MAYBE 107.13/31.97 MAYBE 107.13/31.97 107.13/31.97 We are left with following problem, upon which TcT provides the 107.13/31.97 certificate MAYBE. 107.13/31.97 107.13/31.97 Strict Trs: 107.13/31.97 { dbl(X) -> n__dbl(X) 107.13/31.97 , dbl(0()) -> 0() 107.13/31.97 , dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) 107.13/31.97 , s(X) -> n__s(X) 107.13/31.97 , activate(X) -> X 107.13/31.97 , activate(n__s(X)) -> s(X) 107.13/31.97 , activate(n__dbl(X)) -> dbl(X) 107.13/31.97 , activate(n__dbls(X)) -> dbls(X) 107.13/31.97 , activate(n__sel(X1, X2)) -> sel(X1, X2) 107.13/31.97 , activate(n__indx(X1, X2)) -> indx(X1, X2) 107.13/31.97 , activate(n__from(X)) -> from(X) 107.13/31.97 , dbls(X) -> n__dbls(X) 107.13/31.97 , dbls(nil()) -> nil() 107.13/31.97 , dbls(cons(X, Y)) -> 107.13/31.97 cons(n__dbl(activate(X)), n__dbls(activate(Y))) 107.13/31.97 , sel(X1, X2) -> n__sel(X1, X2) 107.13/31.97 , sel(0(), cons(X, Y)) -> activate(X) 107.13/31.97 , sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z)) 107.13/31.97 , indx(X1, X2) -> n__indx(X1, X2) 107.13/31.97 , indx(nil(), X) -> nil() 107.13/31.97 , indx(cons(X, Y), Z) -> 107.13/31.97 cons(n__sel(activate(X), activate(Z)), 107.13/31.97 n__indx(activate(Y), activate(Z))) 107.13/31.97 , from(X) -> cons(activate(X), n__from(n__s(activate(X)))) 107.13/31.97 , from(X) -> n__from(X) } 107.13/31.97 Obligation: 107.13/31.97 innermost runtime complexity 107.13/31.97 Answer: 107.13/31.97 MAYBE 107.13/31.97 107.13/31.97 Arguments of following rules are not normal-forms: 107.13/31.97 107.13/31.97 { dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) 107.13/31.97 , sel(s(X), cons(Y, Z)) -> sel(activate(X), activate(Z)) } 107.13/31.97 107.13/31.97 All above mentioned rules can be savely removed. 107.13/31.97 107.13/31.97 We are left with following problem, upon which TcT provides the 107.13/31.97 certificate MAYBE. 107.13/31.97 107.13/31.97 Strict Trs: 107.13/31.97 { dbl(X) -> n__dbl(X) 107.13/31.97 , dbl(0()) -> 0() 107.13/31.97 , s(X) -> n__s(X) 107.13/31.97 , activate(X) -> X 107.13/31.97 , activate(n__s(X)) -> s(X) 107.13/31.97 , activate(n__dbl(X)) -> dbl(X) 107.13/31.97 , activate(n__dbls(X)) -> dbls(X) 107.13/31.97 , activate(n__sel(X1, X2)) -> sel(X1, X2) 107.13/31.97 , activate(n__indx(X1, X2)) -> indx(X1, X2) 107.13/31.97 , activate(n__from(X)) -> from(X) 107.13/31.97 , dbls(X) -> n__dbls(X) 107.13/31.97 , dbls(nil()) -> nil() 107.13/31.97 , dbls(cons(X, Y)) -> 107.13/31.97 cons(n__dbl(activate(X)), n__dbls(activate(Y))) 107.13/31.97 , sel(X1, X2) -> n__sel(X1, X2) 107.13/31.97 , sel(0(), cons(X, Y)) -> activate(X) 107.13/31.97 , indx(X1, X2) -> n__indx(X1, X2) 107.13/31.97 , indx(nil(), X) -> nil() 107.13/31.97 , indx(cons(X, Y), Z) -> 107.13/31.97 cons(n__sel(activate(X), activate(Z)), 107.13/31.97 n__indx(activate(Y), activate(Z))) 107.13/31.97 , from(X) -> cons(activate(X), n__from(n__s(activate(X)))) 107.13/31.97 , from(X) -> n__from(X) } 107.13/31.97 Obligation: 107.13/31.97 innermost runtime complexity 107.13/31.97 Answer: 107.13/31.97 MAYBE 107.13/31.97 107.13/31.97 None of the processors succeeded. 107.13/31.97 107.13/31.97 Details of failed attempt(s): 107.13/31.97 ----------------------------- 107.13/31.97 1) 'empty' failed due to the following reason: 107.13/31.97 107.13/31.97 Empty strict component of the problem is NOT empty. 107.13/31.97 107.13/31.97 2) 'Best' failed due to the following reason: 107.13/31.97 107.13/31.97 None of the processors succeeded. 