MAYBE 726.97/297.04 MAYBE 726.97/297.04 726.97/297.04 We are left with following problem, upon which TcT provides the 726.97/297.04 certificate MAYBE. 726.97/297.04 726.97/297.04 Strict Trs: 726.97/297.04 { from(X) -> cons(X, n__from(n__s(X))) 726.97/297.04 , from(X) -> n__from(X) 726.97/297.04 , sel(0(), cons(X, XS)) -> X 726.97/297.04 , sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) 726.97/297.04 , s(X) -> n__s(X) 726.97/297.04 , activate(X) -> X 726.97/297.04 , activate(n__from(X)) -> from(activate(X)) 726.97/297.04 , activate(n__s(X)) -> s(activate(X)) 726.97/297.04 , activate(n__zWquot(X1, X2)) -> zWquot(activate(X1), activate(X2)) 726.97/297.04 , minus(X, 0()) -> 0() 726.97/297.04 , minus(s(X), s(Y)) -> minus(X, Y) 726.97/297.04 , quot(0(), s(Y)) -> 0() 726.97/297.04 , quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) 726.97/297.04 , zWquot(X1, X2) -> n__zWquot(X1, X2) 726.97/297.04 , zWquot(XS, nil()) -> nil() 726.97/297.04 , zWquot(cons(X, XS), cons(Y, YS)) -> 726.97/297.04 cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) 726.97/297.04 , zWquot(nil(), XS) -> nil() } 726.97/297.04 Obligation: 726.97/297.04 innermost runtime complexity 726.97/297.04 Answer: 726.97/297.04 MAYBE 726.97/297.04 726.97/297.04 Arguments of following rules are not normal-forms: 726.97/297.04 726.97/297.04 { sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) 726.97/297.04 , minus(s(X), s(Y)) -> minus(X, Y) 726.97/297.04 , quot(0(), s(Y)) -> 0() 726.97/297.04 , quot(s(X), s(Y)) -> s(quot(minus(X, Y), s(Y))) } 726.97/297.04 726.97/297.04 All above mentioned rules can be savely removed. 726.97/297.04 726.97/297.04 We are left with following problem, upon which TcT provides the 726.97/297.04 certificate MAYBE. 726.97/297.04 726.97/297.04 Strict Trs: 726.97/297.04 { from(X) -> cons(X, n__from(n__s(X))) 726.97/297.04 , from(X) -> n__from(X) 726.97/297.04 , sel(0(), cons(X, XS)) -> X 726.97/297.04 , s(X) -> n__s(X) 726.97/297.04 , activate(X) -> X 726.97/297.04 , activate(n__from(X)) -> from(activate(X)) 726.97/297.04 , activate(n__s(X)) -> s(activate(X)) 726.97/297.04 , activate(n__zWquot(X1, X2)) -> zWquot(activate(X1), activate(X2)) 726.97/297.04 , minus(X, 0()) -> 0() 726.97/297.04 , zWquot(X1, X2) -> n__zWquot(X1, X2) 726.97/297.04 , zWquot(XS, nil()) -> nil() 726.97/297.04 , zWquot(cons(X, XS), cons(Y, YS)) -> 726.97/297.04 cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) 726.97/297.04 , zWquot(nil(), XS) -> nil() } 726.97/297.04 Obligation: 726.97/297.04 innermost runtime complexity 726.97/297.04 Answer: 726.97/297.04 MAYBE 726.97/297.04 726.97/297.04 None of the processors succeeded. 726.97/297.04 726.97/297.04 Details of failed attempt(s): 726.97/297.04 ----------------------------- 726.97/297.04 1) 'empty' failed due to the following reason: 726.97/297.04 726.97/297.04 Empty strict component of the problem is NOT empty. 726.97/297.04 726.97/297.04 2) 'Best' failed due to the following reason: 726.97/297.04 726.97/297.04 None of the processors succeeded. 726.97/297.04 726.97/297.04 Details of failed attempt(s): 726.97/297.04 ----------------------------- 726.97/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 726.97/297.04 following reason: 726.97/297.04 726.97/297.04 Computation stopped due to timeout after 297.0 seconds. 726.97/297.04 726.97/297.04 2) 'Best' failed due to the following reason: 726.97/297.04 726.97/297.04 None of the processors succeeded. 726.97/297.04 726.97/297.04 Details of failed attempt(s): 726.97/297.04 ----------------------------- 726.97/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 726.97/297.04 seconds)' failed due to the following reason: 726.97/297.04 726.97/297.04 None of the processors succeeded. 