YES(O(1),O(n^2)) 207.84/60.04 YES(O(1),O(n^2)) 207.84/60.04 207.84/60.04 We are left with following problem, upon which TcT provides the 207.84/60.04 certificate YES(O(1),O(n^2)). 207.84/60.04 207.84/60.04 Strict Trs: 207.84/60.04 { 1(q0(1(x1))) -> 0(1(q1(x1))) 207.84/60.04 , 1(q0(0(x1))) -> 0(0(q1(x1))) 207.84/60.04 , 1(q1(1(x1))) -> 1(1(q1(x1))) 207.84/60.04 , 1(q1(0(x1))) -> 1(0(q1(x1))) 207.84/60.04 , 1(q2(x1)) -> q2(1(x1)) 207.84/60.04 , 0(q1(x1)) -> q2(1(x1)) 207.84/60.04 , 0(q2(x1)) -> 0(q0(x1)) } 207.84/60.04 Obligation: 207.84/60.04 derivational complexity 207.84/60.04 Answer: 207.84/60.04 YES(O(1),O(n^2)) 207.84/60.04 207.84/60.04 The weightgap principle applies (using the following nonconstant 207.84/60.04 growth matrix-interpretation) 207.84/60.04 207.84/60.04 TcT has computed the following triangular matrix interpretation. 207.84/60.04 Note that the diagonal of the component-wise maxima of 207.84/60.04 interpretation-entries contains no more than 1 non-zero entries. 207.84/60.04 207.84/60.04 [1](x1) = [1] x1 + [0] 207.84/60.04 207.84/60.04 [q0](x1) = [1] x1 + [0] 207.84/60.04 207.84/60.04 [0](x1) = [1] x1 + [0] 207.84/60.04 207.84/60.04 [q1](x1) = [1] x1 + [0] 207.84/60.04 207.84/60.04 [q2](x1) = [1] x1 + [1] 207.84/60.04 207.84/60.04 The order satisfies the following ordering constraints: 207.84/60.04 207.84/60.04 [1(q0(1(x1)))] = [1] x1 + [0] 207.84/60.04 >= [1] x1 + [0] 207.84/60.04 = [0(1(q1(x1)))] 207.84/60.04 207.84/60.04 [1(q0(0(x1)))] = [1] x1 + [0] 207.84/60.04 >= [1] x1 + [0] 207.84/60.04 = [0(0(q1(x1)))] 207.84/60.04 207.84/60.04 [1(q1(1(x1)))] = [1] x1 + [0] 207.84/60.04 >= [1] x1 + [0] 207.84/60.04 = [1(1(q1(x1)))] 207.84/60.04 207.84/60.04 [1(q1(0(x1)))] = [1] x1 + [0] 207.84/60.04 >= [1] x1 + [0] 207.84/60.04 = [1(0(q1(x1)))] 207.84/60.04 207.84/60.04 [1(q2(x1))] = [1] x1 + [1] 207.84/60.04 >= [1] x1 + [1] 207.84/60.04 = [q2(1(x1))] 207.84/60.04 207.84/60.04 [0(q1(x1))] = [1] x1 + [0] 207.84/60.04 ? [1] x1 + [1] 207.84/60.04 = [q2(1(x1))] 207.84/60.04 207.84/60.04 [0(q2(x1))] = [1] x1 + [1] 207.84/60.04 > [1] x1 + [0] 207.84/60.04 = [0(q0(x1))] 207.84/60.04 207.84/60.04 207.84/60.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 207.84/60.04 207.84/60.04 We are left with following problem, upon which TcT provides the 207.84/60.04 certificate YES(O(1),O(n^2)). 207.84/60.04 207.84/60.04 Strict Trs: 207.84/60.04 { 1(q0(1(x1))) -> 0(1(q1(x1))) 207.84/60.04 , 1(q0(0(x1))) -> 0(0(q1(x1))) 207.84/60.04 , 1(q1(1(x1))) -> 1(1(q1(x1))) 207.84/60.04 , 1(q1(0(x1))) -> 1(0(q1(x1))) 207.84/60.04 , 1(q2(x1)) -> q2(1(x1)) 207.84/60.04 , 0(q1(x1)) -> q2(1(x1)) } 207.84/60.04 Weak Trs: { 0(q2(x1)) -> 0(q0(x1)) } 207.84/60.04 Obligation: 207.84/60.04 derivational complexity 207.84/60.04 Answer: 207.84/60.04 YES(O(1),O(n^2)) 207.84/60.04 207.84/60.04 The weightgap principle applies (using the following nonconstant 207.84/60.04 growth matrix-interpretation) 207.84/60.04 207.84/60.04 TcT has computed the following triangular matrix interpretation. 