MAYBE 107.68/31.87 MAYBE 107.68/31.87 107.68/31.87 We are left with following problem, upon which TcT provides the 107.68/31.87 certificate MAYBE. 107.68/31.87 107.68/31.87 Strict Trs: 107.68/31.87 { dbl(X) -> n__dbl(X) 107.68/31.87 , dbl(0()) -> 0() 107.68/31.87 , dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) 107.68/31.87 , s(X) -> n__s(X) 107.68/31.87 , activate(X) -> X 107.68/31.87 , activate(n__s(X)) -> s(X) 107.68/31.87 , activate(n__dbl(X)) -> dbl(X) 107.68/31.87 , activate(n__dbls(X)) -> dbls(X) 107.68/31.87 , activate(n__sel(X1, X2)) -> sel(X1, X2) 107.68/31.87 , activate(n__indx(X1, X2)) -> indx(X1, X2) 107.68/31.87 , activate(n__from(X)) -> from(X) 107.68/31.87 , dbls(X) -> n__dbls(X) 107.68/31.87 , dbls(nil()) -> nil() 107.68/31.87 , dbls(cons(X, Y)) -> 107.68/31.87 cons(n__dbl(activate(X)), n__dbls(activate(Y))) 107.68/31.87 , sel(X1, X2) -> n__sel(X1, X2) 107.68/31.87 , sel(0(), cons(X, Y)) -> activate(X) 107.68/31.87 , sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z)) 107.68/31.87 , indx(X1, X2) -> n__indx(X1, X2) 107.68/31.87 , indx(nil(), X) -> nil() 107.68/31.87 , indx(cons(X, Y), Z) -> 107.68/31.87 cons(n__sel(activate(X), activate(Z)), 107.68/31.87 n__indx(activate(Y), activate(Z))) 107.68/31.87 , from(X) -> cons(activate(X), n__from(n__s(activate(X)))) 107.68/31.87 , from(X) -> n__from(X) 107.68/31.87 , dbl1(0()) -> 01() 107.68/31.87 , dbl1(s(X)) -> s1(s1(dbl1(activate(X)))) 107.68/31.87 , sel1(0(), cons(X, Y)) -> activate(X) 107.68/31.87 , sel1(s(X), cons(Y, Z)) -> sel1(activate(X), activate(Z)) 107.68/31.87 , quote(dbl(X)) -> dbl1(X) 107.68/31.87 , quote(0()) -> 01() 107.68/31.87 , quote(s(X)) -> s1(quote(activate(X))) 107.68/31.87 , quote(sel(X, Y)) -> sel1(X, Y) } 107.68/31.87 Obligation: 107.68/31.87 innermost runtime complexity 107.68/31.87 Answer: 107.68/31.87 MAYBE 107.68/31.87 107.68/31.87 Arguments of following rules are not normal-forms: 107.68/31.87 107.68/31.87 { dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) 107.68/31.87 , sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z)) 107.68/31.87 , dbl1(s(X)) -> s1(s1(dbl1(activate(X)))) 107.68/31.87 , sel1(s(X), cons(Y, Z)) -> sel1(activate(X), activate(Z)) 107.68/31.87 , quote(dbl(X)) -> dbl1(X) 107.68/31.87 , quote(s(X)) -> s1(quote(activate(X))) 107.68/31.87 , quote(sel(X, Y)) -> sel1(X, Y) } 107.68/31.87 107.68/31.87 All above mentioned rules can be savely removed. 107.68/31.87 107.68/31.87 We are left with following problem, upon which TcT provides the 107.68/31.87 certificate MAYBE. 107.68/31.87 107.68/31.87 Strict Trs: 107.68/31.87 { dbl(X) -> n__dbl(X) 107.68/31.87 , dbl(0()) -> 0() 107.68/31.87 , s(X) -> n__s(X) 107.68/31.87 , activate(X) -> X 107.68/31.87 , activate(n__s(X)) -> s(X) 107.68/31.87 , activate(n__dbl(X)) -> dbl(X) 107.68/31.87 , activate(n__dbls(X)) -> dbls(X) 107.68/31.87 , activate(n__sel(X1, X2)) -> sel(X1, X2) 107.68/31.87 , activate(n__indx(X1, X2)) -> indx(X1, X2) 107.68/31.87 , activate(n__from(X)) -> from(X) 107.68/31.87 , dbls(X) -> n__dbls(X) 107.68/31.87 , dbls(nil()) -> nil() 107.68/31.87 , dbls(cons(X, Y)) -> 107.68/31.87 cons(n__dbl(activate(X)), n__dbls(activate(Y))) 107.68/31.87 , sel(X1, X2) -> n__sel(X1, X2) 107.68/31.87 , sel(0(), cons(X, Y)) -> activate(X) 107.68/31.87 , indx(X1, X2) -> n__indx(X1, X2) 107.68/31.87 , indx(nil(), X) -> nil() 107.68/31.87 , indx(cons(X, Y), Z) -> 107.68/31.87 cons(n__sel(activate(X), activate(Z)), 107.68/31.87 n__indx(activate(Y), activate(Z))) 107.68/31.87 , from(X) -> cons(activate(X), n__from(n__s(activate(X)))) 107.68/31.87 , from(X) -> n__from(X) 107.68/31.87 , dbl1(0()) -> 01() 107.68/31.87 , sel1(0(), cons(X, Y)) -> activate(X) 107.68/31.87 , quote(0()) -> 01() } 107.68/31.87 Obligation: 107.68/31.87 innermost runtime complexity 107.68/31.87 Answer: 107.68/31.87 MAYBE 107.68/31.87 107.68/31.87 None of the processors succeeded. 107.68/31.87 107.68/31.87 Details of failed attempt(s): 107.68/31.87 ----------------------------- 107.68/31.87 1) 'empty' failed due to the following reason: 107.68/31.87 107.68/31.87 Empty strict component of the problem is NOT empty. 107.68/31.87 107.68/31.87 2) 'Best' failed due to the following reason: 107.68/31.87 107.68/31.87 None of the processors succeeded. 107.68/31.87 107.68/31.87 Details of failed attempt(s): 107.68/31.87 ----------------------------- 107.68/31.87 1) 'Best' failed due to the following reason: 107.68/31.87 107.68/31.87 None of the processors succeeded. 107.68/31.87 107.68/31.87 Details of failed attempt(s): 107.68/31.87 ----------------------------- 107.68/31.87 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 107.68/31.87 seconds)' failed due to the following reason: 107.68/31.87 107.68/31.87 None of the processors succeeded. 107.68/31.87 107.68/31.87 Details of failed attempt(s): 107.68/31.87 ----------------------------- 107.68/31.87 1) 'empty' failed due to the following reason: 107.68/31.87 107.68/31.87 Empty strict component of the problem is NOT empty. 