YES(O(1),O(n^1)) 0.00/0.65 YES(O(1),O(n^1)) 0.00/0.65 0.00/0.65 We are left with following problem, upon which TcT provides the 0.00/0.65 certificate YES(O(1),O(n^1)). 0.00/0.65 0.00/0.65 Strict Trs: 0.00/0.65 { 2nd(cons(X, n__cons(Y, Z))) -> activate(Y) 0.00/0.65 , cons(X1, X2) -> n__cons(X1, X2) 0.00/0.65 , activate(X) -> X 0.00/0.65 , activate(n__cons(X1, X2)) -> cons(X1, X2) 0.00/0.65 , activate(n__from(X)) -> from(X) 0.00/0.65 , from(X) -> cons(X, n__from(s(X))) 0.00/0.65 , from(X) -> n__from(X) } 0.00/0.65 Obligation: 0.00/0.65 runtime complexity 0.00/0.65 Answer: 0.00/0.65 YES(O(1),O(n^1)) 0.00/0.65 0.00/0.65 The weightgap principle applies (using the following nonconstant 0.00/0.65 growth matrix-interpretation) 0.00/0.65 0.00/0.65 The following argument positions are usable: 0.00/0.65 none 0.00/0.65 0.00/0.65 TcT has computed the following matrix interpretation satisfying 0.00/0.65 not(EDA) and not(IDA(1)). 0.00/0.65 0.00/0.65 [2nd](x1) = [1] x1 + [1] 0.00/0.65 0.00/0.65 [cons](x1, x2) = [1] x1 + [1] x2 + [7] 0.00/0.65 0.00/0.65 [n__cons](x1, x2) = [1] x1 + [1] x2 + [7] 0.00/0.65 0.00/0.65 [activate](x1) = [1] x1 + [7] 0.00/0.65 0.00/0.65 [from](x1) = [1] x1 + [3] 0.00/0.65 0.00/0.65 [n__from](x1) = [1] x1 + [7] 0.00/0.65 0.00/0.65 [s](x1) = [0] 0.00/0.65 0.00/0.65 The order satisfies the following ordering constraints: 0.00/0.65 0.00/0.65 [2nd(cons(X, n__cons(Y, Z)))] = [1] X + [1] Y + [1] Z + [15] 0.00/0.65 > [1] Y + [7] 0.00/0.65 = [activate(Y)] 0.00/0.65 0.00/0.65 [cons(X1, X2)] = [1] X1 + [1] X2 + [7] 0.00/0.65 >= [1] X1 + [1] X2 + [7] 0.00/0.65 = [n__cons(X1, X2)] 0.00/0.65 0.00/0.65 [activate(X)] = [1] X + [7] 0.00/0.65 > [1] X + [0] 0.00/0.65 = [X] 0.00/0.65 0.00/0.65 [activate(n__cons(X1, X2))] = [1] X1 + [1] X2 + [14] 0.00/0.65 > [1] X1 + [1] X2 + [7] 0.00/0.65 = [cons(X1, X2)] 0.00/0.65 0.00/0.65 [activate(n__from(X))] = [1] X + [14] 0.00/0.65 > [1] X + [3] 0.00/0.65 = [from(X)] 0.00/0.65 0.00/0.65 [from(X)] = [1] X + [3] 0.00/0.65 ? [1] X + [14] 0.00/0.65 = [cons(X, n__from(s(X)))] 0.00/0.65 0.00/0.65 [from(X)] = [1] X + [3] 0.00/0.65 ? [1] X + [7] 0.00/0.65 = [n__from(X)] 0.00/0.65 0.00/0.65 0.00/0.65 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 0.00/0.65 0.00/0.65 We are left with following problem, upon which TcT provides the 0.00/0.65 certificate YES(O(1),O(n^1)). 