207.84/60.04 Note that the diagonal of the component-wise maxima of 207.84/60.04 interpretation-entries contains no more than 1 non-zero entries. 207.84/60.04 207.84/60.04 [1](x1) = [1] x1 + [0] 207.84/60.04 207.84/60.04 [q0](x1) = [1] x1 + [0] 207.84/60.04 207.84/60.04 [0](x1) = [1] x1 + [0] 207.84/60.04 207.84/60.04 [q1](x1) = [1] x1 + [1] 207.84/60.04 207.84/60.04 [q2](x1) = [1] x1 + [0] 207.84/60.04 207.84/60.04 The order satisfies the following ordering constraints: 207.84/60.04 207.84/60.04 [1(q0(1(x1)))] = [1] x1 + [0] 207.84/60.04 ? [1] x1 + [1] 207.84/60.04 = [0(1(q1(x1)))] 207.84/60.04 207.84/60.04 [1(q0(0(x1)))] = [1] x1 + [0] 207.84/60.04 ? [1] x1 + [1] 207.84/60.04 = [0(0(q1(x1)))] 207.84/60.04 207.84/60.04 [1(q1(1(x1)))] = [1] x1 + [1] 207.84/60.04 >= [1] x1 + [1] 207.84/60.04 = [1(1(q1(x1)))] 207.84/60.04 207.84/60.04 [1(q1(0(x1)))] = [1] x1 + [1] 207.84/60.04 >= [1] x1 + [1] 207.84/60.04 = [1(0(q1(x1)))] 207.84/60.04 207.84/60.04 [1(q2(x1))] = [1] x1 + [0] 207.84/60.04 >= [1] x1 + [0] 207.84/60.04 = [q2(1(x1))] 207.84/60.04 207.84/60.04 [0(q1(x1))] = [1] x1 + [1] 207.84/60.04 > [1] x1 + [0] 207.84/60.04 = [q2(1(x1))] 207.84/60.04 207.84/60.04 [0(q2(x1))] = [1] x1 + [0] 207.84/60.04 >= [1] x1 + [0] 207.84/60.04 = [0(q0(x1))] 207.84/60.04 207.84/60.04 207.84/60.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 207.84/60.04 207.84/60.04 We are left with following problem, upon which TcT provides the 207.84/60.04 certificate YES(O(1),O(n^2)). 207.84/60.04 207.84/60.04 Strict Trs: 207.84/60.04 { 1(q0(1(x1))) -> 0(1(q1(x1))) 207.84/60.04 , 1(q0(0(x1))) -> 0(0(q1(x1))) 207.84/60.04 , 1(q1(1(x1))) -> 1(1(q1(x1))) 207.84/60.04 , 1(q1(0(x1))) -> 1(0(q1(x1))) 207.84/60.04 , 1(q2(x1)) -> q2(1(x1)) } 207.84/60.04 Weak Trs: 207.84/60.04 { 0(q1(x1)) -> q2(1(x1)) 207.84/60.04 , 0(q2(x1)) -> 0(q0(x1)) } 207.84/60.04 Obligation: 207.84/60.04 derivational complexity 207.84/60.04 Answer: 207.84/60.04 YES(O(1),O(n^2)) 207.84/60.04 207.84/60.04 The weightgap principle applies (using the following nonconstant 207.84/60.04 growth matrix-interpretation) 207.84/60.04 207.84/60.04 TcT has computed the following triangular matrix interpretation. 207.84/60.04 Note that the diagonal of the component-wise maxima of 207.84/60.04 interpretation-entries contains no more than 1 non-zero entries. 