107.68/31.87 107.68/31.87 2) 'With Problem ...' failed due to the following reason: 107.68/31.87 107.68/31.87 None of the processors succeeded. 107.68/31.87 107.68/31.87 Details of failed attempt(s): 107.68/31.87 ----------------------------- 107.68/31.87 1) 'empty' failed due to the following reason: 107.68/31.87 107.68/31.87 Empty strict component of the problem is NOT empty. 107.68/31.87 107.68/31.87 2) 'Fastest' failed due to the following reason: 107.68/31.87 107.68/31.87 None of the processors succeeded. 107.68/31.87 107.68/31.87 Details of failed attempt(s): 107.68/31.87 ----------------------------- 107.68/31.87 1) 'With Problem ...' failed due to the following reason: 107.68/31.87 107.68/31.87 None of the processors succeeded. 107.68/31.87 107.68/31.87 Details of failed attempt(s): 107.68/31.87 ----------------------------- 107.68/31.87 1) 'empty' failed due to the following reason: 107.68/31.87 107.68/31.87 Empty strict component of the problem is NOT empty. 107.68/31.87 107.68/31.87 2) 'With Problem ...' failed due to the following reason: 107.68/31.87 107.68/31.87 None of the processors succeeded. 107.68/31.87 107.68/31.87 Details of failed attempt(s): 107.68/31.87 ----------------------------- 107.68/31.87 1) 'empty' failed due to the following reason: 107.68/31.87 107.68/31.87 Empty strict component of the problem is NOT empty. 107.68/31.87 107.68/31.87 2) 'With Problem ...' failed due to the following reason: 107.68/31.87 107.68/31.87 None of the processors succeeded. 107.68/31.87 107.68/31.87 Details of failed attempt(s): 107.68/31.87 ----------------------------- 107.68/31.87 1) 'empty' failed due to the following reason: 107.68/31.87 107.68/31.87 Empty strict component of the problem is NOT empty. 107.68/31.87 107.68/31.87 2) 'With Problem ...' failed due to the following reason: 107.68/31.87 107.68/31.87 Empty strict component of the problem is NOT empty. 107.68/31.87 107.68/31.87 107.68/31.87 107.68/31.87 107.68/31.87 2) 'With Problem ...' failed due to the following reason: 107.68/31.87 107.68/31.87 None of the processors succeeded. 107.68/31.87 107.68/31.87 Details of failed attempt(s): 107.68/31.87 ----------------------------- 107.68/31.87 1) 'empty' failed due to the following reason: 107.68/31.87 107.68/31.87 Empty strict component of the problem is NOT empty. 107.68/31.87 107.68/31.87 2) 'With Problem ...' failed due to the following reason: 107.68/31.87 107.68/31.87 Empty strict component of the problem is NOT empty. 107.68/31.87 107.68/31.87 107.68/31.87 107.68/31.87 107.68/31.87 107.68/31.87 2) 'Best' failed due to the following reason: 107.68/31.87 107.68/31.87 None of the processors succeeded. 107.68/31.87 107.68/31.87 Details of failed attempt(s): 107.68/31.87 ----------------------------- 107.68/31.87 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 107.68/31.87 following reason: 107.68/31.87 107.68/31.87 The input cannot be shown compatible 107.68/31.87 107.68/31.87 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 107.68/31.87 to the following reason: 107.68/31.87 107.68/31.87 The input cannot be shown compatible 107.68/31.87 107.68/31.87 107.68/31.87 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 107.68/31.87 failed due to the following reason: 107.68/31.87 107.68/31.87 None of the processors succeeded. 107.68/31.87 107.68/31.87 Details of failed attempt(s): 107.68/31.87 ----------------------------- 107.68/31.87 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 107.68/31.87 failed due to the following reason: 107.68/31.87 107.68/31.87 match-boundness of the problem could not be verified. 107.68/31.87 107.68/31.87 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 107.68/31.87 failed due to the following reason: 107.68/31.87 107.68/31.87 match-boundness of the problem could not be verified. 107.68/31.87 107.68/31.87 107.68/31.87 107.68/31.87 2) 'With Problem ... (timeout of 297 seconds)' failed due to the 107.68/31.87 following reason: 107.68/31.87 107.68/31.87 We add the following weak dependency pairs: 107.68/31.87 107.68/31.87 Strict DPs: 107.68/31.87 { dbl^#(X) -> c_1() 107.68/31.87 , dbl^#(0()) -> c_2() 107.68/31.87 , s^#(X) -> c_3() 107.68/31.87 , activate^#(X) -> c_4() 107.68/31.87 , activate^#(n__s(X)) -> c_5(s^#(X)) 107.68/31.87 , activate^#(n__dbl(X)) -> c_6(dbl^#(X)) 107.68/31.87 , activate^#(n__dbls(X)) -> c_7(dbls^#(X)) 107.68/31.87 , activate^#(n__sel(X1, X2)) -> c_8(sel^#(X1, X2)) 107.68/31.87 , activate^#(n__indx(X1, X2)) -> c_9(indx^#(X1, X2)) 107.68/31.87 , activate^#(n__from(X)) -> c_10(from^#(X)) 107.68/31.87 , dbls^#(X) -> c_11() 107.68/31.87 , dbls^#(nil()) -> c_12() 107.68/31.87 , dbls^#(cons(X, Y)) -> c_13(activate^#(X), activate^#(Y)) 107.68/31.87 , sel^#(X1, X2) -> c_14() 107.68/31.87 , sel^#(0(), cons(X, Y)) -> c_15(activate^#(X)) 107.68/31.87 , indx^#(X1, X2) -> c_16() 107.68/31.87 , indx^#(nil(), X) -> c_17() 107.68/31.87 , indx^#(cons(X, Y), Z) -> 107.68/31.87 c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.68/31.87 , from^#(X) -> c_19(activate^#(X), activate^#(X)) 107.68/31.87 , from^#(X) -> c_20() 107.68/31.87 , dbl1^#(0()) -> c_21() 107.68/31.87 , sel1^#(0(), cons(X, Y)) -> c_22(activate^#(X)) 107.68/31.87 , quote^#(0()) -> c_23() } 107.68/31.87 107.68/31.87 and mark the set of starting terms. 