YES(O(1),O(n^2)) 699.41/297.57 YES(O(1),O(n^2)) 699.41/297.57 699.41/297.57 We are left with following problem, upon which TcT provides the 699.41/297.57 certificate YES(O(1),O(n^2)). 699.41/297.57 699.41/297.57 Strict Trs: 699.41/297.57 { a__from(X) -> cons(mark(X), from(s(X))) 699.41/297.57 , a__from(X) -> from(X) 699.41/297.57 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 699.41/297.57 , mark(from(X)) -> a__from(mark(X)) 699.41/297.57 , mark(s(X)) -> s(mark(X)) 699.41/297.57 , mark(nil()) -> nil() 699.41/297.57 , mark(0()) -> 0() 699.41/297.57 , mark(length(X)) -> a__length(X) 699.41/297.57 , mark(length1(X)) -> a__length1(X) 699.41/297.57 , a__length(X) -> length(X) 699.41/297.57 , a__length(cons(X, Y)) -> s(a__length1(Y)) 699.41/297.57 , a__length(nil()) -> 0() 699.41/297.57 , a__length1(X) -> a__length(X) 699.41/297.57 , a__length1(X) -> length1(X) } 699.41/297.57 Obligation: 699.41/297.57 innermost runtime complexity 699.41/297.57 Answer: 699.41/297.57 YES(O(1),O(n^2)) 699.41/297.57 699.41/297.57 The weightgap principle applies (using the following nonconstant 699.41/297.57 growth matrix-interpretation) 699.41/297.57 699.41/297.57 The following argument positions are usable: 699.41/297.57 Uargs(a__from) = {1}, Uargs(cons) = {1}, Uargs(s) = {1} 699.41/297.57 699.41/297.57 TcT has computed the following matrix interpretation satisfying 699.41/297.57 not(EDA) and not(IDA(1)). 699.41/297.57 699.41/297.57 [a__from](x1) = [1] x1 + [7] 699.41/297.57 699.41/297.57 [cons](x1, x2) = [1] x1 + [7] 699.41/297.57 699.41/297.57 [mark](x1) = [1] x1 + [7] 699.41/297.57 699.41/297.57 [from](x1) = [1] x1 + [7] 699.41/297.57 699.41/297.57 [s](x1) = [1] x1 + [7] 699.41/297.57 699.41/297.57 [a__length](x1) = [7] 699.41/297.57 699.41/297.57 [nil] = [7] 699.41/297.57 699.41/297.57 [0] = [3] 699.41/297.57 699.41/297.57 [a__length1](x1) = [3] 699.41/297.57 699.41/297.57 [length](x1) = [7] 699.41/297.57 699.41/297.57 [length1](x1) = [7] 699.41/297.57 699.41/297.57 The order satisfies the following ordering constraints: 699.41/297.57 699.41/297.57 [a__from(X)] = [1] X + [7] 699.41/297.57 ? [1] X + [14] 699.41/297.57 = [cons(mark(X), from(s(X)))] 699.41/297.57 699.41/297.57 [a__from(X)] = [1] X + [7] 699.41/297.57 >= [1] X + [7] 699.41/297.57 = [from(X)] 699.41/297.57 699.41/297.57 [mark(cons(X1, X2))] = [1] X1 + [14] 699.41/297.57 >= [1] X1 + [14] 699.41/297.57 = [cons(mark(X1), X2)] 699.41/297.57 699.41/297.57 [mark(from(X))] = [1] X + [14] 699.41/297.57 >= [1] X + [14] 699.41/297.57 = [a__from(mark(X))] 699.41/297.57 699.41/297.57 [mark(s(X))] = [1] X + [14] 699.41/297.57 >= [1] X + [14] 699.41/297.57 = [s(mark(X))] 699.41/297.57 699.41/297.57 [mark(nil())] = [14] 699.41/297.57 > [7] 699.41/297.57 = [nil()] 699.41/297.57 699.41/297.57 [mark(0())] = [10] 699.41/297.57 > [3] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [mark(length(X))] = [14] 699.41/297.57 > [7] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [mark(length1(X))] = [14] 699.41/297.57 > [3] 699.41/297.57 = [a__length1(X)] 699.41/297.57 699.41/297.57 [a__length(X)] = [7] 699.41/297.57 >= [7] 699.41/297.57 = [length(X)] 699.41/297.57 699.41/297.57 [a__length(cons(X, Y))] = [7] 699.41/297.57 ? [10] 699.41/297.57 = [s(a__length1(Y))] 699.41/297.57 699.41/297.57 [a__length(nil())] = [7] 699.41/297.57 > [3] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [a__length1(X)] = [3] 699.41/297.57 ? [7] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [a__length1(X)] = [3] 699.41/297.57 ? [7] 699.41/297.57 = [length1(X)] 699.41/297.57 699.41/297.57 699.41/297.57 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 699.41/297.57 699.41/297.57 We are left with following problem, upon which TcT provides the 699.41/297.57 certificate YES(O(1),O(n^2)). 699.41/297.57 699.41/297.57 Strict Trs: 699.41/297.57 { a__from(X) -> cons(mark(X), from(s(X))) 699.41/297.57 , a__from(X) -> from(X) 699.41/297.57 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 699.41/297.57 , mark(from(X)) -> a__from(mark(X)) 699.41/297.57 , mark(s(X)) -> s(mark(X)) 699.41/297.57 , a__length(X) -> length(X) 699.41/297.57 , a__length(cons(X, Y)) -> s(a__length1(Y)) 699.41/297.57 , a__length1(X) -> a__length(X) 699.41/297.57 , a__length1(X) -> length1(X) } 699.41/297.57 Weak Trs: 699.41/297.57 { mark(nil()) -> nil() 699.41/297.57 , mark(0()) -> 0() 699.41/297.57 , mark(length(X)) -> a__length(X) 699.41/297.57 , mark(length1(X)) -> a__length1(X) 699.41/297.57 , a__length(nil()) -> 0() } 699.41/297.57 Obligation: 699.41/297.57 innermost runtime complexity 699.41/297.57 Answer: 699.41/297.57 YES(O(1),O(n^2)) 699.41/297.57 699.41/297.57 The weightgap principle applies (using the following nonconstant 699.41/297.57 growth matrix-interpretation) 699.41/297.57 699.41/297.57 The following argument positions are usable: 699.41/297.57 Uargs(a__from) = {1}, Uargs(cons) = {1}, Uargs(s) = {1} 699.41/297.57 699.41/297.57 TcT has computed the following matrix interpretation satisfying 699.41/297.57 not(EDA) and not(IDA(1)). 