0.00/0.14 YES 0.00/0.14 0.00/0.14 Problem 1: 0.00/0.14 0.00/0.14 (VAR x) 0.00/0.14 (STRATEGY CONTEXTSENSITIVE 0.00/0.14 (*top*_0 1) 0.00/0.14 (f_0 1) 0.00/0.14 (f_1) 0.00/0.14 (a_1) 0.00/0.14 (c_0) 0.00/0.14 ) 0.00/0.14 (RULES 0.00/0.14 *top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1))) 0.00/0.14 *top*_0(a_1) -> *top*_0(f_0(a_1)) 0.00/0.14 f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1)))) 0.00/0.14 f_1(f_0(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_1(x)))) -> c_0 0.00/0.14 ) 0.00/0.14 0.00/0.14 Problem 1: 0.00/0.14 0.00/0.14 Dependency Pairs Processor: 0.00/0.14 -> Pairs: 0.00/0.14 *TOP*_0(f_0(f_0(a_1))) -> *TOP*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *TOP*_0(f_0(f_0(a_1))) -> F_0(f_0(f_0(a_1))) 0.00/0.14 *TOP*_0(f_0(a_1)) -> *TOP*_0(f_0(f_0(a_1))) 0.00/0.14 *TOP*_0(a_1) -> *TOP*_0(f_0(a_1)) 0.00/0.14 F_0(f_0(f_0(a_1))) -> F_1(f_0(f_0(f_0(a_1)))) 0.00/0.14 -> Rules: 0.00/0.14 *top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1))) 0.00/0.14 *top*_0(a_1) -> *top*_0(f_0(a_1)) 0.00/0.14 f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1)))) 0.00/0.14 f_1(f_0(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_1(x)))) -> c_0 0.00/0.14 -> Unhiding Rules: 0.00/0.14 Empty 0.00/0.14 0.00/0.14 Problem 1: 0.00/0.14 0.00/0.14 SCC Processor: 0.00/0.14 -> Pairs: 0.00/0.14 *TOP*_0(f_0(f_0(a_1))) -> *TOP*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *TOP*_0(f_0(f_0(a_1))) -> F_0(f_0(f_0(a_1))) 0.00/0.14 *TOP*_0(f_0(a_1)) -> *TOP*_0(f_0(f_0(a_1))) 0.00/0.14 *TOP*_0(a_1) -> *TOP*_0(f_0(a_1)) 0.00/0.14 F_0(f_0(f_0(a_1))) -> F_1(f_0(f_0(f_0(a_1)))) 0.00/0.14 -> Rules: 0.00/0.14 *top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1))) 0.00/0.14 *top*_0(a_1) -> *top*_0(f_0(a_1)) 0.00/0.14 f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1)))) 0.00/0.14 f_1(f_0(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_1(x)))) -> c_0 0.00/0.14 -> Unhiding rules: 0.00/0.14 Empty 0.00/0.14 ->Strongly Connected Components: 0.00/0.14 ->->Cycle: 0.00/0.14 ->->-> Pairs: 0.00/0.14 *TOP*_0(f_0(f_0(a_1))) -> *TOP*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *TOP*_0(f_0(a_1)) -> *TOP*_0(f_0(f_0(a_1))) 0.00/0.14 *TOP*_0(a_1) -> *TOP*_0(f_0(a_1)) 0.00/0.14 ->->-> Rules: 0.00/0.14 *top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1))) 0.00/0.14 *top*_0(a_1) -> *top*_0(f_0(a_1)) 0.00/0.14 f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1)))) 0.00/0.14 f_1(f_0(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_1(x)))) -> c_0 0.00/0.14 ->->-> Unhiding rules: 0.00/0.14 Empty 0.00/0.14 0.00/0.14 Problem 1: 0.00/0.14 0.00/0.14 Reduction Pairs Processor: 0.00/0.14 -> Pairs: 0.00/0.14 *TOP*_0(f_0(f_0(a_1))) -> *TOP*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *TOP*_0(f_0(a_1)) -> *TOP*_0(f_0(f_0(a_1))) 0.00/0.14 *TOP*_0(a_1) -> *TOP*_0(f_0(a_1)) 0.00/0.14 -> Rules: 0.00/0.14 *top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1))) 0.00/0.14 *top*_0(a_1) -> *top*_0(f_0(a_1)) 0.00/0.14 f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1)))) 0.00/0.14 f_1(f_0(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_1(x)))) -> c_0 0.00/0.14 -> Unhiding rules: 0.00/0.14 Empty 0.00/0.14 -> Usable rules: 0.00/0.14 f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1)))) 0.00/0.14 