107.68/31.87 107.68/31.87 We are left with following problem, upon which TcT provides the 107.68/31.87 certificate MAYBE. 107.68/31.87 107.68/31.87 Strict DPs: 107.68/31.87 { dbl^#(X) -> c_1() 107.68/31.87 , dbl^#(0()) -> c_2() 107.68/31.87 , s^#(X) -> c_3() 107.68/31.87 , activate^#(X) -> c_4() 107.68/31.87 , activate^#(n__s(X)) -> c_5(s^#(X)) 107.68/31.87 , activate^#(n__dbl(X)) -> c_6(dbl^#(X)) 107.68/31.87 , activate^#(n__dbls(X)) -> c_7(dbls^#(X)) 107.68/31.87 , activate^#(n__sel(X1, X2)) -> c_8(sel^#(X1, X2)) 107.68/31.87 , activate^#(n__indx(X1, X2)) -> c_9(indx^#(X1, X2)) 107.68/31.87 , activate^#(n__from(X)) -> c_10(from^#(X)) 107.68/31.87 , dbls^#(X) -> c_11() 107.68/31.87 , dbls^#(nil()) -> c_12() 107.68/31.87 , dbls^#(cons(X, Y)) -> c_13(activate^#(X), activate^#(Y)) 107.68/31.87 , sel^#(X1, X2) -> c_14() 107.68/31.87 , sel^#(0(), cons(X, Y)) -> c_15(activate^#(X)) 107.68/31.87 , indx^#(X1, X2) -> c_16() 107.68/31.87 , indx^#(nil(), X) -> c_17() 107.68/31.87 , indx^#(cons(X, Y), Z) -> 107.68/31.87 c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.68/31.87 , from^#(X) -> c_19(activate^#(X), activate^#(X)) 107.68/31.87 , from^#(X) -> c_20() 107.68/31.87 , dbl1^#(0()) -> c_21() 107.68/31.87 , sel1^#(0(), cons(X, Y)) -> c_22(activate^#(X)) 107.68/31.87 , quote^#(0()) -> c_23() } 107.68/31.87 Strict Trs: 107.68/31.87 { dbl(X) -> n__dbl(X) 107.68/31.87 , dbl(0()) -> 0() 107.68/31.87 , s(X) -> n__s(X) 107.68/31.87 , activate(X) -> X 107.68/31.87 , activate(n__s(X)) -> s(X) 107.68/31.87 , activate(n__dbl(X)) -> dbl(X) 107.68/31.87 , activate(n__dbls(X)) -> dbls(X) 107.68/31.87 , activate(n__sel(X1, X2)) -> sel(X1, X2) 107.68/31.87 , activate(n__indx(X1, X2)) -> indx(X1, X2) 107.68/31.87 , activate(n__from(X)) -> from(X) 107.68/31.87 , dbls(X) -> n__dbls(X) 107.68/31.87 , dbls(nil()) -> nil() 107.68/31.87 , dbls(cons(X, Y)) -> 107.68/31.87 cons(n__dbl(activate(X)), n__dbls(activate(Y))) 107.68/31.87 , sel(X1, X2) -> n__sel(X1, X2) 107.68/31.87 , sel(0(), cons(X, Y)) -> activate(X) 107.68/31.87 , indx(X1, X2) -> n__indx(X1, X2) 107.68/31.87 , indx(nil(), X) -> nil() 107.68/31.87 , indx(cons(X, Y), Z) -> 107.68/31.87 cons(n__sel(activate(X), activate(Z)), 107.68/31.87 n__indx(activate(Y), activate(Z))) 107.68/31.87 , from(X) -> cons(activate(X), n__from(n__s(activate(X)))) 107.68/31.87 , from(X) -> n__from(X) 107.68/31.87 , dbl1(0()) -> 01() 107.68/31.87 , sel1(0(), cons(X, Y)) -> activate(X) 107.68/31.87 , quote(0()) -> 01() } 107.68/31.87 Obligation: 107.68/31.87 innermost runtime complexity 107.68/31.87 Answer: 107.68/31.87 MAYBE 107.68/31.87 107.68/31.87 No rule is usable, rules are removed from the input problem. 107.68/31.87 107.68/31.87 We are left with following problem, upon which TcT provides the 107.68/31.87 certificate MAYBE. 107.68/31.87 107.68/31.87 Strict DPs: 107.68/31.87 { dbl^#(X) -> c_1() 107.68/31.87 , dbl^#(0()) -> c_2() 107.68/31.87 , s^#(X) -> c_3() 107.68/31.87 , activate^#(X) -> c_4() 107.68/31.87 , activate^#(n__s(X)) -> c_5(s^#(X)) 107.68/31.87 , activate^#(n__dbl(X)) -> c_6(dbl^#(X)) 107.68/31.87 , activate^#(n__dbls(X)) -> c_7(dbls^#(X)) 107.68/31.87 , activate^#(n__sel(X1, X2)) -> c_8(sel^#(X1, X2)) 107.68/31.87 , activate^#(n__indx(X1, X2)) -> c_9(indx^#(X1, X2)) 107.68/31.87 , activate^#(n__from(X)) -> c_10(from^#(X)) 107.68/31.87 , dbls^#(X) -> c_11() 107.68/31.87 , dbls^#(nil()) -> c_12() 107.68/31.87 , dbls^#(cons(X, Y)) -> c_13(activate^#(X), activate^#(Y)) 107.68/31.87 , sel^#(X1, X2) -> c_14() 107.68/31.87 , sel^#(0(), cons(X, Y)) -> c_15(activate^#(X)) 107.68/31.87 , indx^#(X1, X2) -> c_16() 107.68/31.87 , indx^#(nil(), X) -> c_17() 107.68/31.87 , indx^#(cons(X, Y), Z) -> 107.68/31.87 c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.68/31.87 , from^#(X) -> c_19(activate^#(X), activate^#(X)) 107.68/31.87 , from^#(X) -> c_20() 107.68/31.87 , dbl1^#(0()) -> c_21() 107.68/31.87 , sel1^#(0(), cons(X, Y)) -> c_22(activate^#(X)) 107.68/31.87 , quote^#(0()) -> c_23() } 107.68/31.87 Obligation: 107.68/31.87 innermost runtime complexity 107.68/31.87 Answer: 107.68/31.87 MAYBE 107.68/31.87 107.68/31.87 The weightgap principle applies (using the following constant 107.68/31.87 growth matrix-interpretation) 107.68/31.87 107.68/31.87 The following argument positions are usable: 107.68/31.87 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(c_7) = {1}, 107.68/31.87 Uargs(c_8) = {1}, Uargs(c_9) = {1}, Uargs(c_10) = {1}, 107.68/31.87 Uargs(c_13) = {1, 2}, Uargs(c_15) = {1}, 107.68/31.87 Uargs(c_18) = {1, 2, 3, 4}, Uargs(c_19) = {1, 2}, Uargs(c_22) = {1} 107.68/31.87 107.68/31.87 TcT has computed the following constructor-restricted matrix 107.68/31.87 interpretation. 