207.84/60.04 207.84/60.04 [1](x1) = [1 0] x1 + [0] 207.84/60.04 [0 0] [2] 207.84/60.04 207.84/60.04 [q0](x1) = [1 2] x1 + [2] 207.84/60.04 [0 0] [0] 207.84/60.04 207.84/60.04 [0](x1) = [1 2] x1 + [0] 207.84/60.04 [0 0] [1] 207.84/60.04 207.84/60.04 [q1](x1) = [1 0] x1 + [0] 207.84/60.04 [0 0] [2] 207.84/60.04 207.84/60.04 [q2](x1) = [1 2] x1 + [0] 207.84/60.04 [0 0] [1] 207.84/60.04 207.84/60.04 The order satisfies the following ordering constraints: 207.84/60.04 207.84/60.04 [1(q0(1(x1)))] = [1 0] x1 + [6] 207.84/60.04 [0 0] [2] 207.84/60.04 > [1 0] x1 + [4] 207.84/60.04 [0 0] [1] 207.84/60.04 = [0(1(q1(x1)))] 207.84/60.04 207.84/60.04 [1(q0(0(x1)))] = [1 2] x1 + [4] 207.84/60.04 [0 0] [2] 207.84/60.04 ? [1 0] x1 + [6] 207.84/60.04 [0 0] [1] 207.84/60.04 = [0(0(q1(x1)))] 207.84/60.04 207.84/60.04 [1(q1(1(x1)))] = [1 0] x1 + [0] 207.84/60.04 [0 0] [2] 207.84/60.04 >= [1 0] x1 + [0] 207.84/60.04 [0 0] [2] 207.84/60.04 = [1(1(q1(x1)))] 207.84/60.04 207.84/60.04 [1(q1(0(x1)))] = [1 2] x1 + [0] 207.84/60.04 [0 0] [2] 207.84/60.04 ? [1 0] x1 + [4] 207.84/60.04 [0 0] [2] 207.84/60.04 = [1(0(q1(x1)))] 207.84/60.04 207.84/60.04 [1(q2(x1))] = [1 2] x1 + [0] 207.84/60.04 [0 0] [2] 207.84/60.04 ? [1 0] x1 + [4] 207.84/60.04 [0 0] [1] 207.84/60.04 = [q2(1(x1))] 207.84/60.04 207.84/60.04 [0(q1(x1))] = [1 0] x1 + [4] 207.84/60.04 [0 0] [1] 207.84/60.04 >= [1 0] x1 + [4] 207.84/60.04 [0 0] [1] 207.84/60.04 = [q2(1(x1))] 207.84/60.04 207.84/60.04 [0(q2(x1))] = [1 2] x1 + [2] 207.84/60.04 [0 0] [1] 207.84/60.04 >= [1 2] x1 + [2] 207.84/60.04 [0 0] [1] 207.84/60.04 = [0(q0(x1))] 207.84/60.04 207.84/60.04 207.84/60.04 Further, it can be verified that all rules not oriented are covered by the weightgap condition. 207.84/60.04 207.84/60.04 We are left with following problem, upon which TcT provides the 207.84/60.04 certificate YES(O(1),O(n^2)). 207.84/60.04 207.84/60.04 Strict Trs: 207.84/60.04 { 1(q0(0(x1))) -> 0(0(q1(x1))) 207.84/60.04 , 1(q1(1(x1))) -> 1(1(q1(x1))) 207.84/60.04 , 1(q1(0(x1))) -> 1(0(q1(x1))) 207.84/60.04 , 1(q2(x1)) -> q2(1(x1)) } 207.84/60.04 Weak Trs: 207.84/60.04 { 1(q0(1(x1))) -> 0(1(q1(x1))) 207.84/60.04 , 0(q1(x1)) -> q2(1(x1)) 207.84/60.04 , 0(q2(x1)) -> 0(q0(x1)) } 207.84/60.04 Obligation: 207.84/60.04 derivational complexity 207.84/60.04 Answer: 207.84/60.04 YES(O(1),O(n^2)) 207.84/60.04 207.84/60.04 We use the processor 'matrix interpretation of dimension 2' to 207.84/60.04 orient following rules strictly. 207.84/60.04 207.84/60.04 Trs: 207.84/60.04 { 1(q0(0(x1))) -> 0(0(q1(x1))) 207.84/60.04 , 1(q2(x1)) -> q2(1(x1)) } 207.84/60.04 207.84/60.04 The induced complexity on above rules (modulo remaining rules) is 207.84/60.04 YES(?,O(n^2)) . These rules are moved into the corresponding weak 207.84/60.04 component(s). 