MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { fstsplit(0(), x) -> nil() , fstsplit(s(n), nil()) -> nil() , fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t)) , sndsplit(0(), x) -> x , sndsplit(s(n), nil()) -> nil() , sndsplit(s(n), cons(h, t)) -> sndsplit(n, t) , empty(nil()) -> true() , empty(cons(h, t)) -> false() , leq(0(), m) -> true() , leq(s(n), 0()) -> false() , leq(s(n), s(m)) -> leq(n, m) , length(nil()) -> 0() , length(cons(h, t)) -> s(length(t)) , app(nil(), x) -> x , app(cons(h, t), x) -> cons(h, app(t, x)) , map_f(pid, nil()) -> nil() , map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t)) , process(store, m) -> if1(store, m, leq(m, length(store))) , if1(store, m, true()) -> if2(store, m, empty(fstsplit(m, store))) , if1(store, m, false()) -> if3(store, m, empty(fstsplit(m, app(map_f(self(), nil()), store)))) , if2(store, m, false()) -> process(app(map_f(self(), nil()), sndsplit(m, store)), m) , if3(store, m, false()) -> process(sndsplit(m, app(map_f(self(), nil()), store)), m) } 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: { fstsplit^#(0(), x) -> c_1() , fstsplit^#(s(n), nil()) -> c_2() , fstsplit^#(s(n), cons(h, t)) -> c_3(h, fstsplit^#(n, t)) , sndsplit^#(0(), x) -> c_4(x) , sndsplit^#(s(n), nil()) -> c_5() , sndsplit^#(s(n), cons(h, t)) -> c_6(sndsplit^#(n, t)) , empty^#(nil()) -> c_7() , empty^#(cons(h, t)) -> c_8() , leq^#(0(), m) -> c_9() , leq^#(s(n), 0()) -> c_10() , leq^#(s(n), s(m)) -> c_11(leq^#(n, m)) , length^#(nil()) -> c_12() , length^#(cons(h, t)) -> c_13(length^#(t)) , app^#(nil(), x) -> c_14(x) , app^#(cons(h, t), x) -> c_15(h, app^#(t, x)) , map_f^#(pid, nil()) -> c_16() , map_f^#(pid, cons(h, t)) -> c_17(app^#(f(pid, h), map_f(pid, t))) , process^#(store, m) -> c_18(if1^#(store, m, leq(m, length(store)))) , if1^#(store, m, true()) -> c_19(if2^#(store, m, empty(fstsplit(m, store)))) , if1^#(store, m, false()) -> c_20(if3^#(store, m, empty(fstsplit(m, app(map_f(self(), nil()), store))))) , if2^#(store, m, false()) -> c_21(process^#(app(map_f(self(), nil()), sndsplit(m, store)), m)) , if3^#(store, m, false()) -> c_22(process^#(sndsplit(m, app(map_f(self(), nil()), store)), m)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fstsplit^#(0(), x) -> c_1() , fstsplit^#(s(n), nil()) -> c_2() , fstsplit^#(s(n), cons(h, t)) -> c_3(h, fstsplit^#(n, t)) , sndsplit^#(0(), x) -> c_4(x) , sndsplit^#(s(n), nil()) -> c_5() , sndsplit^#(s(n), cons(h, t)) -> c_6(sndsplit^#(n, t)) , empty^#(nil()) -> c_7() , empty^#(cons(h, t)) -> c_8() , leq^#(0(), m) -> c_9() , leq^#(s(n), 0()) -> c_10() , leq^#(s(n), s(m)) -> c_11(leq^#(n, m)) , length^#(nil()) -> c_12() , length^#(cons(h, t)) -> c_13(length^#(t)) , app^#(nil(), x) -> c_14(x) , app^#(cons(h, t), x) -> c_15(h, app^#(t, x)) , map_f^#(pid, nil()) -> c_16() , map_f^#(pid, cons(h, t)) -> c_17(app^#(f(pid, h), map_f(pid, t))) , process^#(store, m) -> c_18(if1^#(store, m, leq(m, length(store)))) , if1^#(store, m, true()) -> c_19(if2^#(store, m, empty(fstsplit(m, store)))) , if1^#(store, m, false()) -> c_20(if3^#(store, m, empty(fstsplit(m, app(map_f(self(), nil()), store))))) , if2^#(store, m, false()) -> c_21(process^#(app(map_f(self(), nil()), sndsplit(m, store)), m)) , if3^#(store, m, false()) -> c_22(process^#(sndsplit(m, app(map_f(self(), nil()), store)), m)) } Strict Trs: { fstsplit(0(), x) -> nil() , fstsplit(s(n), nil()) -> nil() , fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t)) , sndsplit(0(), x) -> x , sndsplit(s(n), nil()) -> nil() , sndsplit(s(n), cons(h, t)) -> sndsplit(n, t) , empty(nil()) -> true() , empty(cons(h, t)) -> false() , leq(0(), m) -> true() , leq(s(n), 0()) -> false() , leq(s(n), s(m)) -> leq(n, m) , length(nil()) -> 0() , length(cons(h, t)) -> s(length(t)) , app(nil(), x) -> x , app(cons(h, t), x) -> cons(h, app(t, x)) , map_f(pid, nil()) -> nil() , map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t)) , process(store, m) -> if1(store, m, leq(m, length(store))) , if1(store, m, true()) -> if2(store, m, empty(fstsplit(m, store))) , if1(store, m, false()) -> if3(store, m, empty(fstsplit(m, app(map_f(self(), nil()), store)))) , if2(store, m, false()) -> process(app(map_f(self(), nil()), sndsplit(m, store)), m) , if3(store, m, false()) -> process(sndsplit(m, app(map_f(self(), nil()), store)), m) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {1,2,5,7,8,9,10,12,16,17} by applications of Pre({1,2,5,7,8,9,10,12,16,17}) = {3,4,6,11,13,14,15}. Here rules are labeled as follows: DPs: { 1: fstsplit^#(0(), x) -> c_1() , 2: fstsplit^#(s(n), nil()) -> c_2() , 3: fstsplit^#(s(n), cons(h, t)) -> c_3(h, fstsplit^#(n, t)) , 4: sndsplit^#(0(), x) -> c_4(x) , 5: sndsplit^#(s(n), nil()) -> c_5() , 6: sndsplit^#(s(n), cons(h, t)) -> c_6(sndsplit^#(n, t)) , 7: empty^#(nil()) -> c_7() , 8: empty^#(cons(h, t)) -> c_8() , 9: leq^#(0(), m) -> c_9() , 10: leq^#(s(n), 0()) -> c_10() , 11: leq^#(s(n), s(m)) -> c_11(leq^#(n, m)) , 12: length^#(nil()) -> c_12() , 13: length^#(cons(h, t)) -> c_13(length^#(t)) , 14: app^#(nil(), x) -> c_14(x) , 15: app^#(cons(h, t), x) -> c_15(h, app^#(t, x)) , 16: map_f^#(pid, nil()) -> c_16() , 17: map_f^#(pid, cons(h, t)) -> c_17(app^#(f(pid, h), map_f(pid, t))) , 18: process^#(store, m) -> c_18(if1^#(store, m, leq(m, length(store)))) , 19: if1^#(store, m, true()) -> c_19(if2^#(store, m, empty(fstsplit(m, store)))) , 20: if1^#(store, m, false()) -> c_20(if3^#(store, m, empty(fstsplit(m, app(map_f(self(), nil()), store))))) , 21: if2^#(store, m, false()) -> c_21(process^#(app(map_f(self(), nil()), sndsplit(m, store)), m)) , 22: if3^#(store, m, false()) -> c_22(process^#(sndsplit(m, app(map_f(self(), nil()), store)), m)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fstsplit^#(s(n), cons(h, t)) -> c_3(h, fstsplit^#(n, t)) , sndsplit^#(0(), x) -> c_4(x) , sndsplit^#(s(n), cons(h, t)) -> c_6(sndsplit^#(n, t)) , leq^#(s(n), s(m)) -> c_11(leq^#(n, m)) , length^#(cons(h, t)) -> c_13(length^#(t)) , app^#(nil(), x) -> c_14(x) , app^#(cons(h, t), x) -> c_15(h, app^#(t, x)) , process^#(store, m) -> c_18(if1^#(store, m, leq(m, length(store)))) , if1^#(store, m, true()) -> c_19(if2^#(store, m, empty(fstsplit(m, store)))) , if1^#(store, m, false()) -> c_20(if3^#(store, m, empty(fstsplit(m, app(map_f(self(), nil()), store))))) , if2^#(store, m, false()) -> c_21(process^#(app(map_f(self(), nil()), sndsplit(m, store)), m)) , if3^#(store, m, false()) -> c_22(process^#(sndsplit(m, app(map_f(self(), nil()), store)), m)) } Strict Trs: { fstsplit(0(), x) -> nil() , fstsplit(s(n), nil()) -> nil() , fstsplit(s(n), cons(h, t)) -> cons(h, fstsplit(n, t)) , sndsplit(0(), x) -> x , sndsplit(s(n), nil()) -> nil() , sndsplit(s(n), cons(h, t)) -> sndsplit(n, t) , empty(nil()) -> true() , empty(cons(h, t)) -> false() , leq(0(), m) -> true() , leq(s(n), 0()) -> false() , leq(s(n), s(m)) -> leq(n, m) , length(nil()) -> 0() , length(cons(h, t)) -> s(length(t)) , app(nil(), x) -> x , app(cons(h, t), x) -> cons(h, app(t, x)) , map_f(pid, nil()) -> nil() , map_f(pid, cons(h, t)) -> app(f(pid, h), map_f(pid, t)) , process(store, m) -> if1(store, m, leq(m, length(store))) , if1(store, m, true()) -> if2(store, m, empty(fstsplit(m, store))) , if1(store, m, false()) -> if3(store, m, empty(fstsplit(m, app(map_f(self(), nil()), store)))) , if2(store, m, false()) -> process(app(map_f(self(), nil()), sndsplit(m, store)), m) , if3(store, m, false()) -> process(sndsplit(m, app(map_f(self(), nil()), store)), m) } Weak DPs: { fstsplit^#(0(), x) -> c_1() , fstsplit^#(s(n), nil()) -> c_2() , sndsplit^#(s(n), nil()) -> c_5() , empty^#(nil()) -> c_7() , empty^#(cons(h, t)) -> c_8() , leq^#(0(), m) -> c_9() , leq^#(s(n), 0()) -> c_10() , length^#(nil()) -> c_12() , map_f^#(pid, nil()) -> c_16() , map_f^#(pid, cons(h, t)) -> c_17(app^#(f(pid, h), map_f(pid, t))) } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..