107.68/31.87 107.68/31.87 [0] = [1] 107.68/31.87 [2] 107.68/31.87 107.68/31.87 [n__s](x1) = [1 2] x1 + [2] 107.68/31.87 [0 1] [1] 107.68/31.87 107.68/31.87 [n__dbl](x1) = [1 2] x1 + [2] 107.68/31.87 [0 1] [1] 107.68/31.87 107.68/31.87 [nil] = [1] 107.68/31.87 [1] 107.68/31.87 107.68/31.87 [cons](x1, x2) = [1 2] x1 + [1 2] x2 + [2] 107.68/31.87 [0 1] [0 1] [2] 107.68/31.87 107.68/31.87 [n__dbls](x1) = [1 2] x1 + [1] 107.68/31.87 [0 1] [2] 107.68/31.87 107.68/31.87 [n__sel](x1, x2) = [1 2] x1 + [1 2] x2 + [1] 107.68/31.87 [0 1] [0 1] [2] 107.68/31.87 107.68/31.87 [n__indx](x1, x2) = [1 2] x1 + [1 2] x2 + [1] 107.68/31.87 [0 1] [0 1] [2] 107.68/31.87 107.68/31.87 [n__from](x1) = [1 2] x1 + [1] 107.68/31.87 [0 1] [2] 107.68/31.87 107.68/31.87 [dbl^#](x1) = [0 0] x1 + [1] 107.68/31.87 [2 1] [2] 107.68/31.87 107.68/31.87 [c_1] = [0] 107.68/31.87 [1] 107.68/31.87 107.68/31.87 [c_2] = [0] 107.68/31.87 [2] 107.68/31.87 107.68/31.88 [s^#](x1) = [0 0] x1 + [1] 107.68/31.88 [1 1] [1] 107.68/31.88 107.68/31.88 [c_3] = [0] 107.68/31.88 [1] 107.68/31.88 107.68/31.88 [activate^#](x1) = [0 0] x1 + [0] 107.68/31.88 [1 1] [1] 107.68/31.88 107.68/31.88 [c_4] = [1] 107.68/31.88 [1] 107.68/31.88 107.68/31.88 [c_5](x1) = [1 0] x1 + [2] 107.68/31.88 [0 1] [2] 107.68/31.88 107.68/31.88 [c_6](x1) = [1 0] x1 + [2] 107.68/31.88 [0 1] [1] 107.68/31.88 107.68/31.88 [c_7](x1) = [1 0] x1 + [2] 107.68/31.88 [0 1] [1] 107.68/31.88 107.68/31.88 [dbls^#](x1) = [0 0] x1 + [1] 107.68/31.88 [1 1] [2] 107.68/31.88 107.68/31.88 [c_8](x1) = [1 0] x1 + [2] 107.68/31.88 [0 1] [2] 107.68/31.88 107.68/31.88 [sel^#](x1, x2) = [0 0] x1 + [0 0] x2 + [1] 107.68/31.88 [1 1] [1 1] [0] 107.68/31.88 107.68/31.88 [c_9](x1) = [1 0] x1 + [2] 107.68/31.88 [0 1] [1] 107.68/31.88 107.68/31.88 [indx^#](x1, x2) = [0 0] x1 + [0 0] x2 + [1] 107.68/31.88 [1 1] [2 1] [2] 107.68/31.88 107.68/31.88 [c_10](x1) = [1 0] x1 + [2] 107.68/31.88 [0 1] [2] 107.68/31.88 107.68/31.88 [from^#](x1) = [0 0] x1 + [1] 107.68/31.88 [1 1] [1] 107.68/31.88 107.68/31.88 [c_11] = [0] 107.68/31.88 [1] 107.68/31.88 107.68/31.88 [c_12] = [0] 107.68/31.88 [0] 107.68/31.88 107.68/31.88 [c_13](x1, x2) = [1 0] x1 + [1 0] x2 + [2] 107.68/31.88 [0 1] [0 1] [1] 107.68/31.88 107.68/31.88 [c_14] = [0] 107.68/31.88 [0] 107.68/31.88 107.68/31.88 [c_15](x1) = [1 0] x1 + [2] 107.68/31.88 [0 1] [1] 107.68/31.88 107.68/31.88 [c_16] = [0] 107.68/31.88 [1] 107.68/31.88 107.68/31.88 [c_17] = [0] 107.68/31.88 [0] 107.68/31.88 107.68/31.88 [c_18](x1, x2, x3, x4) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [1 107.68/31.88 0] x4 + [2] 107.68/31.88 [0 1] [0 1] [0 1] [0 107.68/31.88 1] [2] 107.68/31.88 107.68/31.88 [c_19](x1, x2) = [1 0] x1 + [1 0] x2 + [2] 107.68/31.88 [0 1] [0 1] [1] 107.68/31.88 107.68/31.88 [c_20] = [0] 107.68/31.88 [1] 107.68/31.88 107.68/31.88 [dbl1^#](x1) = [2 1] x1 + [2] 107.68/31.88 [2 1] [2] 107.68/31.88 107.68/31.88 [c_21] = [1] 107.68/31.88 [1] 107.68/31.88 107.68/31.88 [sel1^#](x1, x2) = [1 1] x1 + [1 1] x2 + [0] 107.68/31.88 [1 1] [1 1] [0] 107.68/31.88 107.68/31.88 [c_22](x1) = [1 0] x1 + [2] 107.68/31.88 [0 1] [1] 107.68/31.88 107.68/31.88 [quote^#](x1) = [2 1] x1 + [2] 107.68/31.88 [2 1] [2] 107.68/31.88 107.68/31.88 [c_23] = [1] 107.68/31.88 [1] 107.68/31.88 107.68/31.88 The order satisfies the following ordering constraints: 107.68/31.88 107.68/31.88 [dbl^#(X)] = [0 0] X + [1] 107.68/31.88 [2 1] [2] 107.68/31.88 > [0] 107.68/31.88 [1] 107.68/31.88 = [c_1()] 107.68/31.88 107.68/31.88 [dbl^#(0())] = [1] 107.68/31.88 [6] 107.68/31.88 > [0] 107.68/31.88 [2] 107.68/31.88 = [c_2()] 107.68/31.88 107.68/31.88 [s^#(X)] = [0 0] X + [1] 107.68/31.88 [1 1] [1] 107.68/31.88 > [0] 107.68/31.88 [1] 107.68/31.88 = [c_3()] 107.68/31.88 107.68/31.88 [activate^#(X)] = [0 0] X + [0] 107.68/31.88 [1 1] [1] 107.68/31.88 ? [1] 107.68/31.88 [1] 107.68/31.88 = [c_4()] 107.68/31.88 107.68/31.88 [activate^#(n__s(X))] = [0 0] X + [0] 107.68/31.88 [1 3] [4] 107.68/31.88 ? [0 0] X + [3] 107.68/31.88 [1 1] [3] 107.68/31.88 = [c_5(s^#(X))] 107.68/31.88 107.68/31.88 [activate^#(n__dbl(X))] = [0 0] X + [0] 107.68/31.88 [1 3] [4] 107.68/31.88 ? [0 0] X + [3] 107.68/31.88 [2 1] [3] 107.68/31.88 = [c_6(dbl^#(X))] 107.68/31.88 107.68/31.88 [activate^#(n__dbls(X))] = [0 0] X + [0] 107.68/31.88 [1 3] [4] 107.68/31.88 ? [0 0] X + [3] 107.68/31.88 [1 1] [3] 107.68/31.88 = [c_7(dbls^#(X))] 107.68/31.88 107.68/31.88 [activate^#(n__sel(X1, X2))] = [0 0] X1 + [0 0] X2 + [0] 107.68/31.88 [1 3] [1 3] [4] 107.68/31.88 ? [0 0] X1 + [0 0] X2 + [3] 107.68/31.88 [1 1] [1 1] [2] 