207.84/60.04 207.84/60.04 Sub-proof: 207.84/60.04 ---------- 207.84/60.04 TcT has computed the following triangular matrix interpretation. 207.84/60.04 207.84/60.04 [1](x1) = [1 2] x1 + [0] 207.84/60.04 [0 1] [1] 207.84/60.04 207.84/60.04 [q0](x1) = [1 0] x1 + [0] 207.84/60.04 [0 1] [1] 207.84/60.04 207.84/60.04 [0](x1) = [1 2] x1 + [0] 207.84/60.04 [0 1] [2] 207.84/60.04 207.84/60.04 [q1](x1) = [1 0] x1 + [0] 207.84/60.04 [0 1] [0] 207.84/60.04 207.84/60.04 [q2](x1) = [1 0] x1 + [0] 207.84/60.04 [0 1] [1] 207.84/60.04 207.84/60.04 The order satisfies the following ordering constraints: 207.84/60.04 207.84/60.05 [1(q0(1(x1)))] = [1 4] x1 + [4] 207.84/60.05 [0 1] [3] 207.84/60.05 > [1 4] x1 + [2] 207.84/60.05 [0 1] [3] 207.84/60.05 = [0(1(q1(x1)))] 207.84/60.05 207.84/60.05 [1(q0(0(x1)))] = [1 4] x1 + [6] 207.84/60.05 [0 1] [4] 207.84/60.05 > [1 4] x1 + [4] 207.84/60.05 [0 1] [4] 207.84/60.05 = [0(0(q1(x1)))] 207.84/60.05 207.84/60.05 [1(q1(1(x1)))] = [1 4] x1 + [2] 207.84/60.05 [0 1] [2] 207.84/60.05 >= [1 4] x1 + [2] 207.84/60.05 [0 1] [2] 207.84/60.05 = [1(1(q1(x1)))] 207.84/60.05 207.84/60.05 [1(q1(0(x1)))] = [1 4] x1 + [4] 207.84/60.05 [0 1] [3] 207.84/60.05 >= [1 4] x1 + [4] 207.84/60.05 [0 1] [3] 207.84/60.05 = [1(0(q1(x1)))] 207.84/60.05 207.84/60.05 [1(q2(x1))] = [1 2] x1 + [2] 207.84/60.05 [0 1] [2] 207.84/60.05 > [1 2] x1 + [0] 207.84/60.05 [0 1] [2] 207.84/60.05 = [q2(1(x1))] 207.84/60.05 207.84/60.05 [0(q1(x1))] = [1 2] x1 + [0] 207.84/60.05 [0 1] [2] 207.84/60.05 >= [1 2] x1 + [0] 207.84/60.05 [0 1] [2] 207.84/60.05 = [q2(1(x1))] 207.84/60.05 207.84/60.05 [0(q2(x1))] = [1 2] x1 + [2] 207.84/60.05 [0 1] [3] 207.84/60.05 >= [1 2] x1 + [2] 207.84/60.05 [0 1] [3] 207.84/60.05 = [0(q0(x1))] 207.84/60.05 207.84/60.05 207.84/60.05 We return to the main proof. 207.84/60.05 207.84/60.05 We are left with following problem, upon which TcT provides the 207.84/60.05 certificate YES(O(1),O(n^2)). 207.84/60.05 207.84/60.05 Strict Trs: 207.84/60.05 { 1(q1(1(x1))) -> 1(1(q1(x1))) 207.84/60.05 , 1(q1(0(x1))) -> 1(0(q1(x1))) } 207.84/60.05 Weak Trs: 207.84/60.05 { 1(q0(1(x1))) -> 0(1(q1(x1))) 207.84/60.05 , 1(q0(0(x1))) -> 0(0(q1(x1))) 207.84/60.05 , 1(q2(x1)) -> q2(1(x1)) 207.84/60.05 , 0(q1(x1)) -> q2(1(x1)) 207.84/60.05 , 0(q2(x1)) -> 0(q0(x1)) } 207.84/60.05 Obligation: 207.84/60.05 derivational complexity 207.84/60.05 Answer: 207.84/60.05 YES(O(1),O(n^2)) 207.84/60.05 207.84/60.05 We use the processor 'matrix interpretation of dimension 2' to 207.84/60.05 orient following rules strictly. 207.84/60.05 207.84/60.05 Trs: { 1(q1(0(x1))) -> 1(0(q1(x1))) } 207.84/60.05 207.84/60.05 The induced complexity on above rules (modulo remaining rules) is 207.84/60.05 YES(?,O(n^2)) . These rules are moved into the corresponding weak 207.84/60.05 component(s). 