107.13/31.97 107.13/31.97 Details of failed attempt(s): 107.13/31.97 ----------------------------- 107.13/31.97 1) 'Best' failed due to the following reason: 107.13/31.97 107.13/31.97 None of the processors succeeded. 107.13/31.97 107.13/31.97 Details of failed attempt(s): 107.13/31.97 ----------------------------- 107.13/31.97 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 107.13/31.97 seconds)' failed due to the following reason: 107.13/31.97 107.13/31.97 None of the processors succeeded. 107.13/31.97 107.13/31.97 Details of failed attempt(s): 107.13/31.97 ----------------------------- 107.13/31.97 1) 'empty' failed due to the following reason: 107.13/31.97 107.13/31.97 Empty strict component of the problem is NOT empty. 107.13/31.97 107.13/31.97 2) 'With Problem ...' failed due to the following reason: 107.13/31.97 107.13/31.97 None of the processors succeeded. 107.13/31.97 107.13/31.97 Details of failed attempt(s): 107.13/31.97 ----------------------------- 107.13/31.97 1) 'empty' failed due to the following reason: 107.13/31.97 107.13/31.97 Empty strict component of the problem is NOT empty. 107.13/31.97 107.13/31.97 2) 'Fastest' failed due to the following reason: 107.13/31.97 107.13/31.97 None of the processors succeeded. 107.13/31.97 107.13/31.97 Details of failed attempt(s): 107.13/31.97 ----------------------------- 107.13/31.97 1) 'With Problem ...' failed due to the following reason: 107.13/31.97 107.13/31.97 None of the processors succeeded. 107.13/31.97 107.13/31.97 Details of failed attempt(s): 107.13/31.97 ----------------------------- 107.13/31.97 1) 'empty' failed due to the following reason: 107.13/31.97 107.13/31.97 Empty strict component of the problem is NOT empty. 107.13/31.97 107.13/31.97 2) 'With Problem ...' failed due to the following reason: 107.13/31.97 107.13/31.97 None of the processors succeeded. 107.13/31.97 107.13/31.97 Details of failed attempt(s): 107.13/31.97 ----------------------------- 107.13/31.97 1) 'empty' failed due to the following reason: 107.13/31.97 107.13/31.97 Empty strict component of the problem is NOT empty. 107.13/31.97 107.13/31.97 2) 'With Problem ...' failed due to the following reason: 107.13/31.97 107.13/31.97 None of the processors succeeded. 107.13/31.97 107.13/31.97 Details of failed attempt(s): 107.13/31.97 ----------------------------- 107.13/31.97 1) 'empty' failed due to the following reason: 107.13/31.97 107.13/31.97 Empty strict component of the problem is NOT empty. 107.13/31.97 107.13/31.97 2) 'With Problem ...' failed due to the following reason: 107.13/31.97 107.13/31.97 Empty strict component of the problem is NOT empty. 107.13/31.97 107.13/31.97 107.13/31.97 107.13/31.97 107.13/31.97 2) 'With Problem ...' failed due to the following reason: 107.13/31.97 107.13/31.97 None of the processors succeeded. 107.13/31.97 107.13/31.97 Details of failed attempt(s): 107.13/31.97 ----------------------------- 107.13/31.97 1) 'empty' failed due to the following reason: 107.13/31.97 107.13/31.97 Empty strict component of the problem is NOT empty. 107.13/31.97 107.13/31.97 2) 'With Problem ...' failed due to the following reason: 107.13/31.97 107.13/31.97 Empty strict component of the problem is NOT empty. 107.13/31.97 107.13/31.97 107.13/31.97 107.13/31.97 107.13/31.97 107.13/31.97 2) 'Best' failed due to the following reason: 107.13/31.97 107.13/31.97 None of the processors succeeded. 