107.68/31.88 = [c_8(sel^#(X1, X2))] 107.68/31.88 107.68/31.88 [activate^#(n__indx(X1, X2))] = [0 0] X1 + [0 0] X2 + [0] 107.68/31.88 [1 3] [1 3] [4] 107.68/31.88 ? [0 0] X1 + [0 0] X2 + [3] 107.68/31.88 [1 1] [2 1] [3] 107.68/31.88 = [c_9(indx^#(X1, X2))] 107.68/31.88 107.68/31.88 [activate^#(n__from(X))] = [0 0] X + [0] 107.68/31.88 [1 3] [4] 107.68/31.88 ? [0 0] X + [3] 107.68/31.88 [1 1] [3] 107.68/31.88 = [c_10(from^#(X))] 107.68/31.88 107.68/31.88 [dbls^#(X)] = [0 0] X + [1] 107.68/31.88 [1 1] [2] 107.68/31.88 > [0] 107.68/31.88 [1] 107.68/31.88 = [c_11()] 107.68/31.88 107.68/31.88 [dbls^#(nil())] = [1] 107.68/31.88 [4] 107.68/31.88 > [0] 107.68/31.88 [0] 107.68/31.88 = [c_12()] 107.68/31.88 107.68/31.88 [dbls^#(cons(X, Y))] = [0 0] X + [0 0] Y + [1] 107.68/31.88 [1 3] [1 3] [6] 107.68/31.88 ? [0 0] X + [0 0] Y + [2] 107.68/31.88 [1 1] [1 1] [3] 107.68/31.88 = [c_13(activate^#(X), activate^#(Y))] 107.68/31.88 107.68/31.88 [sel^#(X1, X2)] = [0 0] X1 + [0 0] X2 + [1] 107.68/31.88 [1 1] [1 1] [0] 107.68/31.88 > [0] 107.68/31.88 [0] 107.68/31.88 = [c_14()] 107.68/31.88 107.68/31.88 [sel^#(0(), cons(X, Y))] = [0 0] X + [0 0] Y + [1] 107.68/31.88 [1 3] [1 3] [7] 107.68/31.88 ? [0 0] X + [2] 107.68/31.88 [1 1] [2] 107.68/31.88 = [c_15(activate^#(X))] 107.68/31.88 107.68/31.88 [indx^#(X1, X2)] = [0 0] X1 + [0 0] X2 + [1] 107.68/31.88 [1 1] [2 1] [2] 107.68/31.88 > [0] 107.68/31.88 [1] 107.68/31.88 = [c_16()] 107.68/31.88 107.68/31.88 [indx^#(nil(), X)] = [0 0] X + [1] 107.68/31.88 [2 1] [4] 107.68/31.88 > [0] 107.68/31.88 [0] 107.68/31.88 = [c_17()] 107.68/31.88 107.68/31.88 [indx^#(cons(X, Y), Z)] = [0 0] X + [0 0] Y + [0 0] Z + [1] 107.68/31.88 [1 3] [1 3] [2 1] [6] 107.68/31.88 ? [0 0] X + [0 0] Y + [0 0] Z + [2] 107.68/31.88 [1 1] [1 1] [2 2] [6] 107.68/31.88 = [c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z))] 107.68/31.88 107.68/31.88 [from^#(X)] = [0 0] X + [1] 107.68/31.88 [1 1] [1] 107.68/31.88 ? [0 0] X + [2] 107.68/31.88 [2 2] [3] 107.68/31.88 = [c_19(activate^#(X), activate^#(X))] 107.68/31.88 107.68/31.88 [from^#(X)] = [0 0] X + [1] 107.68/31.88 [1 1] [1] 107.68/31.88 > [0] 107.68/31.88 [1] 107.68/31.88 = [c_20()] 107.68/31.88 107.68/31.88 [dbl1^#(0())] = [6] 107.68/31.88 [6] 107.68/31.88 > [1] 107.68/31.88 [1] 107.68/31.88 = [c_21()] 107.68/31.88 107.68/31.88 [sel1^#(0(), cons(X, Y))] = [1 3] X + [1 3] Y + [7] 107.68/31.88 [1 3] [1 3] [7] 107.68/31.88 > [0 0] X + [2] 107.68/31.88 [1 1] [2] 107.68/31.88 = [c_22(activate^#(X))] 107.68/31.88 107.68/31.88 [quote^#(0())] = [6] 107.68/31.88 [6] 107.68/31.88 > [1] 107.68/31.88 [1] 107.68/31.88 = [c_23()] 107.68/31.88 107.68/31.88 107.68/31.88 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 107.68/31.88 107.68/31.88 We are left with following problem, upon which TcT provides the 107.68/31.88 certificate MAYBE. 107.68/31.88 107.68/31.88 Strict DPs: 107.68/31.88 { activate^#(X) -> c_4() 107.68/31.88 , activate^#(n__s(X)) -> c_5(s^#(X)) 107.68/31.88 , activate^#(n__dbl(X)) -> c_6(dbl^#(X)) 107.68/31.88 , activate^#(n__dbls(X)) -> c_7(dbls^#(X)) 107.68/31.88 , activate^#(n__sel(X1, X2)) -> c_8(sel^#(X1, X2)) 107.68/31.88 , activate^#(n__indx(X1, X2)) -> c_9(indx^#(X1, X2)) 107.68/31.88 , activate^#(n__from(X)) -> c_10(from^#(X)) 107.68/31.88 , dbls^#(cons(X, Y)) -> c_13(activate^#(X), activate^#(Y)) 107.68/31.88 , sel^#(0(), cons(X, Y)) -> c_15(activate^#(X)) 107.68/31.88 , indx^#(cons(X, Y), Z) -> 107.68/31.88 c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.68/31.88 , from^#(X) -> c_19(activate^#(X), activate^#(X)) } 107.68/31.88 Weak DPs: 107.68/31.88 { dbl^#(X) -> c_1() 107.68/31.88 , dbl^#(0()) -> c_2() 107.68/31.88 , s^#(X) -> c_3() 107.68/31.88 , dbls^#(X) -> c_11() 107.68/31.88 , dbls^#(nil()) -> c_12() 107.68/31.88 , sel^#(X1, X2) -> c_14() 107.68/31.88 , indx^#(X1, X2) -> c_16() 107.68/31.88 , indx^#(nil(), X) -> c_17() 107.68/31.88 , from^#(X) -> c_20() 107.68/31.88 , dbl1^#(0()) -> c_21() 107.68/31.88 , sel1^#(0(), cons(X, Y)) -> c_22(activate^#(X)) 107.68/31.88 , quote^#(0()) -> c_23() } 107.68/31.88 Obligation: 107.68/31.88 innermost runtime complexity 107.68/31.88 Answer: 107.68/31.88 MAYBE 107.68/31.88 107.68/31.88 The following weak DPs constitute a sub-graph of the DG that is 107.68/31.88 closed under successors. The DPs are removed. 107.68/31.88 107.68/31.88 { dbl^#(X) -> c_1() 107.68/31.88 , dbl^#(0()) -> c_2() 107.68/31.88 , s^#(X) -> c_3() 107.68/31.88 , dbls^#(X) -> c_11() 107.68/31.88 , dbls^#(nil()) -> c_12() 107.68/31.88 , sel^#(X1, X2) -> c_14() 107.68/31.88 , indx^#(X1, X2) -> c_16() 107.68/31.88 , indx^#(nil(), X) -> c_17() 107.68/31.88 , from^#(X) -> c_20() 107.68/31.88 , dbl1^#(0()) -> c_21() 107.68/31.88 , quote^#(0()) -> c_23() } 107.68/31.88 107.68/31.88 We are left with following problem, upon which TcT provides the 107.68/31.88 certificate MAYBE. 