699.41/297.57 699.41/297.57 [a__from](x1) = [1] x1 + [1] 699.41/297.57 699.41/297.57 [cons](x1, x2) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [mark](x1) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [from](x1) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [s](x1) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [a__length](x1) = [0] 699.41/297.57 699.41/297.57 [nil] = [7] 699.41/297.57 699.41/297.57 [0] = [0] 699.41/297.57 699.41/297.57 [a__length1](x1) = [0] 699.41/297.57 699.41/297.57 [length](x1) = [4] 699.41/297.57 699.41/297.57 [length1](x1) = [4] 699.41/297.57 699.41/297.57 The order satisfies the following ordering constraints: 699.41/297.57 699.41/297.57 [a__from(X)] = [1] X + [1] 699.41/297.57 > [1] X + [0] 699.41/297.57 = [cons(mark(X), from(s(X)))] 699.41/297.57 699.41/297.57 [a__from(X)] = [1] X + [1] 699.41/297.57 > [1] X + [0] 699.41/297.57 = [from(X)] 699.41/297.57 699.41/297.57 [mark(cons(X1, X2))] = [1] X1 + [0] 699.41/297.57 >= [1] X1 + [0] 699.41/297.57 = [cons(mark(X1), X2)] 699.41/297.57 699.41/297.57 [mark(from(X))] = [1] X + [0] 699.41/297.57 ? [1] X + [1] 699.41/297.57 = [a__from(mark(X))] 699.41/297.57 699.41/297.57 [mark(s(X))] = [1] X + [0] 699.41/297.57 >= [1] X + [0] 699.41/297.57 = [s(mark(X))] 699.41/297.57 699.41/297.57 [mark(nil())] = [7] 699.41/297.57 >= [7] 699.41/297.57 = [nil()] 699.41/297.57 699.41/297.57 [mark(0())] = [0] 699.41/297.57 >= [0] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [mark(length(X))] = [4] 699.41/297.57 > [0] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [mark(length1(X))] = [4] 699.41/297.57 > [0] 699.41/297.57 = [a__length1(X)] 699.41/297.57 699.41/297.57 [a__length(X)] = [0] 699.41/297.57 ? [4] 699.41/297.57 = [length(X)] 699.41/297.57 699.41/297.57 [a__length(cons(X, Y))] = [0] 699.41/297.57 >= [0] 699.41/297.57 = [s(a__length1(Y))] 699.41/297.57 699.41/297.57 [a__length(nil())] = [0] 699.41/297.57 >= [0] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [a__length1(X)] = [0] 699.41/297.57 >= [0] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [a__length1(X)] = [0] 699.41/297.57 ? [4] 699.41/297.57 = [length1(X)] 699.41/297.57 699.41/297.57 699.41/297.57 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 699.41/297.57 699.41/297.57 We are left with following problem, upon which TcT provides the 699.41/297.57 certificate YES(O(1),O(n^2)). 699.41/297.57 699.41/297.57 Strict Trs: 699.41/297.57 { mark(cons(X1, X2)) -> cons(mark(X1), X2) 699.41/297.57 , mark(from(X)) -> a__from(mark(X)) 699.41/297.57 , mark(s(X)) -> s(mark(X)) 699.41/297.57 , a__length(X) -> length(X) 699.41/297.57 , a__length(cons(X, Y)) -> s(a__length1(Y)) 699.41/297.57 , a__length1(X) -> a__length(X) 699.41/297.57 , a__length1(X) -> length1(X) } 699.41/297.57 Weak Trs: 699.41/297.57 { a__from(X) -> cons(mark(X), from(s(X))) 699.41/297.57 , a__from(X) -> from(X) 699.41/297.57 , mark(nil()) -> nil() 699.41/297.57 , mark(0()) -> 0() 699.41/297.57 , mark(length(X)) -> a__length(X) 699.41/297.57 , mark(length1(X)) -> a__length1(X) 699.41/297.57 , a__length(nil()) -> 0() } 699.41/297.57 Obligation: 699.41/297.57 innermost runtime complexity 699.41/297.57 Answer: 699.41/297.57 YES(O(1),O(n^2)) 699.41/297.57 699.41/297.57 The weightgap principle applies (using the following nonconstant 699.41/297.57 growth matrix-interpretation) 699.41/297.57 699.41/297.57 The following argument positions are usable: 699.41/297.57 Uargs(a__from) = {1}, Uargs(cons) = {1}, Uargs(s) = {1} 699.41/297.57 699.41/297.57 TcT has computed the following matrix interpretation satisfying 699.41/297.57 not(EDA) and not(IDA(1)). 