107.13/31.97 107.13/31.97 Details of failed attempt(s): 107.13/31.97 ----------------------------- 107.13/31.97 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 107.13/31.97 following reason: 107.13/31.97 107.13/31.97 The input cannot be shown compatible 107.13/31.97 107.13/31.97 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 107.13/31.97 to the following reason: 107.13/31.97 107.13/31.97 The input cannot be shown compatible 107.13/31.97 107.13/31.97 107.13/31.97 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 107.13/31.97 failed due to the following reason: 107.13/31.97 107.13/31.97 None of the processors succeeded. 107.13/31.97 107.13/31.97 Details of failed attempt(s): 107.13/31.97 ----------------------------- 107.13/31.97 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 107.13/31.97 failed due to the following reason: 107.13/31.97 107.13/31.97 match-boundness of the problem could not be verified. 107.13/31.97 107.13/31.97 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 107.13/31.97 failed due to the following reason: 107.13/31.97 107.13/31.97 match-boundness of the problem could not be verified. 107.13/31.97 107.13/31.97 107.13/31.97 107.13/31.97 2) 'With Problem ... (timeout of 297 seconds)' failed due to the 107.13/31.97 following reason: 107.13/31.97 107.13/31.97 We add the following weak dependency pairs: 107.13/31.97 107.13/31.97 Strict DPs: 107.13/31.97 { dbl^#(X) -> c_1() 107.13/31.97 , dbl^#(0()) -> c_2() 107.13/31.97 , s^#(X) -> c_3() 107.13/31.97 , activate^#(X) -> c_4() 107.13/31.97 , activate^#(n__s(X)) -> c_5(s^#(X)) 107.13/31.97 , activate^#(n__dbl(X)) -> c_6(dbl^#(X)) 107.13/31.97 , activate^#(n__dbls(X)) -> c_7(dbls^#(X)) 107.13/31.97 , activate^#(n__sel(X1, X2)) -> c_8(sel^#(X1, X2)) 107.13/31.97 , activate^#(n__indx(X1, X2)) -> c_9(indx^#(X1, X2)) 107.13/31.97 , activate^#(n__from(X)) -> c_10(from^#(X)) 107.13/31.97 , dbls^#(X) -> c_11() 107.13/31.97 , dbls^#(nil()) -> c_12() 107.13/31.97 , dbls^#(cons(X, Y)) -> c_13(activate^#(X), activate^#(Y)) 107.13/31.97 , sel^#(X1, X2) -> c_14() 107.13/31.97 , sel^#(0(), cons(X, Y)) -> c_15(activate^#(X)) 107.13/31.97 , indx^#(X1, X2) -> c_16() 107.13/31.97 , indx^#(nil(), X) -> c_17() 107.13/31.97 , indx^#(cons(X, Y), Z) -> 107.13/31.97 c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.13/31.97 , from^#(X) -> c_19(activate^#(X), activate^#(X)) 107.13/31.97 , from^#(X) -> c_20() } 107.13/31.97 107.13/31.97 and mark the set of starting terms. 107.13/31.97 107.13/31.97 We are left with following problem, upon which TcT provides the 107.13/31.97 certificate MAYBE. 107.13/31.97 107.13/31.97 Strict DPs: 107.13/31.97 { dbl^#(X) -> c_1() 107.13/31.97 , dbl^#(0()) -> c_2() 107.13/31.97 , s^#(X) -> c_3() 107.13/31.97 , activate^#(X) -> c_4() 107.13/31.97 , activate^#(n__s(X)) -> c_5(s^#(X)) 107.13/31.97 , activate^#(n__dbl(X)) -> c_6(dbl^#(X)) 107.13/31.97 , activate^#(n__dbls(X)) -> c_7(dbls^#(X)) 107.13/31.97 , activate^#(n__sel(X1, X2)) -> c_8(sel^#(X1, X2)) 107.13/31.97 , activate^#(n__indx(X1, X2)) -> c_9(indx^#(X1, X2)) 107.13/31.97 , activate^#(n__from(X)) -> c_10(from^#(X)) 107.13/31.97 , dbls^#(X) -> c_11() 107.13/31.97 , dbls^#(nil()) -> c_12() 107.13/31.97 , dbls^#(cons(X, Y)) -> c_13(activate^#(X), activate^#(Y)) 107.13/31.97 , sel^#(X1, X2) -> c_14() 107.13/31.97 , sel^#(0(), cons(X, Y)) -> c_15(activate^#(X)) 107.13/31.97 , indx^#(X1, X2) -> c_16() 107.13/31.97 , indx^#(nil(), X) -> c_17() 107.13/31.97 , indx^#(cons(X, Y), Z) -> 107.13/31.97 