726.97/297.04 726.97/297.04 Details of failed attempt(s): 726.97/297.04 ----------------------------- 726.97/297.04 1) 'empty' failed due to the following reason: 726.97/297.04 726.97/297.04 Empty strict component of the problem is NOT empty. 726.97/297.04 726.97/297.04 2) 'With Problem ...' failed due to the following reason: 726.97/297.04 726.97/297.04 None of the processors succeeded. 726.97/297.04 726.97/297.04 Details of failed attempt(s): 726.97/297.04 ----------------------------- 726.97/297.04 1) 'empty' failed due to the following reason: 726.97/297.04 726.97/297.04 Empty strict component of the problem is NOT empty. 726.97/297.04 726.97/297.04 2) 'Fastest' failed due to the following reason: 726.97/297.04 726.97/297.04 None of the processors succeeded. 726.97/297.04 726.97/297.04 Details of failed attempt(s): 726.97/297.04 ----------------------------- 726.97/297.04 1) 'With Problem ...' failed due to the following reason: 726.97/297.04 726.97/297.04 We use the processor 'matrix interpretation of dimension 3' to 726.97/297.04 orient following rules strictly. 726.97/297.04 726.97/297.04 Trs: 726.97/297.04 { sel(0(), cons(X, XS)) -> X 726.97/297.04 , minus(X, 0()) -> 0() 726.97/297.04 , zWquot(XS, nil()) -> nil() 726.97/297.04 , zWquot(nil(), XS) -> nil() } 726.97/297.04 726.97/297.04 The induced complexity on above rules (modulo remaining rules) is 726.97/297.04 YES(?,O(n^1)) . These rules are moved into the corresponding weak 726.97/297.04 component(s). 726.97/297.04 726.97/297.04 Sub-proof: 726.97/297.04 ---------- 726.97/297.04 The following argument positions are usable: 726.97/297.04 Uargs(from) = {1}, Uargs(cons) = {2}, Uargs(s) = {1}, 726.97/297.04 Uargs(zWquot) = {1, 2}, Uargs(n__zWquot) = {1, 2} 726.97/297.04 726.97/297.04 TcT has computed the following constructor-based matrix 726.97/297.04 interpretation satisfying not(EDA) and not(IDA(1)). 726.97/297.04 726.97/297.04 [1 0 0] [0] 726.97/297.04 [from](x1) = [1 0 0] x1 + [0] 726.97/297.04 [0 1 1] [0] 726.97/297.04 726.97/297.04 [0 0 0] [1 0 0] [0] 726.97/297.04 [cons](x1, x2) = [1 0 0] x1 + [0 0 0] x2 + [0] 726.97/297.04 [0 1 1] [0 0 0] [0] 726.97/297.04 726.97/297.04 [1 0 0] [0] 726.97/297.04 [n__from](x1) = [1 0 0] x1 + [0] 726.97/297.04 [0 1 1] [0] 726.97/297.04 726.97/297.04 [1 0 0] [0] 726.97/297.04 [n__s](x1) = [0 0 0] x1 + [0] 726.97/297.04 [0 0 0] [0] 726.97/297.04 726.97/297.04 [7 4 0] [0 1 0] [7] 726.97/297.04 [sel](x1, x2) = [7 7 7] x1 + [0 0 1] x2 + [7] 726.97/297.04 [7 7 7] [0 0 1] [7] 726.97/297.04 726.97/297.04 [0] 726.97/297.04 [0] = [0] 726.97/297.04 [0] 726.97/297.04 726.97/297.04 [1 0 0] [0] 726.97/297.04 [s](x1) = [0 0 0] x1 + [0] 726.97/297.04 [0 0 0] [0] 726.97/297.04 726.97/297.04 [1 0 0] [0] 726.97/297.04 [activate](x1) = [0 1 0] x1 + [0] 726.97/297.04 [0 0 1] [0] 726.97/297.04 726.97/297.04 [7 7 0] [7 4 0] [7] 726.97/297.04 [minus](x1, x2) = [0 0 0] x1 + [7 7 7] x2 + [7] 726.97/297.04 [0 0 0] [7 7 7] [7] 726.97/297.04 726.97/297.04 [0] 726.97/297.04 [quot](x1, x2) = [0] 726.97/297.04 [0] 726.97/297.04 726.97/297.04 [1 0 0] [1 0 0] [1] 726.97/297.04 [zWquot](x1, x2) = [1 0 0] x1 + [0 0 0] x2 + [0] 726.97/297.04 [0 1 1] [0 0 0] [0] 726.97/297.04 726.97/297.04 [7] 726.97/297.04 [nil] = [0] 726.97/297.04 [0] 726.97/297.04 726.97/297.04 [1 0 0] [1 0 0] [1] 726.97/297.04 [n__zWquot](x1, x2) = [1 0 0] x1 + [0 0 0] x2 + [0] 726.97/297.04 [0 1 1] [0 0 0] [0] 726.97/297.04 726.97/297.04 The order satisfies the following ordering constraints: 726.97/297.04 726.97/297.04 [from(X)] = [1 0 0] [0] 726.97/297.04 [1 0 0] X + [0] 726.97/297.04 [0 1 1] [0] 726.97/297.04 >= [1 0 0] [0] 726.97/297.04 [1 0 0] X + [0] 726.97/297.04 [0 1 1] [0] 726.97/297.04 = [cons(X, n__from(n__s(X)))] 726.97/297.04 726.97/297.04 [from(X)] = [1 0 0] [0] 726.97/297.04 [1 0 0] X + [0] 