107.68/31.88 107.68/31.88 Strict DPs: 107.68/31.88 { activate^#(X) -> c_4() 107.68/31.88 , activate^#(n__s(X)) -> c_5(s^#(X)) 107.68/31.88 , activate^#(n__dbl(X)) -> c_6(dbl^#(X)) 107.68/31.88 , activate^#(n__dbls(X)) -> c_7(dbls^#(X)) 107.68/31.88 , activate^#(n__sel(X1, X2)) -> c_8(sel^#(X1, X2)) 107.68/31.88 , activate^#(n__indx(X1, X2)) -> c_9(indx^#(X1, X2)) 107.68/31.88 , activate^#(n__from(X)) -> c_10(from^#(X)) 107.68/31.88 , dbls^#(cons(X, Y)) -> c_13(activate^#(X), activate^#(Y)) 107.68/31.88 , sel^#(0(), cons(X, Y)) -> c_15(activate^#(X)) 107.68/31.88 , indx^#(cons(X, Y), Z) -> 107.68/31.88 c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.68/31.88 , from^#(X) -> c_19(activate^#(X), activate^#(X)) } 107.68/31.88 Weak DPs: { sel1^#(0(), cons(X, Y)) -> c_22(activate^#(X)) } 107.68/31.88 Obligation: 107.68/31.88 innermost runtime complexity 107.68/31.88 Answer: 107.68/31.88 MAYBE 107.68/31.88 107.68/31.88 Due to missing edges in the dependency-graph, the right-hand sides 107.68/31.88 of following rules could be simplified: 107.68/31.88 107.68/31.88 { activate^#(n__s(X)) -> c_5(s^#(X)) 107.68/31.88 , activate^#(n__dbl(X)) -> c_6(dbl^#(X)) } 107.68/31.88 107.68/31.88 We are left with following problem, upon which TcT provides the 107.68/31.88 certificate MAYBE. 107.68/31.88 107.68/31.88 Strict DPs: 107.68/31.88 { activate^#(X) -> c_1() 107.68/31.88 , activate^#(n__s(X)) -> c_2() 107.68/31.88 , activate^#(n__dbl(X)) -> c_3() 107.68/31.88 , activate^#(n__dbls(X)) -> c_4(dbls^#(X)) 107.68/31.88 , activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) 107.68/31.88 , activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) 107.68/31.88 , activate^#(n__from(X)) -> c_7(from^#(X)) 107.68/31.88 , dbls^#(cons(X, Y)) -> c_8(activate^#(X), activate^#(Y)) 107.68/31.88 , sel^#(0(), cons(X, Y)) -> c_9(activate^#(X)) 107.68/31.88 , indx^#(cons(X, Y), Z) -> 107.68/31.88 c_10(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.68/31.88 , from^#(X) -> c_11(activate^#(X), activate^#(X)) } 107.68/31.88 Weak DPs: { sel1^#(0(), cons(X, Y)) -> c_12(activate^#(X)) } 107.68/31.88 Obligation: 107.68/31.88 innermost runtime complexity 107.68/31.88 Answer: 107.68/31.88 MAYBE 107.68/31.88 107.68/31.88 Consider the dependency graph 107.68/31.88 107.68/31.88 1: activate^#(X) -> c_1() 107.68/31.88 107.68/31.88 2: activate^#(n__s(X)) -> c_2() 107.68/31.88 107.68/31.88 3: activate^#(n__dbl(X)) -> c_3() 107.68/31.88 107.68/31.88 4: activate^#(n__dbls(X)) -> c_4(dbls^#(X)) 107.68/31.88 -->_1 dbls^#(cons(X, Y)) -> c_8(activate^#(X), activate^#(Y)) :8 107.68/31.88 107.68/31.88 5: activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) 107.68/31.88 -->_1 sel^#(0(), cons(X, Y)) -> c_9(activate^#(X)) :9 107.68/31.88 107.68/31.88 6: activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) 107.68/31.88 -->_1 indx^#(cons(X, Y), Z) -> 107.68/31.88 c_10(activate^#(X), 107.68/31.88 activate^#(Z), 107.68/31.88 activate^#(Y), 107.68/31.88 activate^#(Z)) :10 107.68/31.88 107.68/31.88 7: activate^#(n__from(X)) -> c_7(from^#(X)) 107.68/31.88 -->_1 from^#(X) -> c_11(activate^#(X), activate^#(X)) :11 107.68/31.88 107.68/31.88 8: dbls^#(cons(X, Y)) -> c_8(activate^#(X), activate^#(Y)) 107.68/31.88 -->_2 activate^#(n__from(X)) -> c_7(from^#(X)) :7 107.68/31.88 -->_1 activate^#(n__from(X)) -> c_7(from^#(X)) :7 107.68/31.88 -->_2 activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) :6 107.68/31.88 -->_1 activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) :6 107.68/31.88 -->_2 activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) :5 107.68/31.88 -->_1 activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) :5 107.68/31.88 -->_2 activate^#(n__dbls(X)) -> c_4(dbls^#(X)) :4 107.68/31.88 -->_1 activate^#(n__dbls(X)) -> c_4(dbls^#(X)) :4 107.68/31.88 -->_2 activate^#(n__dbl(X)) -> c_3() :3 107.68/31.88 -->_1 activate^#(n__dbl(X)) -> c_3() :3 107.68/31.88 -->_2 activate^#(n__s(X)) -> c_2() :2 107.68/31.88 -->_1 activate^#(n__s(X)) -> c_2() :2 107.68/31.88 -->_2 activate^#(X) -> c_1() :1 107.68/31.88 -->_1 activate^#(X) -> c_1() :1 107.68/31.88 107.68/31.88 9: sel^#(0(), cons(X, Y)) -> c_9(activate^#(X)) 107.68/31.88 -->_1 activate^#(n__from(X)) -> c_7(from^#(X)) :7 107.68/31.88 -->_1 activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) :6 107.68/31.88 -->_1 activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) :5 107.68/31.88 -->_1 activate^#(n__dbls(X)) -> c_4(dbls^#(X)) :4 107.68/31.88 -->_1 activate^#(n__dbl(X)) -> c_3() :3 107.68/31.88 -->_1 activate^#(n__s(X)) -> c_2() :2 107.68/31.88 -->_1 activate^#(X) -> c_1() :1 107.68/31.88 107.68/31.88 10: indx^#(cons(X, Y), Z) -> 107.68/31.88 c_10(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.68/31.88 -->_4 activate^#(n__from(X)) -> c_7(from^#(X)) :7 107.68/31.88 -->_3 activate^#(n__from(X)) -> c_7(from^#(X)) :7 107.68/31.88 -->_2 activate^#(n__from(X)) -> c_7(from^#(X)) :7 