0.00/0.65 0.00/0.65 Strict Trs: 0.00/0.65 { cons(X1, X2) -> n__cons(X1, X2) 0.00/0.65 , from(X) -> cons(X, n__from(s(X))) 0.00/0.65 , from(X) -> n__from(X) } 0.00/0.65 Weak Trs: 0.00/0.65 { 2nd(cons(X, n__cons(Y, Z))) -> activate(Y) 0.00/0.65 , activate(X) -> X 0.00/0.65 , activate(n__cons(X1, X2)) -> cons(X1, X2) 0.00/0.65 , activate(n__from(X)) -> from(X) } 0.00/0.65 Obligation: 0.00/0.65 runtime complexity 0.00/0.65 Answer: 0.00/0.65 YES(O(1),O(n^1)) 0.00/0.65 0.00/0.65 The weightgap principle applies (using the following nonconstant 0.00/0.65 growth matrix-interpretation) 0.00/0.65 0.00/0.65 The following argument positions are usable: 0.00/0.65 none 0.00/0.65 0.00/0.65 TcT has computed the following matrix interpretation satisfying 0.00/0.65 not(EDA) and not(IDA(1)). 0.00/0.65 0.00/0.65 [2nd](x1) = [1] x1 + [2] 0.00/0.65 0.00/0.65 [cons](x1, x2) = [1] x1 + [1] x2 + [7] 0.00/0.65 0.00/0.65 [n__cons](x1, x2) = [1] x1 + [1] x2 + [6] 0.00/0.65 0.00/0.65 [activate](x1) = [1] x1 + [7] 0.00/0.65 0.00/0.65 [from](x1) = [1] x1 + [7] 0.00/0.65 0.00/0.65 [n__from](x1) = [1] x1 + [6] 0.00/0.65 0.00/0.65 [s](x1) = [1] 0.00/0.65 0.00/0.65 The order satisfies the following ordering constraints: 0.00/0.65 0.00/0.65 [2nd(cons(X, n__cons(Y, Z)))] = [1] X + [1] Y + [1] Z + [15] 0.00/0.65 > [1] Y + [7] 0.00/0.65 = [activate(Y)] 0.00/0.65 0.00/0.65 [cons(X1, X2)] = [1] X1 + [1] X2 + [7] 0.00/0.65 > [1] X1 + [1] X2 + [6] 0.00/0.65 = [n__cons(X1, X2)] 0.00/0.65 0.00/0.65 [activate(X)] = [1] X + [7] 0.00/0.65 > [1] X + [0] 0.00/0.65 = [X] 0.00/0.65 0.00/0.65 [activate(n__cons(X1, X2))] = [1] X1 + [1] X2 + [13] 0.00/0.65 > [1] X1 + [1] X2 + [7] 0.00/0.65 = [cons(X1, X2)] 0.00/0.65 0.00/0.65 [activate(n__from(X))] = [1] X + [13] 0.00/0.65 > [1] X + [7] 0.00/0.65 = [from(X)] 0.00/0.65 0.00/0.65 [from(X)] = [1] X + [7] 0.00/0.65 ? [1] X + [14] 0.00/0.65 = [cons(X, n__from(s(X)))] 0.00/0.65 0.00/0.65 [from(X)] = [1] X + [7] 0.00/0.65 > [1] X + [6] 0.00/0.65 = [n__from(X)] 0.00/0.65 0.00/0.65 0.00/0.65 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 0.00/0.65 0.00/0.65 We are left with following problem, upon which TcT provides the 0.00/0.65 certificate YES(O(1),O(n^1)). 