726.97/297.04 [0 1 1] [0] 726.97/297.04 >= [1 0 0] [0] 726.97/297.04 [1 0 0] X + [0] 726.97/297.04 [0 1 1] [0] 726.97/297.04 = [n__from(X)] 726.97/297.04 726.97/297.04 [sel(0(), cons(X, XS))] = [1 0 0] [7] 726.97/297.04 [0 1 1] X + [7] 726.97/297.04 [0 1 1] [7] 726.97/297.04 > [1 0 0] [0] 726.97/297.04 [0 1 0] X + [0] 726.97/297.04 [0 0 1] [0] 726.97/297.04 = [X] 726.97/297.04 726.97/297.04 [s(X)] = [1 0 0] [0] 726.97/297.04 [0 0 0] X + [0] 726.97/297.04 [0 0 0] [0] 726.97/297.04 >= [1 0 0] [0] 726.97/297.04 [0 0 0] X + [0] 726.97/297.04 [0 0 0] [0] 726.97/297.04 = [n__s(X)] 726.97/297.04 726.97/297.04 [activate(X)] = [1 0 0] [0] 726.97/297.04 [0 1 0] X + [0] 726.97/297.04 [0 0 1] [0] 726.97/297.04 >= [1 0 0] [0] 726.97/297.04 [0 1 0] X + [0] 726.97/297.04 [0 0 1] [0] 726.97/297.04 = [X] 726.97/297.04 726.97/297.04 [activate(n__from(X))] = [1 0 0] [0] 726.97/297.04 [1 0 0] X + [0] 726.97/297.04 [0 1 1] [0] 726.97/297.04 >= [1 0 0] [0] 726.97/297.04 [1 0 0] X + [0] 726.97/297.04 [0 1 1] [0] 726.97/297.04 = [from(activate(X))] 726.97/297.04 726.97/297.04 [activate(n__s(X))] = [1 0 0] [0] 726.97/297.04 [0 0 0] X + [0] 726.97/297.04 [0 0 0] [0] 726.97/297.04 >= [1 0 0] [0] 726.97/297.04 [0 0 0] X + [0] 726.97/297.04 [0 0 0] [0] 726.97/297.04 = [s(activate(X))] 726.97/297.04 726.97/297.04 [activate(n__zWquot(X1, X2))] = [1 0 0] [1 0 0] [1] 726.97/297.04 [1 0 0] X1 + [0 0 0] X2 + [0] 726.97/297.04 [0 1 1] [0 0 0] [0] 726.97/297.04 >= [1 0 0] [1 0 0] [1] 726.97/297.04 [1 0 0] X1 + [0 0 0] X2 + [0] 726.97/297.04 [0 1 1] [0 0 0] [0] 726.97/297.04 = [zWquot(activate(X1), activate(X2))] 726.97/297.04 726.97/297.04 [minus(X, 0())] = [7 7 0] [7] 726.97/297.04 [0 0 0] X + [7] 726.97/297.04 [0 0 0] [7] 726.97/297.04 > [0] 726.97/297.04 [0] 726.97/297.04 [0] 726.97/297.04 = [0()] 726.97/297.04 726.97/297.04 [zWquot(X1, X2)] = [1 0 0] [1 0 0] [1] 726.97/297.04 [1 0 0] X1 + [0 0 0] X2 + [0] 726.97/297.04 [0 1 1] [0 0 0] [0] 726.97/297.04 >= [1 0 0] [1 0 0] [1] 726.97/297.04 [1 0 0] X1 + [0 0 0] X2 + [0] 726.97/297.04 [0 1 1] [0 0 0] [0] 726.97/297.04 = [n__zWquot(X1, X2)] 726.97/297.04 726.97/297.04 [zWquot(XS, nil())] = [1 0 0] [8] 726.97/297.04 [1 0 0] XS + [0] 726.97/297.04 [0 1 1] [0] 726.97/297.04 > [7] 726.97/297.04 [0] 726.97/297.04 [0] 726.97/297.04 = [nil()] 726.97/297.04 726.97/297.04 [zWquot(cons(X, XS), cons(Y, YS))] = [0 0 0] [1 0 0] [1 0 0] [1] 726.97/297.04 [0 0 0] X + [1 0 0] XS + [0 0 0] YS + [0] 726.97/297.04 [1 1 1] [0 0 0] [0 0 0] [0] 726.97/297.04 >= [1 0 0] [1 0 0] [1] 726.97/297.04 [0 0 0] XS + [0 0 0] YS + [0] 726.97/297.04 [0 0 0] [0 0 0] [0] 726.97/297.04 = [cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))] 726.97/297.04 726.97/297.04 [zWquot(nil(), XS)] = [1 0 0] [8] 726.97/297.04 [0 0 0] XS + [7] 726.97/297.04 [0 0 0] [0] 726.97/297.04 > [7] 726.97/297.04 [0] 726.97/297.04 [0] 726.97/297.04 = [nil()] 726.97/297.04 726.97/297.04 726.97/297.04 We return to the main proof. 726.97/297.04 726.97/297.04 We are left with following problem, upon which TcT provides the 726.97/297.04 certificate MAYBE. 726.97/297.04 726.97/297.04 Strict Trs: 726.97/297.04 { from(X) -> cons(X, n__from(n__s(X))) 726.97/297.04 , from(X) -> n__from(X) 726.97/297.04 , s(X) -> n__s(X) 726.97/297.04 , activate(X) -> X 726.97/297.04 , activate(n__from(X)) -> from(activate(X)) 726.97/297.04 , activate(n__s(X)) -> s(activate(X)) 726.97/297.04 , activate(n__zWquot(X1, X2)) -> zWquot(activate(X1), activate(X2)) 726.97/297.04 , zWquot(X1, X2) -> n__zWquot(X1, X2) 726.97/297.04 , zWquot(cons(X, XS), cons(Y, YS)) -> 726.97/297.04 cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) } 726.97/297.04 Weak Trs: 726.97/297.04 { sel(0(), cons(X, XS)) -> X 726.97/297.04 , minus(X, 0()) -> 0() 726.97/297.04 , zWquot(XS, nil()) -> nil() 726.97/297.04 , zWquot(nil(), XS) -> nil() } 726.97/297.04 Obligation: 726.97/297.04 innermost runtime complexity 726.97/297.04 Answer: 726.97/297.04 MAYBE 726.97/297.04 726.97/297.04 None of the processors succeeded. 