YES(O(1),O(n^1)) 214.95/148.08 YES(O(1),O(n^1)) 214.95/148.08 214.95/148.08 We are left with following problem, upon which TcT provides the 214.95/148.08 certificate YES(O(1),O(n^1)). 214.95/148.08 214.95/148.08 Strict Trs: 214.95/148.08 { from(X) -> cons(X, n__from(s(X))) 214.95/148.08 , from(X) -> n__from(X) 214.95/148.08 , sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) 214.95/148.08 , sel(0(), cons(X, Y)) -> X 214.95/148.08 , activate(X) -> X 214.95/148.08 , activate(n__from(X)) -> from(X) } 214.95/148.08 Obligation: 214.95/148.08 runtime complexity 214.95/148.08 Answer: 214.95/148.08 YES(O(1),O(n^1)) 214.95/148.08 214.95/148.08 We add the following weak dependency pairs: 214.95/148.08 214.95/148.08 Strict DPs: 214.95/148.08 { from^#(X) -> c_1(X, X) 214.95/148.08 , from^#(X) -> c_2(X) 214.95/148.08 , sel^#(s(X), cons(Y, Z)) -> c_3(sel^#(X, activate(Z))) 214.95/148.08 , sel^#(0(), cons(X, Y)) -> c_4(X) 214.95/148.08 , activate^#(X) -> c_5(X) 214.95/148.08 , activate^#(n__from(X)) -> c_6(from^#(X)) } 214.95/148.08 214.95/148.08 and mark the set of starting terms. 214.95/148.08 214.95/148.08 We are left with following problem, upon which TcT provides the 214.95/148.08 certificate YES(O(1),O(n^1)). 214.95/148.08 214.95/148.08 Strict DPs: 214.95/148.08 { from^#(X) -> c_1(X, X) 214.95/148.08 , from^#(X) -> c_2(X) 214.95/148.08 , sel^#(s(X), cons(Y, Z)) -> c_3(sel^#(X, activate(Z))) 214.95/148.08 , sel^#(0(), cons(X, Y)) -> c_4(X) 214.95/148.08 , activate^#(X) -> c_5(X) 214.95/148.08 , activate^#(n__from(X)) -> c_6(from^#(X)) } 214.95/148.08 Strict Trs: 214.95/148.08 { from(X) -> cons(X, n__from(s(X))) 214.95/148.08 , from(X) -> n__from(X) 214.95/148.08 , sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) 214.95/148.08 , sel(0(), cons(X, Y)) -> X 214.95/148.08 , activate(X) -> X 214.95/148.08 , activate(n__from(X)) -> from(X) } 214.95/148.08 Obligation: 214.95/148.08 runtime complexity 214.95/148.08 Answer: 214.95/148.08 YES(O(1),O(n^1)) 214.95/148.08 214.95/148.08 We replace rewrite rules by usable rules: 214.95/148.08 214.95/148.08 Strict Usable Rules: 214.95/148.08 { from(X) -> cons(X, n__from(s(X))) 214.95/148.08 , from(X) -> n__from(X) 214.95/148.08 , activate(X) -> X 214.95/148.08 , activate(n__from(X)) -> from(X) } 214.95/148.08 214.95/148.08 We are left with following problem, upon which TcT provides the 214.95/148.08 certificate YES(O(1),O(n^1)). 