c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.13/31.97 , from^#(X) -> c_19(activate^#(X), activate^#(X)) 107.13/31.97 , from^#(X) -> c_20() } 107.13/31.97 Strict Trs: 107.13/31.97 { dbl(X) -> n__dbl(X) 107.13/31.97 , dbl(0()) -> 0() 107.13/31.97 , s(X) -> n__s(X) 107.13/31.97 , activate(X) -> X 107.13/31.97 , activate(n__s(X)) -> s(X) 107.13/31.97 , activate(n__dbl(X)) -> dbl(X) 107.13/31.97 , activate(n__dbls(X)) -> dbls(X) 107.13/31.97 , activate(n__sel(X1, X2)) -> sel(X1, X2) 107.13/31.97 , activate(n__indx(X1, X2)) -> indx(X1, X2) 107.13/31.97 , activate(n__from(X)) -> from(X) 107.13/31.97 , dbls(X) -> n__dbls(X) 107.13/31.97 , dbls(nil()) -> nil() 107.13/31.97 , dbls(cons(X, Y)) -> 107.13/31.97 cons(n__dbl(activate(X)), n__dbls(activate(Y))) 107.13/31.97 , sel(X1, X2) -> n__sel(X1, X2) 107.13/31.97 , sel(0(), cons(X, Y)) -> activate(X) 107.13/31.97 , indx(X1, X2) -> n__indx(X1, X2) 107.13/31.97 , indx(nil(), X) -> nil() 107.13/31.97 , indx(cons(X, Y), Z) -> 107.13/31.97 cons(n__sel(activate(X), activate(Z)), 107.13/31.97 n__indx(activate(Y), activate(Z))) 107.13/31.97 , from(X) -> cons(activate(X), n__from(n__s(activate(X)))) 107.13/31.97 , from(X) -> n__from(X) } 107.13/31.97 Obligation: 107.13/31.97 innermost runtime complexity 107.13/31.97 Answer: 107.13/31.97 MAYBE 107.13/31.97 107.13/31.97 No rule is usable, rules are removed from the input problem. 107.13/31.97 107.13/31.97 We are left with following problem, upon which TcT provides the 107.13/31.97 certificate MAYBE. 107.13/31.97 107.13/31.97 Strict DPs: 107.13/31.97 { dbl^#(X) -> c_1() 107.13/31.97 , dbl^#(0()) -> c_2() 107.13/31.97 , s^#(X) -> c_3() 107.13/31.97 , activate^#(X) -> c_4() 107.13/31.97 , activate^#(n__s(X)) -> c_5(s^#(X)) 107.13/31.97 , activate^#(n__dbl(X)) -> c_6(dbl^#(X)) 107.13/31.97 , activate^#(n__dbls(X)) -> c_7(dbls^#(X)) 107.13/31.97 , activate^#(n__sel(X1, X2)) -> c_8(sel^#(X1, X2)) 107.13/31.97 , activate^#(n__indx(X1, X2)) -> c_9(indx^#(X1, X2)) 107.13/31.97 , activate^#(n__from(X)) -> c_10(from^#(X)) 107.13/31.97 , dbls^#(X) -> c_11() 107.13/31.97 , dbls^#(nil()) -> c_12() 107.13/31.97 , dbls^#(cons(X, Y)) -> c_13(activate^#(X), activate^#(Y)) 107.13/31.97 , sel^#(X1, X2) -> c_14() 107.13/31.97 , sel^#(0(), cons(X, Y)) -> c_15(activate^#(X)) 107.13/31.97 , indx^#(X1, X2) -> c_16() 107.13/31.97 , indx^#(nil(), X) -> c_17() 107.13/31.97 , indx^#(cons(X, Y), Z) -> 107.13/31.97 c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.13/31.97 , from^#(X) -> c_19(activate^#(X), activate^#(X)) 107.13/31.97 , from^#(X) -> c_20() } 107.13/31.97 Obligation: 107.13/31.97 innermost runtime complexity 107.13/31.97 Answer: 107.13/31.97 MAYBE 107.13/31.97 107.13/31.97 The weightgap principle applies (using the following constant 107.13/31.97 growth matrix-interpretation) 107.13/31.97 107.13/31.97 The following argument positions are usable: 107.13/31.97 Uargs(c_5) = {1}, Uargs(c_6) = {1}, Uargs(c_7) = {1}, 107.13/31.97 Uargs(c_8) = {1}, Uargs(c_9) = {1}, Uargs(c_10) = {1}, 107.13/31.97 Uargs(c_13) = {1, 2}, Uargs(c_15) = {1}, 107.13/31.97 Uargs(c_18) = {1, 2, 3, 4}, Uargs(c_19) = {1, 2} 107.13/31.97 107.13/31.97 TcT has computed the following constructor-restricted matrix 107.13/31.97 interpretation. 