726.97/297.04 726.97/297.04 Details of failed attempt(s): 726.97/297.04 ----------------------------- 726.97/297.04 1) 'empty' failed due to the following reason: 726.97/297.04 726.97/297.04 Empty strict component of the problem is NOT empty. 726.97/297.04 726.97/297.04 2) 'With Problem ...' failed due to the following reason: 726.97/297.04 726.97/297.04 The weightgap principle applies (using the following nonconstant 726.97/297.04 growth matrix-interpretation) 726.97/297.04 726.97/297.04 The following argument positions are usable: 726.97/297.04 Uargs(from) = {1}, Uargs(cons) = {2}, Uargs(s) = {1}, 726.97/297.04 Uargs(zWquot) = {1, 2}, Uargs(n__zWquot) = {1, 2} 726.97/297.04 726.97/297.04 TcT has computed the following matrix interpretation satisfying 726.97/297.04 not(EDA) and not(IDA(1)). 726.97/297.04 726.97/297.04 [from](x1) = [1 1] x1 + [4] 726.97/297.04 [0 0] [4] 726.97/297.04 726.97/297.04 [cons](x1, x2) = [0 1] x1 + [1 0] x2 + [0] 726.97/297.04 [1 0] [0 0] [0] 726.97/297.04 726.97/297.04 [n__from](x1) = [1 1] x1 + [0] 726.97/297.04 [0 0] [0] 726.97/297.04 726.97/297.04 [n__s](x1) = [1 0] x1 + [0] 726.97/297.04 [0 0] [0] 726.97/297.04 726.97/297.04 [sel](x1, x2) = [0 1] x1 + [0 1] x2 + [7] 726.97/297.04 [1 0] [1 0] [7] 726.97/297.04 726.97/297.04 [0] = [7] 726.97/297.04 [0] 726.97/297.04 726.97/297.04 [s](x1) = [1 0] x1 + [0] 726.97/297.04 [0 1] [0] 726.97/297.04 726.97/297.04 [activate](x1) = [1 0] x1 + [0] 726.97/297.04 [0 1] [0] 726.97/297.04 726.97/297.04 [minus](x1, x2) = [0 1] x1 + [7] 726.97/297.04 [1 0] [7] 726.97/297.04 726.97/297.04 [quot](x1, x2) = [1 0] x2 + [0] 726.97/297.04 [0 0] [0] 726.97/297.04 726.97/297.04 [zWquot](x1, x2) = [1 0] x1 + [1 0] x2 + [4] 726.97/297.04 [0 0] [0 0] [4] 726.97/297.04 726.97/297.04 [nil] = [0] 726.97/297.04 [0] 726.97/297.04 726.97/297.04 [n__zWquot](x1, x2) = [1 0] x1 + [1 0] x2 + [0] 726.97/297.04 [0 0] [0 1] [0] 726.97/297.04 726.97/297.04 The order satisfies the following ordering constraints: 726.97/297.04 726.97/297.04 [from(X)] = [1 1] X + [4] 726.97/297.04 [0 0] [4] 726.97/297.04 ? [1 1] X + [0] 726.97/297.04 [1 0] [0] 726.97/297.04 = [cons(X, n__from(n__s(X)))] 726.97/297.04 726.97/297.04 [from(X)] = [1 1] X + [4] 726.97/297.04 [0 0] [4] 726.97/297.04 > [1 1] X + [0] 726.97/297.04 [0 0] [0] 726.97/297.04 = [n__from(X)] 726.97/297.04 726.97/297.04 [sel(0(), cons(X, XS))] = [1 0] X + [0 0] XS + [7] 726.97/297.04 [0 1] [1 0] [14] 726.97/297.04 > [1 0] X + [0] 726.97/297.04 [0 1] [0] 726.97/297.04 = [X] 726.97/297.04 726.97/297.04 [s(X)] = [1 0] X + [0] 726.97/297.04 [0 1] [0] 726.97/297.04 >= [1 0] X + [0] 726.97/297.04 [0 0] [0] 726.97/297.04 = [n__s(X)] 726.97/297.04 726.97/297.04 [activate(X)] = [1 0] X + [0] 726.97/297.04 [0 1] [0] 726.97/297.04 >= [1 0] X + [0] 726.97/297.04 [0 1] [0] 726.97/297.04 = [X] 726.97/297.04 726.97/297.04 [activate(n__from(X))] = [1 1] X + [0] 726.97/297.04 [0 0] [0] 726.97/297.04 ? [1 1] X + [4] 726.97/297.04 [0 0] [4] 726.97/297.04 = [from(activate(X))] 726.97/297.04 726.97/297.04 [activate(n__s(X))] = [1 0] X + [0] 726.97/297.04 [0 0] [0] 726.97/297.04 ? [1 0] X + [0] 726.97/297.04 [0 1] [0] 726.97/297.04 = [s(activate(X))] 726.97/297.04 726.97/297.04 [activate(n__zWquot(X1, X2))] = [1 0] X1 + [1 0] X2 + [0] 726.97/297.04 [0 0] [0 1] [0] 726.97/297.04 ? [1 0] X1 + [1 0] X2 + [4] 726.97/297.04 [0 0] [0 0] [4] 726.97/297.04 = [zWquot(activate(X1), activate(X2))] 726.97/297.04 726.97/297.04 [minus(X, 0())] = [0 1] X + [7] 726.97/297.04 [1 0] [7] 726.97/297.04 >= [7] 726.97/297.04 [0] 726.97/297.04 = [0()] 726.97/297.04 726.97/297.04 [zWquot(X1, X2)] = [1 0] X1 + [1 0] X2 + [4] 726.97/297.04 [0 0] [0 0] [4] 726.97/297.04 ? [1 0] X1 + [1 0] X2 + [0] 726.97/297.04 [0 0] [0 1] [0] 726.97/297.04 = [n__zWquot(X1, X2)] 726.97/297.04 726.97/297.04 [zWquot(XS, nil())] = [1 0] XS + [4] 726.97/297.04 [0 0] [4] 726.97/297.04 > [0] 726.97/297.04 [0] 726.97/297.04 = [nil()] 726.97/297.04 726.97/297.04 [zWquot(cons(X, XS), cons(Y, YS))] = [0 1] X + [1 0] XS + [0 1] Y + [1 0] YS + [4] 726.97/297.04 [0 0] [0 0] [0 0] [0 0] [4] 726.97/297.04 ? [1 0] XS + [0 0] Y + [1 0] YS + [0] 726.97/297.04 [0 0] [1 0] [0 0] [0] 726.97/297.04 = [cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))] 726.97/297.04 726.97/297.04 [zWquot(nil(), XS)] = [1 0] XS + [4] 726.97/297.04 [0 0] [4] 726.97/297.04 > [0] 726.97/297.04 [0] 726.97/297.04 = [nil()] 726.97/297.04 726.97/297.04 726.97/297.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 726.97/297.04 726.97/297.04 We are left with following problem, upon which TcT provides the 726.97/297.04 certificate MAYBE. 726.97/297.04 726.97/297.04 Strict Trs: 726.97/297.05 { from(X) -> cons(X, n__from(n__s(X))) 726.97/297.05 , s(X) -> n__s(X) 726.97/297.05 , activate(X) -> X 726.97/297.05 , activate(n__from(X)) -> from(activate(X)) 726.97/297.05 , activate(n__s(X)) -> s(activate(X)) 726.97/297.05 , activate(n__zWquot(X1, X2)) -> zWquot(activate(X1), activate(X2)) 726.97/297.05 , zWquot(X1, X2) -> n__zWquot(X1, X2) 726.97/297.05 , zWquot(cons(X, XS), cons(Y, YS)) -> 726.97/297.05 cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) } 726.97/297.05 Weak Trs: 726.97/297.05 { from(X) -> n__from(X) 726.97/297.05 , sel(0(), cons(X, XS)) -> X 726.97/297.05 , minus(X, 0()) -> 0() 726.97/297.05 , zWquot(XS, nil()) -> nil() 726.97/297.05 , zWquot(nil(), XS) -> nil() } 726.97/297.05 Obligation: 726.97/297.05 innermost runtime complexity 726.97/297.05 Answer: 726.97/297.05 MAYBE 726.97/297.05 726.97/297.05 The weightgap principle applies (using the following nonconstant 726.97/297.05 growth matrix-interpretation) 726.97/297.05 726.97/297.05 The following argument positions are usable: 726.97/297.05 Uargs(from) = {1}, Uargs(cons) = {2}, Uargs(s) = {1}, 726.97/297.05 Uargs(zWquot) = {1, 2}, Uargs(n__zWquot) = {1, 2} 726.97/297.05 726.97/297.05 TcT has computed the following matrix interpretation satisfying 726.97/297.05 not(EDA) and not(IDA(1)). 726.97/297.05 726.97/297.05 [from](x1) = [1 1] x1 + [4] 726.97/297.05 [0 0] [4] 726.97/297.05 726.97/297.05 [cons](x1, x2) = [0 1] x1 + [1 0] x2 + [0] 726.97/297.05 [1 0] [0 0] [0] 726.97/297.05 726.97/297.05 [n__from](x1) = [1 1] x1 + [0] 726.97/297.05 [0 0] [0] 726.97/297.05 726.97/297.05 [n__s](x1) = [1 0] x1 + [0] 726.97/297.05 [0 0] [0] 726.97/297.05 726.97/297.05 [sel](x1, x2) = [0 1] x1 + [0 1] x2 + [7] 726.97/297.05 [1 0] [1 0] [7] 726.97/297.05 726.97/297.05 [0] = [7] 726.97/297.05 [0] 726.97/297.05 726.97/297.05 [s](x1) = [1 0] x1 + [4] 726.97/297.05 [0 1] [4] 726.97/297.05 726.97/297.05 [activate](x1) = [1 0] x1 + [0] 726.97/297.05 [0 1] [0] 726.97/297.05 726.97/297.05 [minus](x1, x2) = [0 1] x1 + [7] 726.97/297.05 [1 0] [7] 726.97/297.05 726.97/297.05 [quot](x1, x2) = [0] 726.97/297.05 [0] 726.97/297.05 726.97/297.05 [zWquot](x1, x2) = [1 0] x1 + [1 0] x2 + [4] 726.97/297.05 [0 0] [0 0] [4] 726.97/297.05 726.97/297.05 [nil] = [0] 726.97/297.05 [0] 726.97/297.05 726.97/297.05 [n__zWquot](x1, x2) = [1 0] x1 + [1 0] x2 + [0] 726.97/297.05 [0 0] [0 0] [0] 726.97/297.05 726.97/297.05 The order satisfies the following ordering constraints: 726.97/297.05 726.97/297.05 [from(X)] = [1 1] X + [4] 726.97/297.05 [0 0] [4] 726.97/297.05 ? [1 1] X + [0] 726.97/297.05 [1 0] [0] 726.97/297.05 = [cons(X, n__from(n__s(X)))] 726.97/297.05 726.97/297.05 [from(X)] = [1 1] X + [4] 726.97/297.05 [0 0] [4] 726.97/297.05 > [1 1] X + [0] 726.97/297.05 [0 0] [0] 726.97/297.05 = [n__from(X)] 726.97/297.05 726.97/297.05 [sel(0(), cons(X, XS))] = [1 0] X + [0 0] XS + [7] 726.97/297.05 [0 1] [1 0] [14] 726.97/297.05 > [1 0] X + [0] 726.97/297.05 [0 1] [0] 726.97/297.05 = [X] 726.97/297.05 726.97/297.05 [s(X)] = [1 0] X + [4] 726.97/297.05 [0 1] [4] 726.97/297.05 > [1 0] X + [0] 726.97/297.05 [0 0] [0] 726.97/297.05 = [n__s(X)] 726.97/297.05 726.97/297.05 [activate(X)] = [1 0] X + [0] 726.97/297.05 [0 1] [0] 726.97/297.05 >= [1 0] X + [0] 726.97/297.05 [0 1] [0] 726.97/297.05 = [X] 726.97/297.05 726.97/297.05 [activate(n__from(X))] = [1 1] X + [0] 726.97/297.05 [0 0] [0] 726.97/297.05 ? [1 1] X + [4] 726.97/297.05 [0 0] [4] 726.97/297.05 = [from(activate(X))] 726.97/297.05 726.97/297.05 [activate(n__s(X))] = [1 0] X + [0] 726.97/297.05 [0 0] [0] 726.97/297.05 ? [1 0] X + [4] 726.97/297.05 [0 1] [4] 726.97/297.05 = [s(activate(X))] 726.97/297.05 726.97/297.05 [activate(n__zWquot(X1, X2))] = [1 0] X1 + [1 0] X2 + [0] 726.97/297.05 [0 0] [0 0] [0] 726.97/297.05 ? [1 0] X1 + [1 0] X2 + [4] 726.97/297.05 [0 0] [0 0] [4] 726.97/297.05 = [zWquot(activate(X1), activate(X2))] 726.97/297.05 726.97/297.05 [minus(X, 0())] = [0 1] X + [7] 726.97/297.05 [1 0] [7] 726.97/297.05 >= [7] 726.97/297.05 [0] 726.97/297.05 = [0()] 726.97/297.05 726.97/297.05 [zWquot(X1, X2)] = [1 0] X1 + [1 0] X2 + [4] 726.97/297.05 [0 0] [0 0] [4] 726.97/297.05 > [1 0] X1 + [1 0] X2 + [0] 726.97/297.05 [0 0] [0 0] [0] 726.97/297.05 = [n__zWquot(X1, X2)] 726.97/297.05 726.97/297.05 [zWquot(XS, nil())] = [1 0] XS + [4] 726.97/297.05 [0 0] [4] 726.97/297.05 > [0] 726.97/297.05 [0] 726.97/297.05 = [nil()] 726.97/297.05 726.97/297.05 [zWquot(cons(X, XS), cons(Y, YS))] = [0 1] X + [1 0] XS + [0 1] Y + [1 0] YS + [4] 726.97/297.05 [0 0] [0 0] [0 0] [0 0] [4] 726.97/297.05 > [1 0] XS + [1 0] YS + [0] 726.97/297.05 [0 0] [0 0] [0] 726.97/297.05 = [cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))] 726.97/297.05 726.97/297.05 [zWquot(nil(), XS)] = [1 0] XS + [4] 726.97/297.05 [0 0] [4] 726.97/297.05 > [0] 726.97/297.05 [0] 726.97/297.05 = [nil()] 726.97/297.05 726.97/297.05 726.97/297.05 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 726.97/297.05 726.97/297.05 We are left with following problem, upon which TcT provides the 726.97/297.05 certificate MAYBE. 726.97/297.05 726.97/297.05 Strict Trs: 726.97/297.05 { from(X) -> cons(X, n__from(n__s(X))) 726.97/297.05 , activate(X) -> X 726.97/297.05 , activate(n__from(X)) -> from(activate(X)) 726.97/297.05 , activate(n__s(X)) -> s(activate(X)) 726.97/297.05 , activate(n__zWquot(X1, X2)) -> 726.97/297.05 zWquot(activate(X1), activate(X2)) } 726.97/297.05 Weak Trs: 726.97/297.05 { from(X) -> n__from(X) 726.97/297.05 , sel(0(), cons(X, XS)) -> X 726.97/297.05 , s(X) -> n__s(X) 726.97/297.05 , minus(X, 0()) -> 0() 726.97/297.05 , zWquot(X1, X2) -> n__zWquot(X1, X2) 726.97/297.05 , zWquot(XS, nil()) -> nil() 726.97/297.05 , zWquot(cons(X, XS), cons(Y, YS)) -> 726.97/297.05 cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) 726.97/297.05 , zWquot(nil(), XS) -> nil() } 726.97/297.05 Obligation: 726.97/297.05 innermost runtime complexity 726.97/297.05 Answer: 726.97/297.05 MAYBE 726.97/297.05 726.97/297.05 The weightgap principle applies (using the following nonconstant 726.97/297.05 growth matrix-interpretation) 726.97/297.05 726.97/297.05 The following argument positions are usable: 726.97/297.05 Uargs(from) = {1}, Uargs(cons) = {2}, Uargs(s) = {1}, 726.97/297.05 Uargs(zWquot) = {1, 2}, Uargs(n__zWquot) = {1, 2} 726.97/297.05 726.97/297.05 TcT has computed the following matrix interpretation satisfying 726.97/297.05 not(EDA) and not(IDA(1)). 