699.41/297.57 699.41/297.57 [a__from](x1) = [1] x1 + [4] 699.41/297.57 699.41/297.57 [cons](x1, x2) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [mark](x1) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [from](x1) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [s](x1) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [a__length](x1) = [2] 699.41/297.57 699.41/297.57 [nil] = [7] 699.41/297.57 699.41/297.57 [0] = [2] 699.41/297.57 699.41/297.57 [a__length1](x1) = [0] 699.41/297.57 699.41/297.57 [length](x1) = [4] 699.41/297.57 699.41/297.57 [length1](x1) = [4] 699.41/297.57 699.41/297.57 The order satisfies the following ordering constraints: 699.41/297.57 699.41/297.57 [a__from(X)] = [1] X + [4] 699.41/297.57 > [1] X + [0] 699.41/297.57 = [cons(mark(X), from(s(X)))] 699.41/297.57 699.41/297.57 [a__from(X)] = [1] X + [4] 699.41/297.57 > [1] X + [0] 699.41/297.57 = [from(X)] 699.41/297.57 699.41/297.57 [mark(cons(X1, X2))] = [1] X1 + [0] 699.41/297.57 >= [1] X1 + [0] 699.41/297.57 = [cons(mark(X1), X2)] 699.41/297.57 699.41/297.57 [mark(from(X))] = [1] X + [0] 699.41/297.57 ? [1] X + [4] 699.41/297.57 = [a__from(mark(X))] 699.41/297.57 699.41/297.57 [mark(s(X))] = [1] X + [0] 699.41/297.57 >= [1] X + [0] 699.41/297.57 = [s(mark(X))] 699.41/297.57 699.41/297.57 [mark(nil())] = [7] 699.41/297.57 >= [7] 699.41/297.57 = [nil()] 699.41/297.57 699.41/297.57 [mark(0())] = [2] 699.41/297.57 >= [2] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [mark(length(X))] = [4] 699.41/297.57 > [2] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [mark(length1(X))] = [4] 699.41/297.57 > [0] 699.41/297.57 = [a__length1(X)] 699.41/297.57 699.41/297.57 [a__length(X)] = [2] 699.41/297.57 ? [4] 699.41/297.57 = [length(X)] 699.41/297.57 699.41/297.57 [a__length(cons(X, Y))] = [2] 699.41/297.57 > [0] 699.41/297.57 = [s(a__length1(Y))] 699.41/297.57 699.41/297.57 [a__length(nil())] = [2] 699.41/297.57 >= [2] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [a__length1(X)] = [0] 699.41/297.57 ? [2] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [a__length1(X)] = [0] 699.41/297.57 ? [4] 699.41/297.57 = [length1(X)] 699.41/297.57 699.41/297.57 699.41/297.57 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 699.41/297.57 699.41/297.57 We are left with following problem, upon which TcT provides the 699.41/297.57 certificate YES(O(1),O(n^2)). 699.41/297.57 699.41/297.57 Strict Trs: 699.41/297.57 { mark(cons(X1, X2)) -> cons(mark(X1), X2) 699.41/297.57 , mark(from(X)) -> a__from(mark(X)) 699.41/297.57 , mark(s(X)) -> s(mark(X)) 699.41/297.57 , a__length(X) -> length(X) 699.41/297.57 , a__length1(X) -> a__length(X) 699.41/297.57 , a__length1(X) -> length1(X) } 699.41/297.57 Weak Trs: 699.41/297.57 { a__from(X) -> cons(mark(X), from(s(X))) 699.41/297.57 , a__from(X) -> from(X) 699.41/297.57 , mark(nil()) -> nil() 699.41/297.57 , mark(0()) -> 0() 699.41/297.57 , mark(length(X)) -> a__length(X) 699.41/297.57 , mark(length1(X)) -> a__length1(X) 699.41/297.57 , a__length(cons(X, Y)) -> s(a__length1(Y)) 699.41/297.57 , a__length(nil()) -> 0() } 699.41/297.57 Obligation: 699.41/297.57 innermost runtime complexity 699.41/297.57 Answer: 699.41/297.57 YES(O(1),O(n^2)) 699.41/297.57 699.41/297.57 The weightgap principle applies (using the following nonconstant 699.41/297.57 growth matrix-interpretation) 699.41/297.57 699.41/297.57 The following argument positions are usable: 699.41/297.57 Uargs(a__from) = {1}, Uargs(cons) = {1}, Uargs(s) = {1} 699.41/297.57 699.41/297.57 TcT has computed the following matrix interpretation satisfying 699.41/297.57 not(EDA) and not(IDA(1)). 699.41/297.57 699.41/297.57 [a__from](x1) = [1] x1 + [4] 699.41/297.57 699.41/297.57 [cons](x1, x2) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [mark](x1) = [1] x1 + [1] 699.41/297.57 699.41/297.57 [from](x1) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [s](x1) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [a__length](x1) = [4] 699.41/297.57 699.41/297.57 [nil] = [7] 699.41/297.57 699.41/297.57 [0] = [3] 699.41/297.57 699.41/297.57 [a__length1](x1) = [0] 699.41/297.57 699.41/297.57 [length](x1) = [3] 699.41/297.57 699.41/297.57 [length1](x1) = [0] 699.41/297.57 699.41/297.57 The order satisfies the following ordering constraints: 699.41/297.57 699.41/297.57 [a__from(X)] = [1] X + [4] 699.41/297.57 > [1] X + [1] 699.41/297.57 = [cons(mark(X), from(s(X)))] 699.41/297.57 699.41/297.57 [a__from(X)] = [1] X + [4] 699.41/297.57 > [1] X + [0] 699.41/297.57 = [from(X)] 699.41/297.57 699.41/297.57 [mark(cons(X1, X2))] = [1] X1 + [1] 699.41/297.57 >= [1] X1 + [1] 699.41/297.57 = [cons(mark(X1), X2)] 699.41/297.57 699.41/297.57 [mark(from(X))] = [1] X + [1] 699.41/297.57 ? [1] X + [5] 699.41/297.57 = [a__from(mark(X))] 699.41/297.57 699.41/297.57 [mark(s(X))] = [1] X + [1] 699.41/297.57 >= [1] X + [1] 699.41/297.57 = [s(mark(X))] 699.41/297.57 699.41/297.57 [mark(nil())] = [8] 699.41/297.57 > [7] 699.41/297.57 = [nil()] 699.41/297.57 699.41/297.57 [mark(0())] = [4] 699.41/297.57 > [3] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [mark(length(X))] = [4] 699.41/297.57 >= [4] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [mark(length1(X))] = [1] 699.41/297.57 > [0] 699.41/297.57 = [a__length1(X)] 699.41/297.57 699.41/297.57 [a__length(X)] = [4] 699.41/297.57 > [3] 699.41/297.57 = [length(X)] 699.41/297.57 699.41/297.57 [a__length(cons(X, Y))] = [4] 699.41/297.57 > [0] 699.41/297.57 = [s(a__length1(Y))] 699.41/297.57 699.41/297.57 [a__length(nil())] = [4] 699.41/297.57 > [3] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [a__length1(X)] = [0] 699.41/297.57 ? [4] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [a__length1(X)] = [0] 699.41/297.57 >= [0] 699.41/297.57 = [length1(X)] 699.41/297.57 699.41/297.57 699.41/297.57 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 699.41/297.57 699.41/297.57 We are left with following problem, upon which TcT provides the 699.41/297.57 certificate YES(O(1),O(n^2)). 699.41/297.57 699.41/297.57 Strict Trs: 699.41/297.57 { mark(cons(X1, X2)) -> cons(mark(X1), X2) 699.41/297.57 , mark(from(X)) -> a__from(mark(X)) 699.41/297.57 , mark(s(X)) -> s(mark(X)) 699.41/297.57 , a__length1(X) -> a__length(X) 699.41/297.57 , a__length1(X) -> length1(X) } 699.41/297.57 Weak Trs: 699.41/297.57 { a__from(X) -> cons(mark(X), from(s(X))) 699.41/297.57 , a__from(X) -> from(X) 699.41/297.57 , mark(nil()) -> nil() 699.41/297.57 , mark(0()) -> 0() 699.41/297.57 , mark(length(X)) -> a__length(X) 699.41/297.57 , mark(length1(X)) -> a__length1(X) 699.41/297.57 , a__length(X) -> length(X) 699.41/297.57 , a__length(cons(X, Y)) -> s(a__length1(Y)) 699.41/297.57 , a__length(nil()) -> 0() } 699.41/297.57 Obligation: 699.41/297.57 innermost runtime complexity 699.41/297.57 Answer: 699.41/297.57 YES(O(1),O(n^2)) 699.41/297.57 699.41/297.57 The weightgap principle applies (using the following nonconstant 699.41/297.57 growth matrix-interpretation) 699.41/297.57 699.41/297.57 The following argument positions are usable: 699.41/297.57 Uargs(a__from) = {1}, Uargs(cons) = {1}, Uargs(s) = {1} 699.41/297.57 699.41/297.57 TcT has computed the following matrix interpretation satisfying 699.41/297.57 not(EDA) and not(IDA(1)). 699.41/297.57 699.41/297.57 [a__from](x1) = [1] x1 + [4] 699.41/297.57 699.41/297.57 [cons](x1, x2) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [mark](x1) = [1] x1 + [1] 699.41/297.57 699.41/297.57 [from](x1) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [s](x1) = [1] x1 + [0] 699.41/297.57 699.41/297.57 [a__length](x1) = [4] 699.41/297.57 699.41/297.57 [nil] = [7] 699.41/297.57 699.41/297.57 [0] = [3] 699.41/297.57 699.41/297.57 [a__length1](x1) = [1] 699.41/297.57 699.41/297.57 [length](x1) = [4] 699.41/297.57 699.41/297.57 [length1](x1) = [0] 699.41/297.57 699.41/297.57 The order satisfies the following ordering constraints: 699.41/297.57 699.41/297.57 [a__from(X)] = [1] X + [4] 699.41/297.57 > [1] X + [1] 699.41/297.57 = [cons(mark(X), from(s(X)))] 699.41/297.57 699.41/297.57 [a__from(X)] = [1] X + [4] 699.41/297.57 > [1] X + [0] 699.41/297.57 = [from(X)] 699.41/297.57 699.41/297.57 [mark(cons(X1, X2))] = [1] X1 + [1] 699.41/297.57 >= [1] X1 + [1] 699.41/297.57 = [cons(mark(X1), X2)] 699.41/297.57 699.41/297.57 [mark(from(X))] = [1] X + [1] 699.41/297.57 ? [1] X + [5] 699.41/297.57 = [a__from(mark(X))] 699.41/297.57 699.41/297.57 [mark(s(X))] = [1] X + [1] 699.41/297.57 >= [1] X + [1] 699.41/297.57 = [s(mark(X))] 699.41/297.57 699.41/297.57 [mark(nil())] = [8] 699.41/297.57 > [7] 699.41/297.57 = [nil()] 699.41/297.57 699.41/297.57 [mark(0())] = [4] 699.41/297.57 > [3] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [mark(length(X))] = [5] 699.41/297.57 > [4] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [mark(length1(X))] = [1] 699.41/297.57 >= [1] 699.41/297.57 = [a__length1(X)] 699.41/297.57 699.41/297.57 [a__length(X)] = [4] 699.41/297.57 >= [4] 699.41/297.57 = [length(X)] 699.41/297.57 699.41/297.57 [a__length(cons(X, Y))] = [4] 699.41/297.57 > [1] 699.41/297.57 = [s(a__length1(Y))] 699.41/297.57 699.41/297.57 [a__length(nil())] = [4] 699.41/297.57 > [3] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [a__length1(X)] = [1] 699.41/297.57 ? [4] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [a__length1(X)] = [1] 699.41/297.57 > [0] 699.41/297.57 = [length1(X)] 699.41/297.57 699.41/297.57 699.41/297.57 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 699.41/297.57 699.41/297.57 We are left with following problem, upon which TcT provides the 699.41/297.57 certificate YES(O(1),O(n^2)). 