107.68/31.88 -->_1 activate^#(n__from(X)) -> c_7(from^#(X)) :7 107.68/31.88 -->_4 activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) :6 107.68/31.88 -->_3 activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) :6 107.68/31.88 -->_2 activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) :6 107.68/31.88 -->_1 activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) :6 107.68/31.88 -->_4 activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) :5 107.68/31.88 -->_3 activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) :5 107.68/31.88 -->_2 activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) :5 107.68/31.88 -->_1 activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) :5 107.68/31.88 -->_4 activate^#(n__dbls(X)) -> c_4(dbls^#(X)) :4 107.68/31.88 -->_3 activate^#(n__dbls(X)) -> c_4(dbls^#(X)) :4 107.68/31.88 -->_2 activate^#(n__dbls(X)) -> c_4(dbls^#(X)) :4 107.68/31.88 -->_1 activate^#(n__dbls(X)) -> c_4(dbls^#(X)) :4 107.68/31.88 -->_4 activate^#(n__dbl(X)) -> c_3() :3 107.68/31.88 -->_3 activate^#(n__dbl(X)) -> c_3() :3 107.68/31.88 -->_2 activate^#(n__dbl(X)) -> c_3() :3 107.68/31.88 -->_1 activate^#(n__dbl(X)) -> c_3() :3 107.68/31.88 -->_4 activate^#(n__s(X)) -> c_2() :2 107.68/31.88 -->_3 activate^#(n__s(X)) -> c_2() :2 107.68/31.88 -->_2 activate^#(n__s(X)) -> c_2() :2 107.68/31.88 -->_1 activate^#(n__s(X)) -> c_2() :2 107.68/31.88 -->_4 activate^#(X) -> c_1() :1 107.68/31.88 -->_3 activate^#(X) -> c_1() :1 107.68/31.88 -->_2 activate^#(X) -> c_1() :1 107.68/31.88 -->_1 activate^#(X) -> c_1() :1 107.68/31.88 107.68/31.88 11: from^#(X) -> c_11(activate^#(X), activate^#(X)) 107.68/31.88 -->_2 activate^#(n__from(X)) -> c_7(from^#(X)) :7 107.68/31.88 -->_1 activate^#(n__from(X)) -> c_7(from^#(X)) :7 107.68/31.88 -->_2 activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) :6 107.68/31.88 -->_1 activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) :6 107.68/31.88 -->_2 activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) :5 107.68/31.88 -->_1 activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) :5 107.68/31.88 -->_2 activate^#(n__dbls(X)) -> c_4(dbls^#(X)) :4 107.68/31.88 -->_1 activate^#(n__dbls(X)) -> c_4(dbls^#(X)) :4 107.68/31.88 -->_2 activate^#(n__dbl(X)) -> c_3() :3 107.68/31.88 -->_1 activate^#(n__dbl(X)) -> c_3() :3 107.68/31.88 -->_2 activate^#(n__s(X)) -> c_2() :2 107.68/31.88 -->_1 activate^#(n__s(X)) -> c_2() :2 107.68/31.88 -->_2 activate^#(X) -> c_1() :1 107.68/31.88 -->_1 activate^#(X) -> c_1() :1 107.68/31.88 107.68/31.88 12: sel1^#(0(), cons(X, Y)) -> c_12(activate^#(X)) 107.68/31.88 -->_1 activate^#(n__from(X)) -> c_7(from^#(X)) :7 107.68/31.88 -->_1 activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) :6 107.68/31.88 -->_1 activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) :5 107.68/31.88 -->_1 activate^#(n__dbls(X)) -> c_4(dbls^#(X)) :4 107.68/31.88 -->_1 activate^#(n__dbl(X)) -> c_3() :3 107.68/31.88 -->_1 activate^#(n__s(X)) -> c_2() :2 107.68/31.88 -->_1 activate^#(X) -> c_1() :1 107.68/31.88 107.68/31.88 107.68/31.88 Following roots of the dependency graph are removed, as the 107.68/31.88 considered set of starting terms is closed under reduction with 107.68/31.88 respect to these rules (modulo compound contexts). 107.68/31.88 107.68/31.88 { sel1^#(0(), cons(X, Y)) -> c_12(activate^#(X)) } 107.68/31.88 107.68/31.88 107.68/31.88 We are left with following problem, upon which TcT provides the 107.68/31.88 certificate MAYBE. 107.68/31.88 107.68/31.88 Strict DPs: 107.68/31.88 { activate^#(X) -> c_1() 107.68/31.88 , activate^#(n__s(X)) -> c_2() 107.68/31.88 , activate^#(n__dbl(X)) -> c_3() 107.68/31.88 , activate^#(n__dbls(X)) -> c_4(dbls^#(X)) 107.68/31.88 , activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) 107.68/31.88 , activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) 107.68/31.88 , activate^#(n__from(X)) -> c_7(from^#(X)) 107.68/31.88 , dbls^#(cons(X, Y)) -> c_8(activate^#(X), activate^#(Y)) 107.68/31.88 , sel^#(0(), cons(X, Y)) -> c_9(activate^#(X)) 107.68/31.88 , indx^#(cons(X, Y), Z) -> 107.68/31.88 c_10(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.68/31.88 , from^#(X) -> c_11(activate^#(X), activate^#(X)) } 107.68/31.88 Obligation: 107.68/31.88 innermost runtime complexity 107.68/31.88 Answer: 107.68/31.88 MAYBE 107.68/31.88 107.68/31.88 We estimate the number of application of {1,2,3} by applications of 107.68/31.88 Pre({1,2,3}) = {8,9,10,11}. Here rules are labeled as follows: 107.68/31.88 107.68/31.88 DPs: 107.68/31.88 { 1: activate^#(X) -> c_1() 107.68/31.88 , 2: activate^#(n__s(X)) -> c_2() 107.68/31.88 , 3: activate^#(n__dbl(X)) -> c_3() 107.68/31.88 , 4: activate^#(n__dbls(X)) -> c_4(dbls^#(X)) 107.68/31.88 , 5: activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) 107.68/31.88 , 6: activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) 107.68/31.88 , 7: activate^#(n__from(X)) -> c_7(from^#(X)) 107.68/31.88 , 8: dbls^#(cons(X, Y)) -> c_8(activate^#(X), activate^#(Y)) 107.68/31.88 , 9: sel^#(0(), cons(X, Y)) -> c_9(activate^#(X)) 107.68/31.88 , 10: indx^#(cons(X, Y), Z) -> 107.68/31.88 c_10(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.68/31.88 , 11: from^#(X) -> c_11(activate^#(X), activate^#(X)) } 107.68/31.88 107.68/31.88 We are left with following problem, upon which TcT provides the 107.68/31.88 certificate MAYBE. 