726.97/297.05 726.97/297.05 [from](x1) = [1 1] x1 + [0] 726.97/297.05 [0 0] [4] 726.97/297.05 726.97/297.05 [cons](x1, x2) = [0 1] x1 + [1 1] x2 + [4] 726.97/297.05 [1 0] [0 0] [0] 726.97/297.05 726.97/297.05 [n__from](x1) = [1 1] x1 + [0] 726.97/297.05 [0 0] [0] 726.97/297.05 726.97/297.05 [n__s](x1) = [1 0] x1 + [0] 726.97/297.05 [0 0] [0] 726.97/297.05 726.97/297.05 [sel](x1, x2) = [0 1] x2 + [7] 726.97/297.05 [1 0] [7] 726.97/297.05 726.97/297.05 [0] = [7] 726.97/297.05 [0] 726.97/297.05 726.97/297.05 [s](x1) = [1 0] x1 + [0] 726.97/297.05 [0 0] [4] 726.97/297.05 726.97/297.05 [activate](x1) = [1 0] x1 + [1] 726.97/297.05 [0 1] [1] 726.97/297.05 726.97/297.05 [minus](x1, x2) = [7] 726.97/297.05 [7] 726.97/297.05 726.97/297.05 [quot](x1, x2) = [0] 726.97/297.05 [0] 726.97/297.05 726.97/297.05 [zWquot](x1, x2) = [1 0] x1 + [1 1] x2 + [0] 726.97/297.05 [0 0] [0 0] [4] 726.97/297.05 726.97/297.05 [nil] = [0] 726.97/297.05 [0] 726.97/297.05 726.97/297.05 [n__zWquot](x1, x2) = [1 0] x1 + [1 1] x2 + [0] 726.97/297.05 [0 0] [0 0] [1] 726.97/297.05 726.97/297.05 The order satisfies the following ordering constraints: 726.97/297.05 726.97/297.05 [from(X)] = [1 1] X + [0] 726.97/297.05 [0 0] [4] 726.97/297.05 ? [1 1] X + [4] 726.97/297.05 [1 0] [0] 726.97/297.05 = [cons(X, n__from(n__s(X)))] 726.97/297.05 726.97/297.05 [from(X)] = [1 1] X + [0] 726.97/297.05 [0 0] [4] 726.97/297.05 >= [1 1] X + [0] 726.97/297.05 [0 0] [0] 726.97/297.05 = [n__from(X)] 726.97/297.05 726.97/297.05 [sel(0(), cons(X, XS))] = [1 0] X + [0 0] XS + [7] 726.97/297.05 [0 1] [1 1] [11] 726.97/297.05 > [1 0] X + [0] 726.97/297.05 [0 1] [0] 726.97/297.05 = [X] 726.97/297.05 726.97/297.05 [s(X)] = [1 0] X + [0] 726.97/297.05 [0 0] [4] 726.97/297.05 >= [1 0] X + [0] 726.97/297.05 [0 0] [0] 726.97/297.05 = [n__s(X)] 726.97/297.05 726.97/297.05 [activate(X)] = [1 0] X + [1] 726.97/297.05 [0 1] [1] 726.97/297.05 > [1 0] X + [0] 726.97/297.05 [0 1] [0] 726.97/297.05 = [X] 726.97/297.05 726.97/297.05 [activate(n__from(X))] = [1 1] X + [1] 726.97/297.05 [0 0] [1] 726.97/297.05 ? [1 1] X + [2] 726.97/297.05 [0 0] [4] 726.97/297.05 = [from(activate(X))] 726.97/297.05 726.97/297.05 [activate(n__s(X))] = [1 0] X + [1] 726.97/297.05 [0 0] [1] 726.97/297.05 ? [1 0] X + [1] 726.97/297.05 [0 0] [4] 726.97/297.05 = [s(activate(X))] 726.97/297.05 726.97/297.05 [activate(n__zWquot(X1, X2))] = [1 0] X1 + [1 1] X2 + [1] 726.97/297.05 [0 0] [0 0] [2] 726.97/297.05 ? [1 0] X1 + [1 1] X2 + [3] 726.97/297.05 [0 0] [0 0] [4] 726.97/297.05 = [zWquot(activate(X1), activate(X2))] 726.97/297.05 726.97/297.05 [minus(X, 0())] = [7] 726.97/297.05 [7] 726.97/297.05 >= [7] 726.97/297.05 [0] 726.97/297.05 = [0()] 726.97/297.05 726.97/297.05 [zWquot(X1, X2)] = [1 0] X1 + [1 1] X2 + [0] 726.97/297.05 [0 0] [0 0] [4] 726.97/297.05 >= [1 0] X1 + [1 1] X2 + [0] 726.97/297.05 [0 0] [0 0] [1] 726.97/297.05 = [n__zWquot(X1, X2)] 726.97/297.05 726.97/297.05 [zWquot(XS, nil())] = [1 0] XS + [0] 726.97/297.05 [0 0] [4] 726.97/297.05 >= [0] 726.97/297.05 [0] 726.97/297.05 = [nil()] 726.97/297.05 726.97/297.05 [zWquot(cons(X, XS), cons(Y, YS))] = [0 1] X + [1 1] XS + [1 1] Y + [1 1] YS + [8] 726.97/297.05 [0 0] [0 0] [0 0] [0 0] [4] 726.97/297.05 >= [1 0] XS + [1 1] YS + [8] 726.97/297.05 [0 0] [0 0] [0] 726.97/297.05 = [cons(quot(X, Y), n__zWquot(activate(XS), activate(YS)))] 726.97/297.05 726.97/297.05 [zWquot(nil(), XS)] = [1 1] XS + [0] 726.97/297.05 [0 0] [4] 726.97/297.05 >= [0] 726.97/297.05 [0] 726.97/297.05 = [nil()] 726.97/297.05 726.97/297.05 726.97/297.05 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 726.97/297.05 726.97/297.05 We are left with following problem, upon which TcT provides the 726.97/297.05 certificate MAYBE. 