699.41/297.57 699.41/297.57 Strict Trs: 699.41/297.57 { mark(cons(X1, X2)) -> cons(mark(X1), X2) 699.41/297.57 , mark(from(X)) -> a__from(mark(X)) 699.41/297.57 , mark(s(X)) -> s(mark(X)) 699.41/297.57 , a__length1(X) -> a__length(X) } 699.41/297.57 Weak Trs: 699.41/297.57 { a__from(X) -> cons(mark(X), from(s(X))) 699.41/297.57 , a__from(X) -> from(X) 699.41/297.57 , mark(nil()) -> nil() 699.41/297.57 , mark(0()) -> 0() 699.41/297.57 , mark(length(X)) -> a__length(X) 699.41/297.57 , mark(length1(X)) -> a__length1(X) 699.41/297.57 , a__length(X) -> length(X) 699.41/297.57 , a__length(cons(X, Y)) -> s(a__length1(Y)) 699.41/297.57 , a__length(nil()) -> 0() 699.41/297.57 , a__length1(X) -> length1(X) } 699.41/297.57 Obligation: 699.41/297.57 innermost runtime complexity 699.41/297.57 Answer: 699.41/297.57 YES(O(1),O(n^2)) 699.41/297.57 699.41/297.57 We use the processor 'matrix interpretation of dimension 2' to 699.41/297.57 orient following rules strictly. 699.41/297.57 699.41/297.57 Trs: { a__length1(X) -> a__length(X) } 699.41/297.57 699.41/297.57 The induced complexity on above rules (modulo remaining rules) is 699.41/297.57 YES(?,O(n^1)) . These rules are moved into the corresponding weak 699.41/297.57 component(s). 699.41/297.57 699.41/297.57 Sub-proof: 699.41/297.57 ---------- 699.41/297.57 The following argument positions are usable: 699.41/297.57 Uargs(a__from) = {1}, Uargs(cons) = {1}, Uargs(s) = {1} 699.41/297.57 699.41/297.57 TcT has computed the following constructor-based matrix 699.41/297.57 interpretation satisfying not(EDA) and not(IDA(1)). 699.41/297.57 699.41/297.57 [a__from](x1) = [1 0] x1 + [0] 699.41/297.57 [0 0] [1] 699.41/297.57 699.41/297.57 [cons](x1, x2) = [1 0] x1 + [0 0] x2 + [0] 699.41/297.57 [0 0] [0 1] [1] 699.41/297.57 699.41/297.57 [mark](x1) = [1 0] x1 + [0] 699.41/297.57 [0 4] [1] 699.41/297.57 699.41/297.57 [from](x1) = [1 0] x1 + [0] 699.41/297.57 [0 0] [0] 699.41/297.57 699.41/297.57 [s](x1) = [1 0] x1 + [0] 699.41/297.57 [0 0] [0] 699.41/297.57 699.41/297.57 [a__length](x1) = [0 1] x1 + [0] 699.41/297.57 [2 0] [1] 699.41/297.57 699.41/297.57 [nil] = [2] 699.41/297.57 [0] 699.41/297.57 699.41/297.57 [0] = [0] 699.41/297.57 [1] 699.41/297.57 699.41/297.57 [a__length1](x1) = [0 1] x1 + [1] 699.41/297.57 [4 0] [1] 699.41/297.57 699.41/297.57 [length](x1) = [0 1] x1 + [0] 699.41/297.57 [1 0] [1] 699.41/297.57 699.41/297.57 [length1](x1) = [0 1] x1 + [1] 699.41/297.57 [1 0] [1] 699.41/297.57 699.41/297.57 The order satisfies the following ordering constraints: 699.41/297.57 699.41/297.57 [a__from(X)] = [1 0] X + [0] 699.41/297.57 [0 0] [1] 699.41/297.57 >= [1 0] X + [0] 699.41/297.57 [0 0] [1] 699.41/297.57 = [cons(mark(X), from(s(X)))] 699.41/297.57 699.41/297.57 [a__from(X)] = [1 0] X + [0] 699.41/297.57 [0 0] [1] 699.41/297.57 >= [1 0] X + [0] 699.41/297.57 [0 0] [0] 699.41/297.57 = [from(X)] 699.41/297.57 699.41/297.57 [mark(cons(X1, X2))] = [1 0] X1 + [0 0] X2 + [0] 699.41/297.57 [0 0] [0 4] [5] 699.41/297.57 >= [1 0] X1 + [0 0] X2 + [0] 699.41/297.57 [0 0] [0 1] [1] 699.41/297.57 = [cons(mark(X1), X2)] 699.41/297.57 699.41/297.57 [mark(from(X))] = [1 0] X + [0] 699.41/297.57 [0 0] [1] 699.41/297.57 >= [1 0] X + [0] 699.41/297.57 [0 0] [1] 699.41/297.57 = [a__from(mark(X))] 699.41/297.57 699.41/297.57 [mark(s(X))] = [1 0] X + [0] 699.41/297.57 [0 0] [1] 699.41/297.57 >= [1 0] X + [0] 699.41/297.57 [0 0] [0] 699.41/297.57 = [s(mark(X))] 699.41/297.57 699.41/297.57 [mark(nil())] = [2] 699.41/297.57 [1] 699.41/297.57 >= [2] 699.41/297.57 [0] 699.41/297.57 = [nil()] 699.41/297.57 699.41/297.57 [mark(0())] = [0] 699.41/297.57 [5] 699.41/297.57 >= [0] 699.41/297.57 [1] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [mark(length(X))] = [0 1] X + [0] 699.41/297.57 [4 0] [5] 699.41/297.57 >= [0 1] X + [0] 699.41/297.57 [2 0] [1] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [mark(length1(X))] = [0 1] X + [1] 699.41/297.57 [4 0] [5] 699.41/297.57 >= [0 1] X + [1] 699.41/297.57 [4 0] [1] 699.41/297.57 = [a__length1(X)] 699.41/297.57 699.41/297.57 [a__length(X)] = [0 1] X + [0] 699.41/297.57 [2 0] [1] 699.41/297.57 >= [0 1] X + [0] 699.41/297.57 [1 0] [1] 699.41/297.57 = [length(X)] 699.41/297.57 699.41/297.57 [a__length(cons(X, Y))] = [0 0] X + [0 1] Y + [1] 699.41/297.57 [2 0] [0 0] [1] 699.41/297.57 >= [0 1] Y + [1] 699.41/297.57 [0 0] [0] 699.41/297.57 = [s(a__length1(Y))] 699.41/297.57 699.41/297.57 [a__length(nil())] = [0] 699.41/297.57 [5] 699.41/297.57 >= [0] 699.41/297.57 [1] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [a__length1(X)] = [0 1] X + [1] 699.41/297.57 [4 0] [1] 699.41/297.57 > [0 1] X + [0] 699.41/297.57 [2 0] [1] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [a__length1(X)] = [0 1] X + [1] 699.41/297.57 [4 0] [1] 699.41/297.57 >= [0 1] X + [1] 699.41/297.57 [1 0] [1] 699.41/297.57 = [length1(X)] 699.41/297.57 699.41/297.57 699.41/297.57 We return to the main proof. 699.41/297.57 699.41/297.57 We are left with following problem, upon which TcT provides the 699.41/297.57 certificate YES(O(1),O(n^2)). 699.41/297.57 699.41/297.57 Strict Trs: 699.41/297.57 { mark(cons(X1, X2)) -> cons(mark(X1), X2) 699.41/297.57 , mark(from(X)) -> a__from(mark(X)) 699.41/297.57 , mark(s(X)) -> s(mark(X)) } 699.41/297.57 Weak Trs: 699.41/297.57 { a__from(X) -> cons(mark(X), from(s(X))) 699.41/297.57 , a__from(X) -> from(X) 699.41/297.57 , mark(nil()) -> nil() 699.41/297.57 , mark(0()) -> 0() 699.41/297.57 , mark(length(X)) -> a__length(X) 699.41/297.57 , mark(length1(X)) -> a__length1(X) 699.41/297.57 , a__length(X) -> length(X) 699.41/297.57 , a__length(cons(X, Y)) -> s(a__length1(Y)) 699.41/297.57 , a__length(nil()) -> 0() 699.41/297.57 , a__length1(X) -> a__length(X) 699.41/297.57 , a__length1(X) -> length1(X) } 699.41/297.57 Obligation: 699.41/297.57 innermost runtime complexity 699.41/297.57 Answer: 699.41/297.57 YES(O(1),O(n^2)) 699.41/297.57 699.41/297.57 We use the processor 'matrix interpretation of dimension 2' to 699.41/297.57 orient following rules strictly. 699.41/297.57 699.41/297.57 Trs: 699.41/297.57 { mark(cons(X1, X2)) -> cons(mark(X1), X2) 699.41/297.57 , mark(from(X)) -> a__from(mark(X)) } 699.41/297.57 699.41/297.57 The induced complexity on above rules (modulo remaining rules) is 699.41/297.57 YES(?,O(n^2)) . These rules are moved into the corresponding weak 699.41/297.57 component(s). 699.41/297.57 699.41/297.57 Sub-proof: 699.41/297.57 ---------- 699.41/297.57 The following argument positions are usable: 699.41/297.57 Uargs(a__from) = {1}, Uargs(cons) = {1}, Uargs(s) = {1} 699.41/297.57 699.41/297.57 TcT has computed the following constructor-based matrix 699.41/297.57 interpretation satisfying not(EDA). 699.41/297.57 699.41/297.57 [a__from](x1) = [1 2] x1 + [0] 699.41/297.57 [0 1] [4] 699.41/297.57 699.41/297.57 [cons](x1, x2) = [1 0] x1 + [0] 699.41/297.57 [0 1] [4] 699.41/297.57 699.41/297.57 [mark](x1) = [1 1] x1 + [0] 699.41/297.57 [0 1] [0] 699.41/297.57 699.41/297.57 [from](x1) = [1 2] x1 + [0] 699.41/297.57 [0 1] [4] 699.41/297.57 699.41/297.57 [s](x1) = [1 0] x1 + [0] 699.41/297.57 [0 1] [0] 699.41/297.57 699.41/297.57 [a__length](x1) = [0] 699.41/297.57 [0] 699.41/297.57 699.41/297.57 [nil] = [0] 699.41/297.57 [0] 699.41/297.57 699.41/297.57 [0] = [0] 699.41/297.57 [0] 699.41/297.57 699.41/297.57 [a__length1](x1) = [0] 699.41/297.57 [0] 699.41/297.57 699.41/297.57 [length](x1) = [0] 699.41/297.57 [0] 699.41/297.57 699.41/297.57 [length1](x1) = [0] 699.41/297.57 [0] 699.41/297.57 699.41/297.57 The order satisfies the following ordering constraints: 699.41/297.57 699.41/297.57 [a__from(X)] = [1 2] X + [0] 699.41/297.57 [0 1] [4] 699.41/297.57 >= [1 1] X + [0] 699.41/297.57 [0 1] [4] 699.41/297.57 = [cons(mark(X), from(s(X)))] 699.41/297.57 699.41/297.57 [a__from(X)] = [1 2] X + [0] 699.41/297.57 [0 1] [4] 699.41/297.57 >= [1 2] X + [0] 699.41/297.57 [0 1] [4] 699.41/297.57 = [from(X)] 699.41/297.57 699.41/297.57 [mark(cons(X1, X2))] = [1 1] X1 + [4] 699.41/297.57 [0 1] [4] 699.41/297.57 > [1 1] X1 + [0] 699.41/297.57 [0 1] [4] 699.41/297.57 = [cons(mark(X1), X2)] 699.41/297.57 699.41/297.57 [mark(from(X))] = [1 3] X + [4] 699.41/297.57 [0 1] [4] 699.41/297.57 > [1 3] X + [0] 699.41/297.57 [0 1] [4] 699.41/297.57 = [a__from(mark(X))] 699.41/297.57 699.41/297.57 [mark(s(X))] = [1 1] X + [0] 699.41/297.57 [0 1] [0] 699.41/297.57 >= [1 1] X + [0] 699.41/297.57 [0 1] [0] 699.41/297.57 = [s(mark(X))] 699.41/297.57 699.41/297.57 [mark(nil())] = [0] 699.41/297.57 [0] 699.41/297.57 >= [0] 699.41/297.57 [0] 699.41/297.57 = [nil()] 699.41/297.57 699.41/297.57 [mark(0())] = [0] 699.41/297.57 [0] 699.41/297.57 >= [0] 699.41/297.57 [0] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [mark(length(X))] = [0] 699.41/297.57 [0] 699.41/297.57 >= [0] 699.41/297.57 [0] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [mark(length1(X))] = [0] 699.41/297.57 [0] 699.41/297.57 >= [0] 699.41/297.57 [0] 699.41/297.57 = [a__length1(X)] 699.41/297.57 699.41/297.57 [a__length(X)] = [0] 699.41/297.57 [0] 699.41/297.57 >= [0] 699.41/297.57 [0] 699.41/297.57 = [length(X)] 699.41/297.57 699.41/297.57 [a__length(cons(X, Y))] = [0] 699.41/297.57 [0] 699.41/297.57 >= [0] 699.41/297.57 [0] 699.41/297.57 = [s(a__length1(Y))] 699.41/297.57 699.41/297.57 [a__length(nil())] = [0] 699.41/297.57 [0] 699.41/297.57 >= [0] 699.41/297.57 [0] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [a__length1(X)] = [0] 699.41/297.57 [0] 699.41/297.57 >= [0] 699.41/297.57 [0] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [a__length1(X)] = [0] 699.41/297.57 [0] 699.41/297.57 >= [0] 699.41/297.57 [0] 699.41/297.57 = [length1(X)] 699.41/297.57 699.41/297.57 699.41/297.57 We return to the main proof. 699.41/297.57 699.41/297.57 We are left with following problem, upon which TcT provides the 699.41/297.57 certificate YES(O(1),O(n^2)). 699.41/297.57 699.41/297.57 Strict Trs: { mark(s(X)) -> s(mark(X)) } 699.41/297.57 Weak Trs: 699.41/297.57 { a__from(X) -> cons(mark(X), from(s(X))) 699.41/297.57 , a__from(X) -> from(X) 699.41/297.57 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 699.41/297.57 , mark(from(X)) -> a__from(mark(X)) 699.41/297.57 , mark(nil()) -> nil() 699.41/297.57 , mark(0()) -> 0() 699.41/297.57 , mark(length(X)) -> a__length(X) 699.41/297.57 , mark(length1(X)) -> a__length1(X) 699.41/297.57 , a__length(X) -> length(X) 699.41/297.57 , a__length(cons(X, Y)) -> s(a__length1(Y)) 699.41/297.57 , a__length(nil()) -> 0() 699.41/297.57 , a__length1(X) -> a__length(X) 699.41/297.57 , a__length1(X) -> length1(X) } 699.41/297.57 Obligation: 699.41/297.57 innermost runtime complexity 699.41/297.57 Answer: 699.41/297.57 YES(O(1),O(n^2)) 699.41/297.57 699.41/297.57 We use the processor 'matrix interpretation of dimension 3' to 699.41/297.57 orient following rules strictly. 699.41/297.57 699.41/297.57 Trs: { mark(s(X)) -> s(mark(X)) } 699.41/297.57 699.41/297.57 The induced complexity on above rules (modulo remaining rules) is 699.41/297.57 YES(?,O(n^2)) . These rules are moved into the corresponding weak 699.41/297.57 component(s). 699.41/297.57 699.41/297.57 Sub-proof: 699.41/297.57 ---------- 699.41/297.57 The following argument positions are usable: 699.41/297.57 Uargs(a__from) = {1}, Uargs(cons) = {1}, Uargs(s) = {1} 699.41/297.57 699.41/297.57 TcT has computed the following constructor-based matrix 699.41/297.57 interpretation satisfying not(EDA) and not(IDA(2)). 699.41/297.57 699.41/297.57 [1 2 0] [1] 699.41/297.57 [a__from](x1) = [0 1 0] x1 + [0] 699.41/297.57 [0 0 0] [4] 699.41/297.57 699.41/297.57 [1 0 0] [0 0 1] [1] 699.41/297.57 [cons](x1, x2) = [0 1 0] x1 + [0 0 0] x2 + [0] 699.41/297.57 [0 0 0] [0 0 1] [4] 699.41/297.57 699.41/297.57 [1 2 0] [0] 699.41/297.57 [mark](x1) = [0 1 0] x1 + [0] 699.41/297.57 [2 0 0] [2] 699.41/297.57 699.41/297.57 [1 2 0] [1] 699.41/297.57 [from](x1) = [0 1 0] x1 + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 699.41/297.57 [1 0 0] [1] 699.41/297.57 [s](x1) = [0 1 0] x1 + [4] 699.41/297.57 [0 0 0] [0] 699.41/297.57 699.41/297.57 [0 0 2] [0] 699.41/297.57 [a__length](x1) = [0 0 1] x1 + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 699.41/297.57 [1] 699.41/297.57 [nil] = [2] 699.41/297.57 [2] 699.41/297.57 699.41/297.57 [0] 699.41/297.57 [0] = [0] 699.41/297.57 [0] 699.41/297.57 699.41/297.57 [0 0 2] [0] 699.41/297.57 [a__length1](x1) = [0 0 1] x1 + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 699.41/297.57 [0 0 0] [0] 699.41/297.57 [length](x1) = [0 0 1] x1 + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 699.41/297.57 [0 0 0] [0] 699.41/297.57 [length1](x1) = [0 0 