107.13/31.97 107.13/31.97 [0] = [1] 107.13/31.97 [1] 107.13/31.97 107.13/31.97 [n__s](x1) = [1 2] x1 + [1] 107.13/31.97 [0 1] [2] 107.13/31.97 107.13/31.97 [n__dbl](x1) = [1 2] x1 + [1] 107.13/31.97 [0 1] [1] 107.13/31.97 107.13/31.97 [nil] = [1] 107.13/31.97 [1] 107.13/31.97 107.13/31.97 [cons](x1, x2) = [1 2] x1 + [1 1] x2 + [1] 107.13/31.97 [0 1] [0 1] [1] 107.13/31.97 107.13/31.97 [n__dbls](x1) = [1 2] x1 + [1] 107.13/31.97 [0 1] [1] 107.13/31.97 107.13/31.97 [n__sel](x1, x2) = [1 2] x1 + [1 2] x2 + [1] 107.13/31.97 [0 1] [0 1] [1] 107.13/31.97 107.13/31.97 [n__indx](x1, x2) = [1 2] x1 + [1 2] x2 + [1] 107.13/31.97 [0 1] [0 1] [2] 107.13/31.97 107.13/31.97 [n__from](x1) = [1 2] x1 + [1] 107.13/31.97 [0 1] [2] 107.13/31.97 107.13/31.97 [dbl^#](x1) = [0 0] x1 + [1] 107.13/31.97 [2 1] [1] 107.13/31.97 107.13/31.97 [c_1] = [0] 107.13/31.97 [1] 107.13/31.97 107.13/31.97 [c_2] = [0] 107.13/31.97 [0] 107.13/31.97 107.13/31.97 [s^#](x1) = [0 0] x1 + [1] 107.13/31.97 [1 1] [1] 107.13/31.97 107.13/31.97 [c_3] = [0] 107.13/31.97 [1] 107.13/31.97 107.13/31.97 [activate^#](x1) = [0 0] x1 + [1] 107.13/31.97 [1 1] [0] 107.13/31.97 107.13/31.97 [c_4] = [0] 107.13/31.97 [0] 107.13/31.97 107.13/31.97 [c_5](x1) = [1 0] x1 + [2] 107.13/31.97 [0 1] [2] 107.13/31.98 107.13/31.98 [c_6](x1) = [1 0] x1 + [2] 107.13/31.98 [0 1] [1] 107.13/31.98 107.13/31.98 [c_7](x1) = [1 0] x1 + [2] 107.13/31.98 [0 1] [1] 107.13/31.98 107.13/31.98 [dbls^#](x1) = [0 0] x1 + [1] 107.13/31.98 [2 2] [2] 107.13/31.98 107.13/31.98 [c_8](x1) = [1 0] x1 + [2] 107.13/31.98 [0 1] [2] 107.13/31.98 107.13/31.98 [sel^#](x1, x2) = [0 0] x1 + [0 0] x2 + [1] 107.13/31.98 [1 2] [2 2] [0] 107.13/31.98 107.13/31.98 [c_9](x1) = [1 0] x1 + [2] 107.13/31.98 [0 1] [1] 107.13/31.98 107.13/31.98 [indx^#](x1, x2) = [0 0] x1 + [0 0] x2 + [1] 107.13/31.98 [1 1] [2 1] [2] 107.13/31.98 107.13/31.98 [c_10](x1) = [1 0] x1 + [2] 107.13/31.98 [0 1] [2] 107.13/31.98 107.13/31.98 [from^#](x1) = [0 0] x1 + [1] 107.13/31.98 [1 1] [1] 107.13/31.98 107.13/31.98 [c_11] = [0] 107.13/31.98 [1] 107.13/31.98 107.13/31.98 [c_12] = [0] 107.13/31.98 [1] 107.13/31.98 107.13/31.98 [c_13](x1, x2) = [1 0] x1 + [1 0] x2 + [1] 107.13/31.98 [0 1] [0 1] [2] 107.13/31.98 107.13/31.98 [c_14] = [0] 107.13/31.98 [0] 107.13/31.98 107.13/31.98 [c_15](x1) = [1 0] x1 + [1] 107.13/31.98 [0 1] [2] 107.13/31.98 107.13/31.98 [c_16] = [0] 107.13/31.98 [1] 107.13/31.98 107.13/31.98 [c_17] = [0] 107.13/31.98 [0] 107.13/31.98 107.13/31.98 [c_18](x1, x2, x3, x4) = [1 0] x1 + [1 0] x2 + [1 0] x3 + [1 107.13/31.98 0] x4 + [2] 107.13/31.98 [0 1] [0 1] [0 1] [0 107.13/31.98 1] [2] 107.13/31.98 107.13/31.98 [c_19](x1, x2) = [1 0] x1 + [1 0] x2 + [1] 107.13/31.98 [0 1] [0 1] [2] 107.13/31.98 107.13/31.98 [c_20] = [0] 107.13/31.98 [1] 107.13/31.98 107.13/31.98 The order satisfies the following ordering constraints: 107.13/31.98 107.13/31.98 [dbl^#(X)] = [0 0] X + [1] 107.13/31.98 [2 1] [1] 107.13/31.98 > [0] 107.13/31.98 [1] 107.13/31.98 = [c_1()] 107.13/31.98 107.13/31.98 [dbl^#(0())] = [1] 107.13/31.98 [4] 107.13/31.98 > [0] 107.13/31.98 [0] 107.13/31.98 = [c_2()] 107.13/31.98 107.13/31.98 [s^#(X)] = [0 0] X + [1] 107.13/31.98 [1 1] [1] 107.13/31.98 > [0] 107.13/31.98 [1] 107.13/31.98 = [c_3()] 107.13/31.98 107.13/31.98 [activate^#(X)] = [0 0] X + [1] 107.13/31.98 [1 1] [0] 107.13/31.98 > [0] 107.13/31.98 [0] 107.13/31.98 = [c_4()] 107.13/31.98 107.13/31.98 [activate^#(n__s(X))] = [0 0] X + [1] 107.13/31.98 [1 3] [3] 107.13/31.98 ? [0 0] X + [3] 107.13/31.98 [1 1] [3] 107.13/31.98 = [c_5(s^#(X))] 107.13/31.98 107.13/31.98 [activate^#(n__dbl(X))] = [0 0] X + [1] 107.13/31.98 [1 3] [2] 107.13/31.98 ? [0 0] X + [3] 107.13/31.98 [2 1] [2] 107.13/31.98 = [c_6(dbl^#(X))] 107.13/31.98 107.13/31.98 [activate^#(n__dbls(X))] = [0 0] X + [1] 107.13/31.98 [1 3] [2] 107.13/31.98 ? [0 0] X + [3] 107.13/31.98 [2 2] [3] 107.13/31.98 = [c_7(dbls^#(X))] 107.13/31.98 107.13/31.98 [activate^#(n__sel(X1, X2))] = [0 0] X1 + [0 0] X2 + [1] 107.13/31.98 [1 3] [1 3] [2] 107.13/31.98 ? [0 0] X1 + [0 0] X2 + [3] 107.13/31.98 [1 2] [2 2] [2] 107.13/31.98 = [c_8(sel^#(X1, X2))] 107.13/31.98 107.13/31.98 [activate^#(n__indx(X1, X2))] = [0 0] X1 + [0 0] X2 + [1] 107.13/31.98 [1 3] [1 3] [3] 107.13/31.98 ? [0 0] X1 + [0 0] X2 + [3] 107.13/31.98 [1 1] [2 1] [3] 107.13/31.98 = [c_9(indx^#(X1, X2))] 107.13/31.98 107.13/31.98 [activate^#(n__from(X))] = [0 0] X + [1] 107.13/31.98 [1 3] [3] 107.13/31.98 ? [0 0] X + [3] 107.13/31.98 [1 1] [3] 107.13/31.98 = [c_10(from^#(X))] 107.13/31.98 107.13/31.98 [dbls^#(X)] = [0 0] X + [1] 107.13/31.98 [2 2] [2] 107.13/31.98 > [0] 107.13/31.98 [1] 107.13/31.98 = [c_11()] 107.13/31.98 107.13/31.98 [dbls^#(nil())] = [1] 107.13/31.98 [6] 107.13/31.98 > [0] 107.13/31.98 [1] 107.13/31.98 = [c_12()] 107.13/31.98 107.13/31.98 [dbls^#(cons(X, Y))] = [0 0] X + [0 0] Y + [1] 107.13/31.98 [2 6] [2 4] [6] 107.13/31.98 ? [0 0] X + [0 0] Y + [3] 107.13/31.98 [1 1] [1 1] [2] 107.13/31.98 = [c_13(activate^#(X), activate^#(Y))] 107.13/31.98 107.13/31.98 [sel^#(X1, X2)] = [0 0] X1 + [0 0] X2 + [1] 107.13/31.98 [1 2] [2 2] [0] 107.13/31.98 > [0] 107.13/31.98 [0] 107.13/31.98 = [c_14()] 107.13/31.98 107.13/31.98 [sel^#(0(), cons(X, Y))] = [0 0] X + [0 0] Y + [1] 107.13/31.98 [2 6] [2 4] [7] 107.13/31.98 ? [0 0] X + [2] 107.13/31.98 [1 1] [2] 107.13/31.98 = [c_15(activate^#(X))] 107.13/31.98 107.13/31.98 [indx^#(X1, X2)] = [0 0] X1 + [0 0] X2 + [1] 107.13/31.98 [1 1] [2 1] [2] 107.13/31.98 > [0] 107.13/31.98 [1] 107.13/31.98 = [c_16()] 107.13/31.98 107.13/31.98 [indx^#(nil(), X)] = [0 0] X + [1] 107.13/31.98 [2 1] [4] 107.13/31.98 > [0] 107.13/31.98 [0] 107.13/31.98 = [c_17()] 107.13/31.98 107.13/31.98 [indx^#(cons(X, Y), Z)] = [0 0] X + [0 0] Y + [0 0] Z + [1] 107.13/31.98 [1 3] [1 2] [2 1] [4] 107.13/31.98 ? [0 0] X + [0 0] Y + [0 0] Z + [6] 107.13/31.98 [1 1] [1 1] [2 2] [2] 107.13/31.98 = [c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z))] 107.13/31.98 107.13/31.98 [from^#(X)] = [0 0] X + [1] 107.13/31.98 [1 1] [1] 107.13/31.98 ? [0 0] X + [3] 107.13/31.98 [2 2] [2] 107.13/31.98 = [c_19(activate^#(X), activate^#(X))] 107.13/31.98 107.13/31.98 [from^#(X)] = [0 0] X + [1] 107.13/31.98 [1 1] [1] 107.13/31.98 > [0] 107.13/31.98 [1] 107.13/31.98 = [c_20()] 107.13/31.98 107.13/31.98 107.13/31.98 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 107.13/31.98 107.13/31.98 We are left with following problem, upon which TcT provides the 107.13/31.98 certificate MAYBE. 107.13/31.98 107.13/31.98 Strict DPs: 107.13/31.98 { activate^#(n__s(X)) -> c_5(s^#(X)) 107.13/31.98 , activate^#(n__dbl(X)) -> c_6(dbl^#(X)) 107.13/31.98 , activate^#(n__dbls(X)) -> c_7(dbls^#(X)) 107.13/31.98 , activate^#(n__sel(X1, X2)) -> c_8(sel^#(X1, X2)) 107.13/31.98 , activate^#(n__indx(X1, X2)) -> c_9(indx^#(X1, X2)) 107.13/31.98 , activate^#(n__from(X)) -> c_10(from^#(X)) 107.13/31.98 , dbls^#(cons(X, Y)) -> c_13(activate^#(X), activate^#(Y)) 107.13/31.98 , sel^#(0(), cons(X, Y)) -> c_15(activate^#(X)) 107.13/31.98 , indx^#(cons(X, Y), Z) -> 107.13/31.98 c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.13/31.98 , from^#(X) -> c_19(activate^#(X), activate^#(X)) } 107.13/31.98 Weak DPs: 