2(x) 821.50/297.06 , max^#(cons(x, cons(y, xs))) -> c_3(if1^#(ge(x, y), x, y, xs)) 821.50/297.06 , if1^#(true(), x, y, xs) -> c_4(max^#(cons(x, xs))) 821.50/297.06 , if1^#(false(), x, y, xs) -> c_5(max^#(cons(y, xs))) 821.50/297.06 , ge^#(x, 0()) -> c_6() 821.50/297.06 , ge^#(0(), s(x)) -> c_7() 821.50/297.06 , ge^#(s(x), s(y)) -> c_8(ge^#(x, y)) 821.50/297.06 , del^#(x, nil()) -> c_9() 821.50/297.06 , del^#(x, cons(y, xs)) -> c_10(if2^#(eq(x, y), x, y, xs)) 821.50/297.06 , if2^#(true(), x, y, xs) -> c_11(xs) 821.50/297.06 , if2^#(false(), x, y, xs) -> c_12(y, del^#(x, xs)) 821.50/297.06 , eq^#(0(), 0()) -> c_13() 821.50/297.06 , eq^#(0(), s(y)) -> c_14() 821.50/297.06 , eq^#(s(x), 0()) -> c_15() 821.50/297.06 , eq^#(s(x), s(y)) -> c_16(eq^#(x, y)) 821.50/297.06 , sort^#(nil()) -> c_17() 821.50/297.06 , sort^#(cons(x, xs)) -> 821.50/297.06 c_18(max^#(cons(x, xs)), 821.50/297.06 sort^#(del(max(cons(x, xs)), cons(x, xs)))) } 821.50/297.06 821.50/297.06 and mark the set of starting terms. 821.50/297.06 821.50/297.06 We are left with following problem, upon which TcT provides the 821.50/297.06 certificate MAYBE. 821.50/297.06 821.50/297.06 Strict DPs: 821.50/297.06 { max^#(nil()) -> c_1() 821.50/297.06 , max^#(cons(x, nil())) -> c_2(x) 821.50/297.06 , max^#(cons(x, cons(y, xs))) -> c_3(if1^#(ge(x, y), x, y, xs)) 821.50/297.06 , if1^#(true(), x, y, xs) -> c_4(max^#(cons(x, xs))) 821.50/297.06 , if1^#(false(), x, y, xs) -> c_5(max^#(cons(y, xs))) 821.50/297.06 , ge^#(x, 0()) -> c_6() 821.50/297.06 , ge^#(0(), s(x)) -> c_7() 821.50/297.06 , ge^#(s(x), s(y)) -> c_8(ge^#(x, y)) 821.50/297.06 , del^#(x, nil()) -> c_9() 821.50/297.06 , del^#(x, cons(y, xs)) -> c_10(if2^#(eq(x, y), x, y, xs)) 821.50/297.06 , if2^#(true(), x, y, xs) -> c_11(xs) 821.50/297.06 , if2^#(false(), x, y, xs) -> c_12(y, del^#(x, xs)) 821.50/297.06 , eq^#(0(), 0()) -> c_13() 821.50/297.06 , eq^#(0(), s(y)) -> c_14() 821.50/297.06 , eq^#(s(x), 0()) -> c_15() 821.50/297.06 , eq^#(s(x), s(y)) -> c_16(eq^#(x, y)) 821.50/297.06 , sort^#(nil()) -> c_17() 821.50/297.06 , sort^#(cons(x, xs)) -> 821.50/297.06 c_18(max^#(cons(x, xs)), 821.50/297.06 sort^#(del(max(cons(x, xs)), cons(x, xs)))) } 821.50/297.06 Strict Trs: 821.50/297.06 { max(nil()) -> 0() 821.50/297.06 , max(cons(x, nil())) -> x 821.50/297.06 , max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs) 821.50/297.06 , if1(true(), x, y, xs) -> max(cons(x, xs)) 821.50/297.06 , if1(false(), x, y, xs) -> max(cons(y, xs)) 821.50/297.06 , ge(x, 0()) -> true() 821.50/297.06 , ge(0(), s(x)) -> false() 821.50/297.06 , ge(s(x), s(y)) -> ge(x, y) 821.50/297.06 , del(x, nil()) -> nil() 821.50/297.06 , del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) 821.50/297.06 , if2(true(), x, y, xs) -> xs 821.50/297.06 , if2(false(), x, y, xs) -> cons(y, del(x, xs)) 821.50/297.06 , eq(0(), 0()) -> true() 821.50/297.06 , eq(0(), s(y)) -> false() 821.50/297.06 , eq(s(x), 0()) -> false() 821.50/297.06 , eq(s(x), s(y)) -> eq(x, y) 821.50/297.06 , sort(nil()) -> nil() 821.50/297.06 , sort(cons(x, xs)) -> 821.50/297.06 cons(max(cons(x, xs)), sort(del(max(cons(x, xs)), cons(x, xs)))) } 821.50/297.06 Obligation: 821.50/297.06 runtime complexity 821.50/297.06 Answer: 821.50/297.06 MAYBE 821.50/297.06 821.50/297.06 We estimate the number of application of {1,6,7,9,13,14,15,17} by 821.50/297.06 applications of Pre({1,6,7,9,13,14,15,17}) = {2,8,11,12,16,18}. 