214.95/148.08 214.95/148.08 Strict DPs: 214.95/148.08 { from^#(X) -> c_1(X, X) 214.95/148.08 , from^#(X) -> c_2(X) 214.95/148.08 , sel^#(s(X), cons(Y, Z)) -> c_3(sel^#(X, activate(Z))) 214.95/148.08 , sel^#(0(), cons(X, Y)) -> c_4(X) 214.95/148.08 , activate^#(X) -> c_5(X) 214.95/148.08 , activate^#(n__from(X)) -> c_6(from^#(X)) } 214.95/148.08 Strict Trs: 214.95/148.08 { from(X) -> cons(X, n__from(s(X))) 214.95/148.08 , from(X) -> n__from(X) 214.95/148.08 , activate(X) -> X 214.95/148.08 , activate(n__from(X)) -> from(X) } 214.95/148.08 Obligation: 214.95/148.08 runtime complexity 214.95/148.08 Answer: 214.95/148.08 YES(O(1),O(n^1)) 214.95/148.08 214.95/148.08 The weightgap principle applies (using the following constant 214.95/148.08 growth matrix-interpretation) 214.95/148.08 214.95/148.08 The following argument positions are usable: 214.95/148.08 Uargs(sel^#) = {2}, Uargs(c_3) = {1}, Uargs(c_6) = {1} 214.95/148.08 214.95/148.08 TcT has computed the following constructor-restricted matrix 214.95/148.08 interpretation. 214.95/148.08 214.95/148.08 [from](x1) = [1] 214.95/148.08 [0] 214.95/148.08 214.95/148.08 [cons](x1, x2) = [1 0] x2 + [0] 214.95/148.08 [0 0] [0] 214.95/148.08 214.95/148.08 [n__from](x1) = [0] 214.95/148.08 [0] 214.95/148.08 214.95/148.08 [s](x1) = [1 2] x1 + [0] 214.95/148.08 [0 0] [0] 214.95/148.08 214.95/148.08 [0] = [0] 214.95/148.08 [0] 214.95/148.08 214.95/148.08 [activate](x1) = [1 0] x1 + [2] 214.95/148.08 [0 2] [0] 214.95/148.08 214.95/148.08 [from^#](x1) = [0 0] x1 + [1] 214.95/148.08 [1 2] [1] 214.95/148.08 214.95/148.08 [c_1](x1, x2) = [0 0] x1 + [0 0] x2 + [1] 214.95/148.08 [1 2] [2 2] [1] 214.95/148.08 214.95/148.08 [c_2](x1) = [0 0] x1 + [2] 214.95/148.08 [1 1] [1] 214.95/148.08 214.95/148.08 [sel^#](x1, x2) = [1 0] x2 + [0] 214.95/148.08 [0 0] [0] 214.95/148.08 214.95/148.08 [c_3](x1) = [1 0] x1 + [2] 214.95/148.08 [0 1] [2] 214.95/148.08 214.95/148.08 [c_4](x1) = [1] 214.95/148.08 [0] 214.95/148.08 214.95/148.08 [activate^#](x1) = [1 1] x1 + [2] 214.95/148.08 [1 1] [2] 214.95/148.08 214.95/148.08 [c_5](x1) = [1 1] x1 + [1] 214.95/148.08 [1 1] [1] 214.95/148.08 214.95/148.08 [c_6](x1) = [1 0] x1 + [2] 214.95/148.08 [0 1] [2] 214.95/148.08 214.95/148.08 The order satisfies the following ordering constraints: 214.95/148.08 214.95/148.08 [from(X)] = [1] 214.95/148.08 [0] 214.95/148.08 > [0] 214.95/148.08 [0] 214.95/148.08 = [cons(X, n__from(s(X)))] 214.95/148.08 214.95/148.08 [from(X)] = [1] 214.95/148.08 [0] 214.95/148.08 > [0] 214.95/148.08 [0] 214.95/148.08 = [n__from(X)] 214.95/148.08 214.95/148.08 [activate(X)] = [1 0] X + [2] 214.95/148.08 [0 2] [0] 214.95/148.08 > [1 0] X + [0] 214.95/148.08 [0 1] [0] 214.95/148.08 = [X] 214.95/148.08 214.95/148.08 [activate(n__from(X))] = [2] 214.95/148.08 [0] 214.95/148.08 > [1] 214.95/148.08 [0] 214.95/148.08 = [from(X)] 214.95/148.08 214.95/148.08 [from^#(X)] = [0 0] X + [1] 214.95/148.08 [1 2] [1] 214.95/148.08 ? [0 0] X + [1] 214.95/148.08 [3 4] [1] 214.95/148.08 = [c_1(X, X)] 214.95/148.08 214.95/148.08 [from^#(X)] = [0 0] X + [1] 214.95/148.08 [1 2] [1] 214.95/148.08 ? [0 0] X + [2] 214.95/148.08 [1 1] [1] 214.95/148.08 = [c_2(X)] 214.95/148.08 214.95/148.08 [sel^#(s(X), cons(Y, Z))] = [1 0] Z + [0] 214.95/148.08 [0 0] [0] 214.95/148.08 ? [1 0] Z + [4] 214.95/148.08 [0 0] [2] 214.95/148.08 = [c_3(sel^#(X, activate(Z)))] 214.95/148.08 214.95/148.08 [sel^#(0(), cons(X, Y))] = [1 0] Y + [0] 214.95/148.08 [0 0] [0] 214.95/148.08 ? [1] 214.95/148.08 [0] 214.95/148.08 = [c_4(X)] 214.95/148.08 214.95/148.08 [activate^#(X)] = [1 1] X + [2] 214.95/148.08 [1 1] [2] 214.95/148.08 > [1 1] X + [1] 214.95/148.08 [1 1] [1] 214.95/148.08 = [c_5(X)] 214.95/148.08 214.95/148.08 [activate^#(n__from(X))] = [2] 214.95/148.08 [2] 214.95/148.08 ? [0 0] X + [3] 214.95/148.08 [1 2] [3] 214.95/148.08 = [c_6(from^#(X))] 214.95/148.08 214.95/148.08 214.95/148.08 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 214.95/148.08 214.95/148.08 We are left with following problem, upon which TcT provides the 214.95/148.08 certificate YES(O(1),O(n^1)). 214.95/148.08 214.95/148.08 Strict DPs: 214.95/148.08 { from^#(X) -> c_1(X, X) 214.95/148.08 , from^#(X) -> c_2(X) 214.95/148.08 , sel^#(s(X), cons(Y, Z)) -> c_3(sel^#(X, activate(Z))) 214.95/148.08 , sel^#(0(), cons(X, Y)) -> c_4(X) 214.95/148.08 , activate^#(n__from(X)) -> c_6(from^#(X)) } 214.95/148.08 Weak DPs: { activate^#(X) -> c_5(X) } 214.95/148.08 Weak Trs: 214.95/148.08 { from(X) -> cons(X, n__from(s(X))) 214.95/148.08 , from(X) -> n__from(X) 214.95/148.08 , activate(X) -> X 214.95/148.08 , activate(n__from(X)) -> from(X) } 214.95/148.08 Obligation: 214.95/148.08 runtime complexity 214.95/148.08 Answer: 214.95/148.08 YES(O(1),O(n^1)) 214.95/148.08 214.95/148.08 We use the processor 'matrix interpretation of dimension 1' to 214.95/148.08 orient following rules strictly. 214.95/148.08 214.95/148.08 DPs: 214.95/148.08 { 4: sel^#(0(), cons(X, Y)) -> c_4(X) 214.95/148.08 , 5: activate^#(n__from(X)) -> c_6(from^#(X)) 214.95/148.08 , 6: activate^#(X) -> c_5(X) } 214.95/148.08 214.95/148.08 Sub-proof: 214.95/148.08 ---------- 214.95/148.08 The following argument positions are usable: 214.95/148.08 Uargs(c_3) = {1}, Uargs(c_6) = {1} 214.95/148.08 214.95/148.08 TcT has computed the following constructor-based matrix 214.95/148.08 interpretation satisfying not(EDA). 214.95/148.08 214.95/148.08 [from](x1) = [4] x1 + [0] 214.95/148.08 214.95/148.08 [cons](x1, x2) = [1] x1 + [0] 214.95/148.08 214.95/148.08 [n__from](x1) = [1] x1 + [0] 214.95/148.08 214.95/148.08 [s](x1) = [1] x1 + [0] 214.95/148.08 214.95/148.08 [0] = [1] 214.95/148.08 214.95/148.08 [activate](x1) = [0] 214.95/148.08 214.95/148.08 [from^#](x1) = [2] x1 + [0] 214.95/148.08 214.95/148.08 [c_1](x1, x2) = [2] x1 + [0] 214.95/148.08 214.95/148.08 [c_2](x1) = [1] x1 + [0] 214.95/148.08 214.95/148.08 [sel^#](x1, x2) = [1] x1 + [0] 214.95/148.08 214.95/148.08 [c_3](x1) = [1] x1 + [0] 214.95/148.08 214.95/148.08 [c_4](x1) = [0] 214.95/148.08 214.95/148.08 [activate^#](x1) = [5] x1 + [7] 214.95/148.08 214.95/148.08 [c_5](x1) = [5] x1 + [6] 214.95/148.08 214.95/148.08 [c_6](x1) = [2] x1 + [3] 214.95/148.08 214.95/148.08 The order satisfies the following ordering constraints: 214.95/148.08 214.95/148.08 [from(X)] = [4] X + [0] 214.95/148.08 >= [1] X + [0] 214.95/148.08 = [cons(X, n__from(s(X)))] 214.95/148.08 214.95/148.08 [from(X)] = [4] X + [0] 214.95/148.08 >= [1] X + [0] 214.95/148.08 = [n__from(X)] 214.95/148.08 214.95/148.08 [activate(X)] = [0] 214.95/148.08 ? [1] X + [0] 214.95/148.08 = [X] 214.95/148.08 214.95/148.08 [activate(n__from(X))] = [0] 214.95/148.08 ? [4] X + [0] 214.95/148.08 = [from(X)] 214.95/148.08 214.95/148.08 [from^#(X)] = [2] X + [0] 214.95/148.08 >= [2] X + [0] 214.95/148.08 = [c_1(X, X)] 214.95/148.08 214.95/148.08 [from^#(X)] = [2] X + [0] 214.95/148.08 >= [1] X + [0] 214.95/148.08 = [c_2(X)] 214.95/148.08 214.95/148.08 [sel^#(s(X), cons(Y, Z))] = [1] X + [0] 214.95/148.08 >= [1] X + [0] 214.95/148.08 = [c_3(sel^#(X, activate(Z)))] 214.95/148.08 214.95/148.08 [sel^#(0(), cons(X, Y))] = [1] 214.95/148.08 > [0] 214.95/148.08 = [c_4(X)] 214.95/148.08 214.95/148.08 [activate^#(X)] = [5] X + [7] 214.95/148.08 > [5] X + [6] 214.95/148.08 = [c_5(X)] 214.95/148.08 214.95/148.08 [activate^#(n__from(X))] = [5] X + [7] 214.95/148.08 > [4] X + [3] 214.95/148.08 = [c_6(from^#(X))] 214.95/148.08 214.95/148.08 214.95/148.08 The strictly oriented rules are moved into the weak component. 214.95/148.08 214.95/148.08 We are left with following problem, upon which TcT provides the 214.95/148.08 certificate YES(O(1),O(n^1)). 214.95/148.08 214.95/148.08 Strict DPs: 214.95/148.08 { from^#(X) -> c_1(X, X) 214.95/148.08 , from^#(X) -> c_2(X) 214.95/148.08 , sel^#(s(X), cons(Y, Z)) -> c_3(sel^#(X, activate(Z))) } 214.95/148.08 Weak DPs: 214.95/148.08 { sel^#(0(), cons(X, Y)) -> c_4(X) 214.95/148.08 , activate^#(X) -> c_5(X) 214.95/148.08 , activate^#(n__from(X)) -> c_6(from^#(X)) } 214.95/148.08 Weak Trs: 214.95/148.08 { from(X) -> cons(X, n__from(s(X))) 214.95/148.08 , from(X) -> n__from(X) 214.95/148.08 , activate(X) -> X 214.95/148.08 , activate(n__from(X)) -> from(X) } 214.95/148.08 Obligation: 214.95/148.08 runtime complexity 214.95/148.08 Answer: 214.95/148.08 YES(O(1),O(n^1)) 214.95/148.08 214.95/148.08 We use the processor 'matrix interpretation of dimension 1' to 214.95/148.08 orient following rules strictly. 