207.84/60.05 207.84/60.05 Sub-proof: 207.84/60.05 ---------- 207.84/60.05 TcT has computed the following triangular matrix interpretation. 207.84/60.05 207.84/60.05 [1](x1) = [1 0] x1 + [0] 207.84/60.05 [0 1] [0] 207.84/60.05 207.84/60.05 [q0](x1) = [1 2] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 207.84/60.05 [0](x1) = [1 1] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 207.84/60.05 [q1](x1) = [1 1] x1 + [0] 207.84/60.05 [0 1] [0] 207.84/60.05 207.84/60.05 [q2](x1) = [1 2] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 207.84/60.05 The order satisfies the following ordering constraints: 207.84/60.05 207.84/60.05 [1(q0(1(x1)))] = [1 2] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 >= [1 2] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 = [0(1(q1(x1)))] 207.84/60.05 207.84/60.05 [1(q0(0(x1)))] = [1 3] x1 + [2] 207.84/60.05 [0 1] [2] 207.84/60.05 > [1 3] x1 + [1] 207.84/60.05 [0 1] [2] 207.84/60.05 = [0(0(q1(x1)))] 207.84/60.05 207.84/60.05 [1(q1(1(x1)))] = [1 1] x1 + [0] 207.84/60.05 [0 1] [0] 207.84/60.05 >= [1 1] x1 + [0] 207.84/60.05 [0 1] [0] 207.84/60.05 = [1(1(q1(x1)))] 207.84/60.05 207.84/60.05 [1(q1(0(x1)))] = [1 2] x1 + [1] 207.84/60.05 [0 1] [1] 207.84/60.05 > [1 2] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 = [1(0(q1(x1)))] 207.84/60.05 207.84/60.05 [1(q2(x1))] = [1 2] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 >= [1 2] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 = [q2(1(x1))] 207.84/60.05 207.84/60.05 [0(q1(x1))] = [1 2] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 >= [1 2] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 = [q2(1(x1))] 207.84/60.05 207.84/60.05 [0(q2(x1))] = [1 3] x1 + [1] 207.84/60.05 [0 1] [2] 207.84/60.05 >= [1 3] x1 + [1] 207.84/60.05 [0 1] [2] 207.84/60.05 = [0(q0(x1))] 207.84/60.05 207.84/60.05 207.84/60.05 We return to the main proof. 207.84/60.05 207.84/60.05 We are left with following problem, upon which TcT provides the 207.84/60.05 certificate YES(O(1),O(n^2)). 207.84/60.05 207.84/60.05 Strict Trs: { 1(q1(1(x1))) -> 1(1(q1(x1))) } 207.84/60.05 Weak Trs: 207.84/60.05 { 1(q0(1(x1))) -> 0(1(q1(x1))) 207.84/60.05 , 1(q0(0(x1))) -> 0(0(q1(x1))) 207.84/60.05 , 1(q1(0(x1))) -> 1(0(q1(x1))) 207.84/60.05 , 1(q2(x1)) -> q2(1(x1)) 207.84/60.05 , 0(q1(x1)) -> q2(1(x1)) 207.84/60.05 , 0(q2(x1)) -> 0(q0(x1)) } 207.84/60.05 Obligation: 207.84/60.05 derivational complexity 207.84/60.05 Answer: 207.84/60.05 YES(O(1),O(n^2)) 207.84/60.05 207.84/60.05 We use the processor 'matrix interpretation of dimension 2' to 207.84/60.05 orient following rules strictly. 