1] x1 + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 699.41/297.57 The order satisfies the following ordering constraints: 699.41/297.57 699.41/297.57 [a__from(X)] = [1 2 0] [1] 699.41/297.57 [0 1 0] X + [0] 699.41/297.57 [0 0 0] [4] 699.41/297.57 >= [1 2 0] [1] 699.41/297.57 [0 1 0] X + [0] 699.41/297.57 [0 0 0] [4] 699.41/297.57 = [cons(mark(X), from(s(X)))] 699.41/297.57 699.41/297.57 [a__from(X)] = [1 2 0] [1] 699.41/297.57 [0 1 0] X + [0] 699.41/297.57 [0 0 0] [4] 699.41/297.57 >= [1 2 0] [1] 699.41/297.57 [0 1 0] X + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 = [from(X)] 699.41/297.57 699.41/297.57 [mark(cons(X1, X2))] = [1 2 0] [0 0 1] [1] 699.41/297.57 [0 1 0] X1 + [0 0 0] X2 + [0] 699.41/297.57 [2 0 0] [0 0 2] [4] 699.41/297.57 >= [1 2 0] [0 0 1] [1] 699.41/297.57 [0 1 0] X1 + [0 0 0] X2 + [0] 699.41/297.57 [0 0 0] [0 0 1] [4] 699.41/297.57 = [cons(mark(X1), X2)] 699.41/297.57 699.41/297.57 [mark(from(X))] = [1 4 0] [1] 699.41/297.57 [0 1 0] X + [0] 699.41/297.57 [2 4 0] [4] 699.41/297.57 >= [1 4 0] [1] 699.41/297.57 [0 1 0] X + [0] 699.41/297.57 [0 0 0] [4] 699.41/297.57 = [a__from(mark(X))] 699.41/297.57 699.41/297.57 [mark(s(X))] = [1 2 0] [9] 699.41/297.57 [0 1 0] X + [4] 699.41/297.57 [2 0 0] [4] 699.41/297.57 > [1 2 0] [1] 699.41/297.57 [0 1 0] X + [4] 699.41/297.57 [0 0 0] [0] 699.41/297.57 = [s(mark(X))] 699.41/297.57 699.41/297.57 [mark(nil())] = [5] 699.41/297.57 [2] 699.41/297.57 [4] 699.41/297.57 > [1] 699.41/297.57 [2] 699.41/297.57 [2] 699.41/297.57 = [nil()] 699.41/297.57 699.41/297.57 [mark(0())] = [0] 699.41/297.57 [0] 699.41/297.57 [2] 699.41/297.57 >= [0] 699.41/297.57 [0] 699.41/297.57 [0] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [mark(length(X))] = [0 0 2] [0] 699.41/297.57 [0 0 1] X + [0] 699.41/297.57 [0 0 0] [2] 699.41/297.57 >= [0 0 2] [0] 699.41/297.57 [0 0 1] X + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [mark(length1(X))] = [0 0 2] [0] 699.41/297.57 [0 0 1] X + [0] 699.41/297.57 [0 0 0] [2] 699.41/297.57 >= [0 0 2] [0] 699.41/297.57 [0 0 1] X + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 = [a__length1(X)] 699.41/297.57 699.41/297.57 [a__length(X)] = [0 0 2] [0] 699.41/297.57 [0 0 1] X + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 >= [0 0 0] [0] 699.41/297.57 [0 0 1] X + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 = [length(X)] 699.41/297.57 699.41/297.57 [a__length(cons(X, Y))] = [0 0 2] [8] 699.41/297.57 [0 0 1] Y + [4] 699.41/297.57 [0 0 0] [0] 699.41/297.57 > [0 0 2] [1] 699.41/297.57 [0 0 1] Y + [4] 699.41/297.57 [0 0 0] [0] 699.41/297.57 = [s(a__length1(Y))] 699.41/297.57 699.41/297.57 [a__length(nil())] = [4] 699.41/297.57 [2] 699.41/297.57 [0] 699.41/297.57 > [0] 699.41/297.57 [0] 699.41/297.57 [0] 699.41/297.57 = [0()] 699.41/297.57 699.41/297.57 [a__length1(X)] = [0 0 2] [0] 699.41/297.57 [0 0 1] X + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 >= [0 0 2] [0] 699.41/297.57 [0 0 1] X + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 = [a__length(X)] 699.41/297.57 699.41/297.57 [a__length1(X)] = [0 0 2] [0] 699.41/297.57 [0 0 1] X + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 >= [0 0 0] [0] 699.41/297.57 [0 0 1] X + [0] 699.41/297.57 [0 0 0] [0] 699.41/297.57 = [length1(X)] 699.41/297.57 699.41/297.57 699.41/297.57 We return to the main proof. 699.41/297.57 699.41/297.57 We are left with following problem, upon which TcT provides the 699.41/297.57 certificate YES(O(1),O(1)). 699.41/297.57 699.41/297.57 Weak Trs: 699.41/297.57 { a__from(X) -> cons(mark(X), from(s(X))) 699.41/297.57 , a__from(X) -> from(X) 699.41/297.57 , mark(cons(X1, X2)) -> cons(mark(X1), X2) 699.41/297.57 , mark(from(X)) -> a__from(mark(X)) 699.41/297.57 , mark(s(X)) -> s(mark(X)) 699.41/297.57 , mark(nil()) -> nil() 699.41/297.57 , mark(0()) -> 0() 699.41/297.57 , mark(length(X)) -> a__length(X) 699.41/297.57 , mark(length1(X)) -> a__length1(X) 699.41/297.57 , a__length(X) -> length(X) 699.41/297.57 , a__length(cons(X, Y)) -> s(a__length1(Y)) 699.41/297.57 , a__length(nil()) -> 0() 699.41/297.57 , a__length1(X) -> a__length(X) 699.41/297.57 , a__length1(X) -> length1(X) } 699.41/297.57 Obligation: 699.41/297.57 innermost runtime complexity 699.41/297.57 Answer: 699.41/297.57 YES(O(1),O(1)) 699.41/297.57 699.41/297.57 Empty rules are trivially bounded 699.41/297.57 699.41/297.57 Hurray, we answered YES(O(1),O(n^2)) 699.79/297.72 EOF