214.95/148.08 214.95/148.08 DPs: 214.95/148.08 { 1: from^#(X) -> c_1(X, X) 214.95/148.08 , 2: from^#(X) -> c_2(X) 214.95/148.08 , 5: activate^#(X) -> c_5(X) 214.95/148.08 , 6: activate^#(n__from(X)) -> c_6(from^#(X)) } 214.95/148.08 214.95/148.08 Sub-proof: 214.95/148.08 ---------- 214.95/148.08 The following argument positions are usable: 214.95/148.08 Uargs(c_3) = {1}, Uargs(c_6) = {1} 214.95/148.08 214.95/148.08 TcT has computed the following constructor-restricted matrix 214.95/148.08 interpretation. Note that the diagonal of the component-wise maxima 214.95/148.08 of interpretation-entries (of constructors) contains no more than 0 214.95/148.08 non-zero entries. 214.95/148.08 214.95/148.08 [from](x1) = [7] x1 + [0] 214.95/148.08 214.95/148.08 [cons](x1, x2) = [0] 214.95/148.08 214.95/148.08 [n__from](x1) = [0] 214.95/148.08 214.95/148.08 [s](x1) = [7] 214.95/148.08 214.95/148.08 [0] = [7] 214.95/148.08 214.95/148.08 [activate](x1) = [0] 214.95/148.08 214.95/148.08 [from^#](x1) = [2] 214.95/148.08 214.95/148.08 [c_1](x1, x2) = [0] 214.95/148.08 214.95/148.08 [c_2](x1) = [0] 214.95/148.08 214.95/148.08 [sel^#](x1, x2) = [0] 214.95/148.08 214.95/148.08 [c_3](x1) = [4] x1 + [0] 214.95/148.08 214.95/148.08 [c_4](x1) = [0] 214.95/148.08 214.95/148.08 [activate^#](x1) = [7] x1 + [7] 214.95/148.08 214.95/148.08 [c_5](x1) = [7] x1 + [6] 214.95/148.08 214.95/148.08 [c_6](x1) = [1] x1 + [0] 214.95/148.08 214.95/148.08 The order satisfies the following ordering constraints: 214.95/148.08 214.95/148.08 [from(X)] = [7] X + [0] 214.95/148.08 >= [0] 214.95/148.08 = [cons(X, n__from(s(X)))] 214.95/148.08 214.95/148.08 [from(X)] = [7] X + [0] 214.95/148.08 >= [0] 214.95/148.08 = [n__from(X)] 214.95/148.08 214.95/148.08 [activate(X)] = [0] 214.95/148.08 ? [1] X + [0] 214.95/148.08 = [X] 214.95/148.08 214.95/148.08 [activate(n__from(X))] = [0] 214.95/148.08 ? [7] X + [0] 214.95/148.08 = [from(X)] 214.95/148.08 214.95/148.08 [from^#(X)] = [2] 214.95/148.08 > [0] 214.95/148.08 = [c_1(X, X)] 214.95/148.08 214.95/148.08 [from^#(X)] = [2] 214.95/148.08 > [0] 214.95/148.08 = [c_2(X)] 214.95/148.08 214.95/148.08 [sel^#(s(X), cons(Y, Z))] = [0] 214.95/148.08 >= [0] 214.95/148.08 = [c_3(sel^#(X, activate(Z)))] 214.95/148.08 214.95/148.08 [sel^#(0(), cons(X, Y))] = [0] 214.95/148.08 >= [0] 214.95/148.08 = [c_4(X)] 214.95/148.08 214.95/148.08 [activate^#(X)] = [7] X + [7] 214.95/148.08 > [7] X + [6] 214.95/148.08 = [c_5(X)] 214.95/148.08 214.95/148.08 [activate^#(n__from(X))] = [7] 214.95/148.08 > [2] 214.95/148.08 = [c_6(from^#(X))] 214.95/148.08 214.95/148.08 214.95/148.08 The strictly oriented rules are moved into the weak component. 214.95/148.08 214.95/148.08 We are left with following problem, upon which TcT provides the 214.95/148.08 certificate YES(O(1),O(n^1)). 