0.00/0.65 0.00/0.65 Strict Trs: { from(X) -> cons(X, n__from(s(X))) } 0.00/0.65 Weak Trs: 0.00/0.65 { 2nd(cons(X, n__cons(Y, Z))) -> activate(Y) 0.00/0.65 , cons(X1, X2) -> n__cons(X1, X2) 0.00/0.65 , activate(X) -> X 0.00/0.65 , activate(n__cons(X1, X2)) -> cons(X1, X2) 0.00/0.65 , activate(n__from(X)) -> from(X) 0.00/0.65 , from(X) -> n__from(X) } 0.00/0.65 Obligation: 0.00/0.65 runtime complexity 0.00/0.65 Answer: 0.00/0.65 YES(O(1),O(n^1)) 0.00/0.65 0.00/0.65 The weightgap principle applies (using the following nonconstant 0.00/0.65 growth matrix-interpretation) 0.00/0.65 0.00/0.65 The following argument positions are usable: 0.00/0.65 none 0.00/0.65 0.00/0.65 TcT has computed the following matrix interpretation satisfying 0.00/0.65 not(EDA) and not(IDA(1)). 0.00/0.65 0.00/0.65 [2nd](x1) = [1] x1 + [7] 0.00/0.65 0.00/0.65 [cons](x1, x2) = [1] x1 + [1] x2 + [0] 0.00/0.65 0.00/0.65 [n__cons](x1, x2) = [1] x1 + [1] x2 + [0] 0.00/0.65 0.00/0.65 [activate](x1) = [1] x1 + [7] 0.00/0.65 0.00/0.65 [from](x1) = [1] x1 + [7] 0.00/0.65 0.00/0.65 [n__from](x1) = [1] x1 + [3] 0.00/0.65 0.00/0.65 [s](x1) = [3] 0.00/0.65 0.00/0.65 The order satisfies the following ordering constraints: 0.00/0.65 0.00/0.65 [2nd(cons(X, n__cons(Y, Z)))] = [1] X + [1] Y + [1] Z + [7] 0.00/0.65 >= [1] Y + [7] 0.00/0.65 = [activate(Y)] 0.00/0.65 0.00/0.65 [cons(X1, X2)] = [1] X1 + [1] X2 + [0] 0.00/0.65 >= [1] X1 + [1] X2 + [0] 0.00/0.65 = [n__cons(X1, X2)] 0.00/0.65 0.00/0.65 [activate(X)] = [1] X + [7] 0.00/0.65 > [1] X + [0] 0.00/0.65 = [X] 0.00/0.65 0.00/0.65 [activate(n__cons(X1, X2))] = [1] X1 + [1] X2 + [7] 0.00/0.65 > [1] X1 + [1] X2 + [0] 0.00/0.65 = [cons(X1, X2)] 0.00/0.65 0.00/0.65 [activate(n__from(X))] = [1] X + [10] 0.00/0.65 > [1] X + [7] 0.00/0.65 = [from(X)] 0.00/0.65 0.00/0.65 [from(X)] = [1] X + [7] 0.00/0.65 > [1] X + [6] 0.00/0.65 = [cons(X, n__from(s(X)))] 0.00/0.65 0.00/0.65 [from(X)] = [1] X + [7] 0.00/0.65 > [1] X + [3] 0.00/0.65 = [n__from(X)] 0.00/0.65 0.00/0.65 0.00/0.65 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 0.00/0.65 0.00/0.65 We are left with following problem, upon which TcT provides the 0.00/0.65 certificate YES(O(1),O(1)). 0.00/0.65 0.00/0.65 Weak Trs: 0.00/0.65 { 2nd(cons(X, n__cons(Y, Z))) -> activate(Y) 0.00/0.65 , cons(X1, X2) -> n__cons(X1, X2) 0.00/0.65 , activate(X) -> X 0.00/0.65 , activate(n__cons(X1, X2)) -> cons(X1, X2) 0.00/0.65 , activate(n__from(X)) -> from(X) 0.00/0.65 , from(X) -> cons(X, n__from(s(X))) 0.00/0.65 , from(X) -> n__from(X) } 0.00/0.65 Obligation: 0.00/0.65 runtime complexity 0.00/0.65 Answer: 0.00/0.65 YES(O(1),O(1)) 0.00/0.65 0.00/0.65 Empty rules are trivially bounded 0.00/0.65 0.00/0.65 Hurray, we answered YES(O(1),O(n^1)) 0.00/0.65 EOF