107.13/31.98 { dbl^#(X) -> c_1() 107.13/31.98 , dbl^#(0()) -> c_2() 107.13/31.98 , s^#(X) -> c_3() 107.13/31.98 , activate^#(X) -> c_4() 107.13/31.98 , dbls^#(X) -> c_11() 107.13/31.98 , dbls^#(nil()) -> c_12() 107.13/31.98 , sel^#(X1, X2) -> c_14() 107.13/31.98 , indx^#(X1, X2) -> c_16() 107.13/31.98 , indx^#(nil(), X) -> c_17() 107.13/31.98 , from^#(X) -> c_20() } 107.13/31.98 Obligation: 107.13/31.98 innermost runtime complexity 107.13/31.98 Answer: 107.13/31.98 MAYBE 107.13/31.98 107.13/31.98 We estimate the number of application of {1,2} by applications of 107.13/31.98 Pre({1,2}) = {7,8,9,10}. Here rules are labeled as follows: 107.13/31.98 107.13/31.98 DPs: 107.13/31.98 { 1: activate^#(n__s(X)) -> c_5(s^#(X)) 107.13/31.98 , 2: activate^#(n__dbl(X)) -> c_6(dbl^#(X)) 107.13/31.98 , 3: activate^#(n__dbls(X)) -> c_7(dbls^#(X)) 107.13/31.98 , 4: activate^#(n__sel(X1, X2)) -> c_8(sel^#(X1, X2)) 107.13/31.98 , 5: activate^#(n__indx(X1, X2)) -> c_9(indx^#(X1, X2)) 107.13/31.98 , 6: activate^#(n__from(X)) -> c_10(from^#(X)) 107.13/31.98 , 7: dbls^#(cons(X, Y)) -> c_13(activate^#(X), activate^#(Y)) 107.13/31.98 , 8: sel^#(0(), cons(X, Y)) -> c_15(activate^#(X)) 107.13/31.98 , 9: indx^#(cons(X, Y), Z) -> 107.13/31.98 c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.13/31.98 , 10: from^#(X) -> c_19(activate^#(X), activate^#(X)) 107.13/31.98 , 11: dbl^#(X) -> c_1() 107.13/31.98 , 12: dbl^#(0()) -> c_2() 107.13/31.98 , 13: s^#(X) -> c_3() 107.13/31.98 , 14: activate^#(X) -> c_4() 107.13/31.98 , 15: dbls^#(X) -> c_11() 107.13/31.98 , 16: dbls^#(nil()) -> c_12() 107.13/31.98 , 17: sel^#(X1, X2) -> c_14() 107.13/31.98 , 18: indx^#(X1, X2) -> c_16() 107.13/31.98 , 19: indx^#(nil(), X) -> c_17() 107.13/31.98 , 20: from^#(X) -> c_20() } 107.13/31.98 107.13/31.98 We are left with following problem, upon which TcT provides the 107.13/31.98 certificate MAYBE. 107.13/31.98 107.13/31.98 Strict DPs: 107.13/31.98 { activate^#(n__dbls(X)) -> c_7(dbls^#(X)) 107.13/31.98 , activate^#(n__sel(X1, X2)) -> c_8(sel^#(X1, X2)) 107.13/31.98 , activate^#(n__indx(X1, X2)) -> c_9(indx^#(X1, X2)) 107.13/31.98 , activate^#(n__from(X)) -> c_10(from^#(X)) 107.13/31.98 , dbls^#(cons(X, Y)) -> c_13(activate^#(X), activate^#(Y)) 107.13/31.98 , sel^#(0(), cons(X, Y)) -> c_15(activate^#(X)) 107.13/31.98 , indx^#(cons(X, Y), Z) -> 107.13/31.98 c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.13/31.98 , from^#(X) -> c_19(activate^#(X), activate^#(X)) } 107.13/31.98 Weak DPs: 107.13/31.98 { dbl^#(X) -> c_1() 107.13/31.98 , dbl^#(0()) -> c_2() 107.13/31.98 , s^#(X) -> c_3() 107.13/31.98 , activate^#(X) -> c_4() 107.13/31.98 , activate^#(n__s(X)) -> c_5(s^#(X)) 107.13/31.98 , activate^#(n__dbl(X)) -> c_6(dbl^#(X)) 107.13/31.98 , dbls^#(X) -> c_11() 107.13/31.98 , dbls^#(nil()) -> c_12() 107.13/31.98 , sel^#(X1, X2) -> c_14() 107.13/31.98 , indx^#(X1, X2) -> c_16() 107.13/31.98 , indx^#(nil(), X) -> c_17() 107.13/31.98 , from^#(X) -> c_20() } 107.13/31.98 Obligation: 107.13/31.98 innermost runtime complexity 107.13/31.98 Answer: 107.13/31.98 MAYBE 107.13/31.98 107.13/31.98 The following weak DPs constitute a sub-graph of the DG that is 107.13/31.98 closed under successors. The DPs are removed. 