821.50/297.06 Here rules are labeled as follows: 821.50/297.06 821.50/297.06 DPs: 821.50/297.06 { 1: max^#(nil()) -> c_1() 821.50/297.06 , 2: max^#(cons(x, nil())) -> c_2(x) 821.50/297.06 , 3: max^#(cons(x, cons(y, xs))) -> c_3(if1^#(ge(x, y), x, y, xs)) 821.50/297.06 , 4: if1^#(true(), x, y, xs) -> c_4(max^#(cons(x, xs))) 821.50/297.06 , 5: if1^#(false(), x, y, xs) -> c_5(max^#(cons(y, xs))) 821.50/297.06 , 6: ge^#(x, 0()) -> c_6() 821.50/297.06 , 7: ge^#(0(), s(x)) -> c_7() 821.50/297.06 , 8: ge^#(s(x), s(y)) -> c_8(ge^#(x, y)) 821.50/297.06 , 9: del^#(x, nil()) -> c_9() 821.50/297.06 , 10: del^#(x, cons(y, xs)) -> c_10(if2^#(eq(x, y), x, y, xs)) 821.50/297.06 , 11: if2^#(true(), x, y, xs) -> c_11(xs) 821.50/297.06 , 12: if2^#(false(), x, y, xs) -> c_12(y, del^#(x, xs)) 821.50/297.06 , 13: eq^#(0(), 0()) -> c_13() 821.50/297.06 , 14: eq^#(0(), s(y)) -> c_14() 821.50/297.06 , 15: eq^#(s(x), 0()) -> c_15() 821.50/297.06 , 16: eq^#(s(x), s(y)) -> c_16(eq^#(x, y)) 821.50/297.06 , 17: sort^#(nil()) -> c_17() 821.50/297.06 , 18: sort^#(cons(x, xs)) -> 821.50/297.06 c_18(max^#(cons(x, xs)), 821.50/297.06 sort^#(del(max(cons(x, xs)), cons(x, xs)))) } 821.50/297.06 821.50/297.06 We are left with following problem, upon which TcT provides the 821.50/297.06 certificate MAYBE. 821.50/297.06 821.50/297.06 Strict DPs: 821.50/297.06 { max^#(cons(x, nil())) -> c_2(x) 821.50/297.06 , max^#(cons(x, cons(y, xs))) -> c_3(if1^#(ge(x, y), x, y, xs)) 821.50/297.06 , if1^#(true(), x, y, xs) -> c_4(max^#(cons(x, xs))) 821.50/297.06 , if1^#(false(), x, y, xs) -> c_5(max^#(cons(y, xs))) 821.50/297.06 , ge^#(s(x), s(y)) -> c_8(ge^#(x, y)) 821.50/297.06 , del^#(x, cons(y, xs)) -> c_10(if2^#(eq(x, y), x, y, xs)) 821.50/297.06 , if2^#(true(), x, y, xs) -> c_11(xs) 821.50/297.06 , if2^#(false(), x, y, xs) -> c_12(y, del^#(x, xs)) 821.50/297.06 , eq^#(s(x), s(y)) -> c_16(eq^#(x, y)) 821.50/297.06 , sort^#(cons(x, xs)) -> 821.50/297.06 c_18(max^#(cons(x, xs)), 821.50/297.06 sort^#(del(max(cons(x, xs)), cons(x, xs)))) } 821.50/297.06 Strict Trs: 821.50/297.06 { max(nil()) -> 0() 821.50/297.06 , max(cons(x, nil())) -> x 821.50/297.06 , max(cons(x, cons(y, xs))) -> if1(ge(x, y), x, y, xs) 821.50/297.06 , if1(true(), x, y, xs) -> max(cons(x, xs)) 821.50/297.06 , if1(false(), x, y, xs) -> max(cons(y, xs)) 821.50/297.06 , ge(x, 0()) -> true() 821.50/297.06 , ge(0(), s(x)) -> false() 821.50/297.06 , ge(s(x), s(y)) -> ge(x, y) 821.50/297.06 , del(x, nil()) -> nil() 821.50/297.06 , del(x, cons(y, xs)) -> if2(eq(x, y), x, y, xs) 821.50/297.06 , if2(true(), x, y, xs) -> xs 821.50/297.06 , if2(false(), x, y, xs) -> cons(y, del(x, xs)) 821.50/297.06 , eq(0(), 0()) -> true() 821.50/297.06 , eq(0(), s(y)) -> false() 821.50/297.06 , eq(s(x), 0()) -> false() 821.50/297.06 , eq(s(x), s(y)) -> eq(x, y) 821.50/297.06 , sort(nil()) -> nil() 821.50/297.06 , sort(cons(x, xs)) -> 821.50/297.06 cons(max(cons(x, xs)), sort(del(max(cons(x, xs)), cons(x, xs)))) } 821.50/297.06 Weak DPs: 821.50/297.06 { max^#(nil()) -> c_1() 821.50/297.06 , ge^#(x, 0()) -> c_6() 821.50/297.06 , ge^#(0(), s(x)) -> c_7() 821.50/297.06 , del^#(x, nil()) -> c_9() 821.50/297.06 , eq^#(0(), 0()) -> c_13() 821.50/297.06 , eq^#(0(), s(y)) -> c_14() 821.50/297.06 , eq^#(s(x), 0()) -> c_15() 821.50/297.06 , sort^#(nil()) -> c_17() } 821.50/297.06 Obligation: 821.50/297.06 runtime complexity 821.50/297.06 Answer: 821.50/297.06 MAYBE 821.50/297.06 821.50/297.06 Empty strict component of the problem is NOT empty. 821.50/297.06 821.50/297.06 821.50/297.06 Arrrr.. 821.74/297.27 EOF