207.84/60.05 207.84/60.05 Trs: { 1(q1(1(x1))) -> 1(1(q1(x1))) } 207.84/60.05 207.84/60.05 The induced complexity on above rules (modulo remaining rules) is 207.84/60.05 YES(?,O(n^2)) . These rules are moved into the corresponding weak 207.84/60.05 component(s). 207.84/60.05 207.84/60.05 Sub-proof: 207.84/60.05 ---------- 207.84/60.05 TcT has computed the following triangular matrix interpretation. 207.84/60.05 207.84/60.05 [1](x1) = [1 1] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 207.84/60.05 [q0](x1) = [1 1] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 207.84/60.05 [0](x1) = [1 0] x1 + [1] 207.84/60.05 [0 1] [1] 207.84/60.05 207.84/60.05 [q1](x1) = [1 2] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 207.84/60.05 [q2](x1) = [1 1] x1 + [0] 207.84/60.05 [0 1] [1] 207.84/60.05 207.84/60.05 The order satisfies the following ordering constraints: 207.84/60.05 207.84/60.05 [1(q0(1(x1)))] = [1 3] x1 + [3] 207.84/60.05 [0 1] [3] 207.84/60.05 > [1 3] x1 + [2] 207.84/60.05 [0 1] [3] 207.84/60.05 = [0(1(q1(x1)))] 207.84/60.05 207.84/60.05 [1(q0(0(x1)))] = [1 2] x1 + [4] 207.84/60.05 [0 1] [3] 207.84/60.05 > [1 2] x1 + [2] 207.84/60.05 [0 1] [3] 207.84/60.05 = [0(0(q1(x1)))] 207.84/60.05 207.84/60.05 [1(q1(1(x1)))] = [1 4] x1 + [4] 207.84/60.05 [0 1] [3] 207.84/60.05 > [1 4] x1 + [3] 207.84/60.05 [0 1] [3] 207.84/60.05 = [1(1(q1(x1)))] 207.84/60.05 207.84/60.05 [1(q1(0(x1)))] = [1 3] x1 + [5] 207.84/60.05 [0 1] [3] 207.84/60.05 > [1 3] x1 + [3] 207.84/60.05 [0 1] [3] 207.84/60.05 = [1(0(q1(x1)))] 207.84/60.05 207.84/60.05 [1(q2(x1))] = [1 2] x1 + [1] 207.84/60.05 [0 1] [2] 207.84/60.05 >= [1 2] x1 + [1] 207.84/60.05 [0 1] [2] 207.84/60.05 = [q2(1(x1))] 207.84/60.05 207.84/60.05 [0(q1(x1))] = [1 2] x1 + [1] 207.84/60.05 [0 1] [2] 207.84/60.05 >= [1 2] x1 + [1] 207.84/60.05 [0 1] [2] 207.84/60.05 = [q2(1(x1))] 207.84/60.05 207.84/60.05 [0(q2(x1))] = [1 1] x1 + [1] 207.84/60.05 [0 1] [2] 207.84/60.05 >= [1 1] x1 + [1] 207.84/60.05 [0 1] [2] 207.84/60.05 = [0(q0(x1))] 207.84/60.05 207.84/60.05 207.84/60.05 We return to the main proof. 207.84/60.05 207.84/60.05 We are left with following problem, upon which TcT provides the 207.84/60.05 certificate YES(O(1),O(1)). 207.84/60.05 207.84/60.05 Weak Trs: 207.84/60.05 { 1(q0(1(x1))) -> 0(1(q1(x1))) 207.84/60.05 , 1(q0(0(x1))) -> 0(0(q1(x1))) 207.84/60.05 , 1(q1(1(x1))) -> 1(1(q1(x1))) 207.84/60.05 , 1(q1(0(x1))) -> 1(0(q1(x1))) 207.84/60.05 , 1(q2(x1)) -> q2(1(x1)) 207.84/60.05 , 0(q1(x1)) -> q2(1(x1)) 207.84/60.05 , 0(q2(x1)) -> 0(q0(x1)) } 207.84/60.05 Obligation: 207.84/60.05 derivational complexity 207.84/60.05 Answer: 207.84/60.05 YES(O(1),O(1)) 207.84/60.05 207.84/60.05 Empty rules are trivially bounded 207.84/60.05 207.84/60.05 Hurray, we answered YES(O(1),O(n^2)) 207.84/60.06 EOF