107.13/31.98 107.13/31.98 { dbl^#(X) -> c_1() 107.13/31.98 , dbl^#(0()) -> c_2() 107.13/31.98 , s^#(X) -> c_3() 107.13/31.98 , activate^#(X) -> c_4() 107.13/31.98 , activate^#(n__s(X)) -> c_5(s^#(X)) 107.13/31.98 , activate^#(n__dbl(X)) -> c_6(dbl^#(X)) 107.13/31.98 , dbls^#(X) -> c_11() 107.13/31.98 , dbls^#(nil()) -> c_12() 107.13/31.98 , sel^#(X1, X2) -> c_14() 107.13/31.98 , indx^#(X1, X2) -> c_16() 107.13/31.98 , indx^#(nil(), X) -> c_17() 107.13/31.98 , from^#(X) -> c_20() } 107.13/31.98 107.13/31.98 We are left with following problem, upon which TcT provides the 107.13/31.98 certificate MAYBE. 107.13/31.98 107.13/31.98 Strict DPs: 107.13/31.98 { activate^#(n__dbls(X)) -> c_7(dbls^#(X)) 107.13/31.98 , activate^#(n__sel(X1, X2)) -> c_8(sel^#(X1, X2)) 107.13/31.98 , activate^#(n__indx(X1, X2)) -> c_9(indx^#(X1, X2)) 107.13/31.98 , activate^#(n__from(X)) -> c_10(from^#(X)) 107.13/31.98 , dbls^#(cons(X, Y)) -> c_13(activate^#(X), activate^#(Y)) 107.13/31.98 , sel^#(0(), cons(X, Y)) -> c_15(activate^#(X)) 107.13/31.98 , indx^#(cons(X, Y), Z) -> 107.13/31.98 c_18(activate^#(X), activate^#(Z), activate^#(Y), activate^#(Z)) 107.13/31.98 , from^#(X) -> c_19(activate^#(X), activate^#(X)) } 107.13/31.98 Obligation: 107.13/31.98 innermost runtime complexity 107.13/31.98 Answer: 107.13/31.98 MAYBE 107.13/31.98 107.13/31.98 None of the processors succeeded. 107.13/31.98 107.13/31.98 Details of failed attempt(s): 107.13/31.98 ----------------------------- 107.13/31.98 1) 'empty' failed due to the following reason: 107.13/31.98 107.13/31.98 Empty strict component of the problem is NOT empty. 107.13/31.98 107.13/31.98 2) 'With Problem ...' failed due to the following reason: 107.13/31.98 107.13/31.98 None of the processors succeeded. 107.13/31.98 107.13/31.98 Details of failed attempt(s): 107.13/31.98 ----------------------------- 107.13/31.98 1) 'empty' failed due to the following reason: 107.13/31.98 107.13/31.98 Empty strict component of the problem is NOT empty. 107.13/31.98 107.13/31.98 2) 'Fastest' failed due to the following reason: 107.13/31.98 107.13/31.98 None of the processors succeeded. 107.13/31.98 107.13/31.98 Details of failed attempt(s): 107.13/31.98 ----------------------------- 107.13/31.98 1) 'With Problem ...' failed due to the following reason: 107.13/31.98 107.13/31.98 None of the processors succeeded. 107.13/31.98 107.13/31.98 Details of failed attempt(s): 107.13/31.98 ----------------------------- 107.13/31.98 1) 'empty' failed due to the following reason: 107.13/31.98 107.13/31.98 Empty strict component of the problem is NOT empty. 107.13/31.98 107.13/31.98 2) 'Polynomial Path Order (PS)' failed due to the following reason: 107.13/31.98 107.13/31.98 The input cannot be shown compatible 107.13/31.98 107.13/31.98 107.13/31.98 2) 'Polynomial Path Order (PS)' failed due to the following reason: 107.13/31.98 107.13/31.98 The input cannot be shown compatible 107.13/31.98 107.13/31.98 3) 'Fastest (timeout of 24 seconds)' failed due to the following 107.13/31.98 reason: 107.13/31.98 107.13/31.98 None of the processors succeeded. 107.13/31.98 107.13/31.98 Details of failed attempt(s): 107.13/31.98 ----------------------------- 107.13/31.98 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 107.13/31.98 failed due to the following reason: 107.13/31.98 107.13/31.98 match-boundness of the problem could not be verified. 107.13/31.98 107.13/31.98 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 107.13/31.98 failed due to the following reason: 107.13/31.98 107.13/31.98 match-boundness of the problem could not be verified. 107.13/31.98 107.13/31.98 107.13/31.98 107.13/31.98 107.13/31.98 107.13/31.98 107.13/31.98 107.13/31.98 Arrrr.. 107.35/32.00 EOF