107.68/31.88 107.68/31.88 Strict DPs: 107.68/31.88 { activate^#(n__dbls(X)) -> c_4(dbls^#(X)) 107.68/31.88 , activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) 107.68/31.88 , activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) 107.68/31.88 , activate^#(n__from(X)) -> c_7(from^#(X)) 107.68/31.88 , dbls^#(cons(X, Y)) -> c_8(activate^#(X), activate^#(Y)) 107.68/31.88 , sel^#(0(), cons(X, Y)) -> c_9(activate^#(X)) 107.68/31.88 , indx^#(cons(X, Y), Z) -> 107.68/31.88 c_10(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.68/31.88 , from^#(X) -> c_11(activate^#(X), activate^#(X)) } 107.68/31.88 Weak DPs: 107.68/31.88 { activate^#(X) -> c_1() 107.68/31.88 , activate^#(n__s(X)) -> c_2() 107.68/31.88 , activate^#(n__dbl(X)) -> c_3() } 107.68/31.88 Obligation: 107.68/31.88 innermost runtime complexity 107.68/31.88 Answer: 107.68/31.88 MAYBE 107.68/31.88 107.68/31.88 The following weak DPs constitute a sub-graph of the DG that is 107.68/31.88 closed under successors. The DPs are removed. 107.68/31.88 107.68/31.88 { activate^#(X) -> c_1() 107.68/31.88 , activate^#(n__s(X)) -> c_2() 107.68/31.88 , activate^#(n__dbl(X)) -> c_3() } 107.68/31.88 107.68/31.88 We are left with following problem, upon which TcT provides the 107.68/31.88 certificate MAYBE. 107.68/31.88 107.68/31.88 Strict DPs: 107.68/31.88 { activate^#(n__dbls(X)) -> c_4(dbls^#(X)) 107.68/31.88 , activate^#(n__sel(X1, X2)) -> c_5(sel^#(X1, X2)) 107.68/31.88 , activate^#(n__indx(X1, X2)) -> c_6(indx^#(X1, X2)) 107.68/31.88 , activate^#(n__from(X)) -> c_7(from^#(X)) 107.68/31.88 , dbls^#(cons(X, Y)) -> c_8(activate^#(X), activate^#(Y)) 107.68/31.88 , sel^#(0(), cons(X, Y)) -> c_9(activate^#(X)) 107.68/31.88 , indx^#(cons(X, Y), Z) -> 107.68/31.88 c_10(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.68/31.88 , from^#(X) -> c_11(activate^#(X), activate^#(X)) } 107.68/31.88 Obligation: 107.68/31.88 innermost runtime complexity 107.68/31.88 Answer: 107.68/31.88 MAYBE 107.68/31.88 107.68/31.88 None of the processors succeeded. 107.68/31.88 107.68/31.88 Details of failed attempt(s): 107.68/31.88 ----------------------------- 107.68/31.88 1) 'empty' failed due to the following reason: 107.68/31.88 107.68/31.88 Empty strict component of the problem is NOT empty. 107.68/31.88 107.68/31.88 2) 'With Problem ...' failed due to the following reason: 107.68/31.88 107.68/31.88 None of the processors succeeded. 107.68/31.88 107.68/31.88 Details of failed attempt(s): 107.68/31.88 ----------------------------- 107.68/31.88 1) 'empty' failed due to the following reason: 107.68/31.88 107.68/31.88 Empty strict component of the problem is NOT empty. 107.68/31.88 107.68/31.88 2) 'Fastest' failed due to the following reason: 107.68/31.88 107.68/31.88 None of the processors succeeded. 107.68/31.88 107.68/31.88 Details of failed attempt(s): 107.68/31.88 ----------------------------- 107.68/31.88 1) 'With Problem ...' failed due to the following reason: 107.68/31.88 107.68/31.88 None of the processors succeeded. 107.68/31.88 107.68/31.88 Details of failed attempt(s): 107.68/31.88 ----------------------------- 107.68/31.88 1) 'empty' failed due to the following reason: 107.68/31.88 107.68/31.88 Empty strict component of the problem is NOT empty. 107.68/31.88 107.68/31.88 2) 'Polynomial Path Order (PS)' failed due to the following reason: 107.68/31.88 107.68/31.88 The input cannot be shown compatible 107.68/31.88 107.68/31.88 107.68/31.88 2) 'Polynomial Path Order (PS)' failed due to the following reason: 107.68/31.88 107.68/31.88 The input cannot be shown compatible 107.68/31.88 107.68/31.88 3) 'Fastest (timeout of 24 seconds)' failed due to the following 107.68/31.88 reason: 107.68/31.88 107.68/31.88 None of the processors succeeded. 107.68/31.88 107.68/31.88 Details of failed attempt(s): 107.68/31.88 ----------------------------- 107.68/31.88 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 107.68/31.88 failed due to the following reason: 107.68/31.88 107.68/31.88 match-boundness of the problem could not be verified. 107.68/31.88 107.68/31.88 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 107.68/31.88 failed due to the following reason: 107.68/31.88 107.68/31.88 match-boundness of the problem could not be verified. 107.68/31.88 107.68/31.88 107.68/31.88 107.68/31.88 107.68/31.88 107.68/31.88 107.68/31.88 107.68/31.88 Arrrr.. 107.93/31.91 EOF