726.97/297.05 726.97/297.05 Strict Trs: 726.97/297.05 { from(X) -> cons(X, n__from(n__s(X))) 726.97/297.05 , activate(n__from(X)) -> from(activate(X)) 726.97/297.05 , activate(n__s(X)) -> s(activate(X)) 726.97/297.05 , activate(n__zWquot(X1, X2)) -> 726.97/297.05 zWquot(activate(X1), activate(X2)) } 726.97/297.05 Weak Trs: 726.97/297.05 { from(X) -> n__from(X) 726.97/297.05 , sel(0(), cons(X, XS)) -> X 726.97/297.05 , s(X) -> n__s(X) 726.97/297.05 , activate(X) -> X 726.97/297.05 , minus(X, 0()) -> 0() 726.97/297.05 , zWquot(X1, X2) -> n__zWquot(X1, X2) 726.97/297.05 , zWquot(XS, nil()) -> nil() 726.97/297.05 , zWquot(cons(X, XS), cons(Y, YS)) -> 726.97/297.05 cons(quot(X, Y), n__zWquot(activate(XS), activate(YS))) 726.97/297.05 , zWquot(nil(), XS) -> nil() } 726.97/297.05 Obligation: 726.97/297.05 innermost runtime complexity 726.97/297.05 Answer: 726.97/297.05 MAYBE 726.97/297.05 726.97/297.05 None of the processors succeeded. 726.97/297.05 726.97/297.05 Details of failed attempt(s): 726.97/297.05 ----------------------------- 726.97/297.05 1) 'empty' failed due to the following reason: 726.97/297.05 726.97/297.05 Empty strict component of the problem is NOT empty. 726.97/297.05 726.97/297.05 2) 'With Problem ...' failed due to the following reason: 726.97/297.05 726.97/297.05 None of the processors succeeded. 726.97/297.05 726.97/297.05 Details of failed attempt(s): 726.97/297.05 ----------------------------- 726.97/297.05 1) 'empty' failed due to the following reason: 726.97/297.05 726.97/297.05 Empty strict component of the problem is NOT empty. 726.97/297.05 726.97/297.05 2) 'With Problem ...' failed due to the following reason: 726.97/297.05 726.97/297.05 Empty strict component of the problem is NOT empty. 726.97/297.05 726.97/297.05 726.97/297.05 726.97/297.05 726.97/297.05 2) 'With Problem ...' failed due to the following reason: 726.97/297.05 726.97/297.05 None of the processors succeeded. 726.97/297.05 726.97/297.05 Details of failed attempt(s): 726.97/297.05 ----------------------------- 726.97/297.05 1) 'empty' failed due to the following reason: 726.97/297.05 726.97/297.05 Empty strict component of the problem is NOT empty. 726.97/297.05 726.97/297.05 2) 'With Problem ...' failed due to the following reason: 726.97/297.05 726.97/297.05 Empty strict component of the problem is NOT empty. 726.97/297.05 726.97/297.05 726.97/297.05 726.97/297.05 726.97/297.05 726.97/297.05 2) 'Best' failed due to the following reason: 726.97/297.05 726.97/297.05 None of the processors succeeded. 726.97/297.05 726.97/297.05 Details of failed attempt(s): 726.97/297.05 ----------------------------- 726.97/297.05 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 726.97/297.05 following reason: 726.97/297.05 726.97/297.05 The input cannot be shown compatible 726.97/297.05 726.97/297.05 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 726.97/297.05 to the following reason: 726.97/297.05 726.97/297.05 The input cannot be shown compatible 726.97/297.05 726.97/297.05 726.97/297.05 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 726.97/297.05 failed due to the following reason: 726.97/297.05 726.97/297.05 None of the processors succeeded. 726.97/297.05 726.97/297.05 Details of failed attempt(s): 726.97/297.05 ----------------------------- 726.97/297.05 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 726.97/297.05 failed due to the following reason: 726.97/297.05 726.97/297.05 match-boundness of the problem could not be verified. 726.97/297.05 726.97/297.05 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 726.97/297.05 failed due to the following reason: 726.97/297.05 726.97/297.05 match-boundness of the problem could not be verified. 726.97/297.05 726.97/297.05 726.97/297.05 726.97/297.05 726.97/297.05 726.97/297.05 Arrrr.. 727.71/297.80 EOF