214.95/148.08 214.95/148.08 Strict DPs: 214.95/148.08 { sel^#(s(X), cons(Y, Z)) -> c_3(sel^#(X, activate(Z))) } 214.95/148.08 Weak DPs: 214.95/148.08 { from^#(X) -> c_1(X, X) 214.95/148.08 , from^#(X) -> c_2(X) 214.95/148.08 , sel^#(0(), cons(X, Y)) -> c_4(X) 214.95/148.08 , activate^#(X) -> c_5(X) 214.95/148.08 , activate^#(n__from(X)) -> c_6(from^#(X)) } 214.95/148.08 Weak Trs: 214.95/148.08 { from(X) -> cons(X, n__from(s(X))) 214.95/148.08 , from(X) -> n__from(X) 214.95/148.08 , activate(X) -> X 214.95/148.08 , activate(n__from(X)) -> from(X) } 214.95/148.08 Obligation: 214.95/148.08 runtime complexity 214.95/148.08 Answer: 214.95/148.08 YES(O(1),O(n^1)) 214.95/148.08 214.95/148.08 We use the processor 'matrix interpretation of dimension 1' to 214.95/148.08 orient following rules strictly. 214.95/148.08 214.95/148.08 DPs: 214.95/148.08 { 1: sel^#(s(X), cons(Y, Z)) -> c_3(sel^#(X, activate(Z))) 214.95/148.08 , 5: activate^#(X) -> c_5(X) 214.95/148.08 , 6: activate^#(n__from(X)) -> c_6(from^#(X)) } 214.95/148.08 214.95/148.08 Sub-proof: 214.95/148.08 ---------- 214.95/148.08 The following argument positions are usable: 214.95/148.08 Uargs(c_3) = {1}, Uargs(c_6) = {1} 214.95/148.08 214.95/148.08 TcT has computed the following constructor-based matrix 214.95/148.08 interpretation satisfying not(EDA). 214.95/148.08 214.95/148.08 [from](x1) = [4] x1 + [0] 214.95/148.08 214.95/148.08 [cons](x1, x2) = [1] x1 + [0] 214.95/148.08 214.95/148.08 [n__from](x1) = [1] x1 + [0] 214.95/148.08 214.95/148.08 [s](x1) = [1] x1 + [4] 214.95/148.08 214.95/148.08 [0] = [0] 214.95/148.08 214.95/148.08 [activate](x1) = [0] 214.95/148.08 214.95/148.08 [from^#](x1) = [5] x1 + [0] 214.95/148.08 214.95/148.08 [c_1](x1, x2) = [3] x1 + [2] x2 + [0] 214.95/148.08 214.95/148.08 [c_2](x1) = [5] x1 + [0] 214.95/148.08 214.95/148.08 [sel^#](x1, x2) = [1] x1 + [0] 214.95/148.08 214.95/148.08 [c_3](x1) = [1] x1 + [1] 214.95/148.08 214.95/148.08 [c_4](x1) = [0] 214.95/148.08 214.95/148.08 [activate^#](x1) = [5] x1 + [7] 214.95/148.08 214.95/148.08 [c_5](x1) = [5] x1 + [5] 214.95/148.08 214.95/148.08 [c_6](x1) = [1] x1 + [1] 214.95/148.08 214.95/148.08 The order satisfies the following ordering constraints: 214.95/148.08 214.95/148.08 [from(X)] = [4] X + [0] 214.95/148.08 >= [1] X + [0] 214.95/148.08 = [cons(X, n__from(s(X)))] 214.95/148.08 214.95/148.08 [from(X)] = [4] X + [0] 214.95/148.08 >= [1] X + [0] 214.95/148.08 = [n__from(X)] 214.95/148.08 214.95/148.08 [activate(X)] = [0] 214.95/148.08 ? [1] X + [0] 214.95/148.08 = [X] 214.95/148.08 214.95/148.08 [activate(n__from(X))] = [0] 214.95/148.08 ? [4] X + [0] 214.95/148.08 = [from(X)] 214.95/148.08 214.95/148.08 [from^#(X)] = [5] X + [0] 214.95/148.08 >= [5] X + [0] 214.95/148.08 = [c_1(X, X)] 214.95/148.08 214.95/148.08 [from^#(X)] = [5] X + [0] 214.95/148.08 >= [5] X + [0] 214.95/148.08 = [c_2(X)] 214.95/148.08 214.95/148.08 [sel^#(s(X), cons(Y, Z))] = [1] X + [4] 214.95/148.08 > [1] X + [1] 214.95/148.08 = [c_3(sel^#(X, activate(Z)))] 214.95/148.08 214.95/148.08 [sel^#(0(), cons(X, Y))] = [0] 214.95/148.08 >= [0] 214.95/148.08 = [c_4(X)] 214.95/148.08 214.95/148.08 [activate^#(X)] = [5] X + [7] 214.95/148.08 > [5] X + [5] 214.95/148.08 = [c_5(X)] 214.95/148.08 214.95/148.08 [activate^#(n__from(X))] = [5] X + [7] 214.95/148.08 > [5] X + [1] 214.95/148.08 = [c_6(from^#(X))] 214.95/148.08 214.95/148.08 214.95/148.08 The strictly oriented rules are moved into the weak component. 214.95/148.08 214.95/148.08 We are left with following problem, upon which TcT provides the 214.95/148.08 certificate YES(O(1),O(1)). 214.95/148.08 214.95/148.08 Weak DPs: 214.95/148.08 { from^#(X) -> c_1(X, X) 214.95/148.08 , from^#(X) -> c_2(X) 214.95/148.08 , sel^#(s(X), cons(Y, Z)) -> c_3(sel^#(X, activate(Z))) 214.95/148.08 , sel^#(0(), cons(X, Y)) -> c_4(X) 214.95/148.08 , activate^#(X) -> c_5(X) 214.95/148.08 , activate^#(n__from(X)) -> c_6(from^#(X)) } 214.95/148.08 Weak Trs: 214.95/148.08 { from(X) -> cons(X, n__from(s(X))) 214.95/148.08 , from(X) -> n__from(X) 214.95/148.08 , activate(X) -> X 214.95/148.08 , activate(n__from(X)) -> from(X) } 214.95/148.08 Obligation: 214.95/148.08 runtime complexity 214.95/148.08 Answer: 214.95/148.08 YES(O(1),O(1)) 214.95/148.08 214.95/148.08 The following weak DPs constitute a sub-graph of the DG that is 214.95/148.08 closed under successors. The DPs are removed. 214.95/148.08 214.95/148.08 { from^#(X) -> c_1(X, X) 214.95/148.08 , from^#(X) -> c_2(X) 214.95/148.08 , sel^#(s(X), cons(Y, Z)) -> c_3(sel^#(X, activate(Z))) 214.95/148.08 , sel^#(0(), cons(X, Y)) -> c_4(X) 214.95/148.08 , activate^#(X) -> c_5(X) 214.95/148.08 , activate^#(n__from(X)) -> c_6(from^#(X)) } 214.95/148.08 214.95/148.08 We are left with following problem, upon which TcT provides the 214.95/148.08 certificate YES(O(1),O(1)). 214.95/148.08 214.95/148.08 Weak Trs: 214.95/148.08 { from(X) -> cons(X, n__from(s(X))) 214.95/148.08 , from(X) -> n__from(X) 214.95/148.08 , activate(X) -> X 214.95/148.08 , activate(n__from(X)) -> from(X) } 214.95/148.08 Obligation: 214.95/148.08 runtime complexity 214.95/148.08 Answer: 214.95/148.08 YES(O(1),O(1)) 214.95/148.08 214.95/148.08 No rule is usable, rules are removed from the input problem. 214.95/148.08 214.95/148.08 We are left with following problem, upon which TcT provides the 214.95/148.08 certificate YES(O(1),O(1)). 214.95/148.08 214.95/148.08 Rules: Empty 214.95/148.08 Obligation: 214.95/148.08 runtime complexity 214.95/148.08 Answer: 214.95/148.08 YES(O(1),O(1)) 214.95/148.08 214.95/148.08 Empty rules are trivially bounded 214.95/148.08 214.95/148.08 Hurray, we answered YES(O(1),O(n^1)) 215.15/148.10 EOF