f_1(f_0(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_1(x)))) -> c_0 0.00/0.14 ->Interpretation type: 0.00/0.14 Linear 0.00/0.14 ->Coefficients: 0.00/0.14 Natural Numbers 0.00/0.14 ->Dimension: 0.00/0.14 1 0.00/0.14 ->Bound: 0.00/0.14 2 0.00/0.14 ->Interpretation: 0.00/0.14 0.00/0.14 [f_0](X) = 1 0.00/0.14 [f_1](X) = 1 0.00/0.14 [a_1] = 2 0.00/0.14 [c_0] = 1 0.00/0.14 [*TOP*_0](X) = 2.X 0.00/0.14 0.00/0.14 Problem 1: 0.00/0.14 0.00/0.14 SCC Processor: 0.00/0.14 -> Pairs: 0.00/0.14 *TOP*_0(f_0(f_0(a_1))) -> *TOP*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *TOP*_0(f_0(a_1)) -> *TOP*_0(f_0(f_0(a_1))) 0.00/0.14 -> Rules: 0.00/0.14 *top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1))) 0.00/0.14 *top*_0(a_1) -> *top*_0(f_0(a_1)) 0.00/0.14 f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1)))) 0.00/0.14 f_1(f_0(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_1(x)))) -> c_0 0.00/0.14 -> Unhiding rules: 0.00/0.14 Empty 0.00/0.14 ->Strongly Connected Components: 0.00/0.14 ->->Cycle: 0.00/0.14 ->->-> Pairs: 0.00/0.14 *TOP*_0(f_0(f_0(a_1))) -> *TOP*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *TOP*_0(f_0(a_1)) -> *TOP*_0(f_0(f_0(a_1))) 0.00/0.14 ->->-> Rules: 0.00/0.14 *top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1))) 0.00/0.14 *top*_0(a_1) -> *top*_0(f_0(a_1)) 0.00/0.14 f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1)))) 0.00/0.14 f_1(f_0(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_1(x)))) -> c_0 0.00/0.14 ->->-> Unhiding rules: 0.00/0.14 Empty 0.00/0.14 0.00/0.14 Problem 1: 0.00/0.14 0.00/0.14 Reduction Pairs Processor: 0.00/0.14 -> Pairs: 0.00/0.14 *TOP*_0(f_0(f_0(a_1))) -> *TOP*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *TOP*_0(f_0(a_1)) -> *TOP*_0(f_0(f_0(a_1))) 0.00/0.14 -> Rules: 0.00/0.14 *top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1))) 0.00/0.14 *top*_0(a_1) -> *top*_0(f_0(a_1)) 0.00/0.14 f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1)))) 0.00/0.14 f_1(f_0(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_1(x)))) -> c_0 0.00/0.14 -> Unhiding rules: 0.00/0.14 Empty 0.00/0.14 -> Usable rules: 0.00/0.14 f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1)))) 0.00/0.14 f_1(f_0(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_1(x)))) -> c_0 0.00/0.14 ->Interpretation type: 0.00/0.14 Linear 0.00/0.14 ->Coefficients: 0.00/0.14 All rationals 0.00/0.14 ->Dimension: 0.00/0.14 1 0.00/0.14 ->Bound: 0.00/0.14 2 0.00/0.14 ->Interpretation: 0.00/0.14 0.00/0.14 [f_0](X) = 1/2.X + 1/2 0.00/0.14 [f_1](X) = 0 0.00/0.14 [a_1] = 2 0.00/0.14 [c_0] = 0 0.00/0.14 [*TOP*_0](X) = 1/2.X 0.00/0.14 0.00/0.14 Problem 1: 0.00/0.14 0.00/0.14 SCC Processor: 0.00/0.14 -> Pairs: 0.00/0.14 *TOP*_0(f_0(a_1)) -> *TOP*_0(f_0(f_0(a_1))) 0.00/0.14 -> Rules: 0.00/0.14 *top*_0(f_0(f_0(a_1))) -> *top*_0(f_0(f_0(f_0(a_1)))) 0.00/0.14 *top*_0(f_0(a_1)) -> *top*_0(f_0(f_0(a_1))) 0.00/0.14 *top*_0(a_1) -> *top*_0(f_0(a_1)) 0.00/0.14 f_0(f_0(f_0(a_1))) -> f_1(f_0(f_0(f_0(a_1)))) 0.00/0.14 f_1(f_0(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_0(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_0(x)))) -> c_0 0.00/0.14 f_1(f_1(f_1(f_1(x)))) -> c_0 0.00/0.14 -> Unhiding rules: 0.00/0.14 Empty 0.00/0.14 ->Strongly Connected Components: 0.00/0.14 There is no strongly connected component 0.00/0.14 0.00/0.14 The problem is finite. 0.00/0.14 EOF