0.00/0.05 YES 0.00/0.05 0.00/0.05 Problem 1: 0.00/0.05 0.00/0.05 (VAR x) 0.00/0.05 (STRATEGY CONTEXTSENSITIVE 0.00/0.05 (*top*_0 1) 0.00/0.05 (f_0 1) 0.00/0.05 (f_1) 0.00/0.05 (g_1) 0.00/0.05 (a_0) 0.00/0.05 (b_0) 0.00/0.05 ) 0.00/0.05 (RULES 0.00/0.05 *top*_0(g_1(x)) -> *top*_0(f_0(g_1(x))) 0.00/0.05 f_0(g_1(x)) -> f_1(f_0(g_1(x))) 0.00/0.05 f_1(f_0(x)) -> b_0 0.00/0.05 f_1(f_1(x)) -> b_0 0.00/0.05 f_1(g_1(a_0)) -> a_0 0.00/0.05 g_1(x) -> f_1(g_1(x)) 0.00/0.05 ) 0.00/0.05 0.00/0.05 Problem 1: 0.00/0.05 0.00/0.05 Dependency Pairs Processor: 0.00/0.05 -> Pairs: 0.00/0.05 *TOP*_0(g_1(x)) -> *TOP*_0(f_0(g_1(x))) 0.00/0.05 *TOP*_0(g_1(x)) -> F_0(g_1(x)) 0.00/0.05 F_0(g_1(x)) -> F_1(f_0(g_1(x))) 0.00/0.05 G_1(x) -> F_1(g_1(x)) 0.00/0.05 -> Rules: 0.00/0.05 *top*_0(g_1(x)) -> *top*_0(f_0(g_1(x))) 0.00/0.05 f_0(g_1(x)) -> f_1(f_0(g_1(x))) 0.00/0.05 f_1(f_0(x)) -> b_0 0.00/0.05 f_1(f_1(x)) -> b_0 0.00/0.05 f_1(g_1(a_0)) -> a_0 0.00/0.05 g_1(x) -> f_1(g_1(x)) 0.00/0.05 -> Unhiding Rules: 0.00/0.05 Empty 0.00/0.05 0.00/0.05 Problem 1: 0.00/0.05 0.00/0.05 SCC Processor: 0.00/0.05 -> Pairs: 0.00/0.05 *TOP*_0(g_1(x)) -> *TOP*_0(f_0(g_1(x))) 0.00/0.05 *TOP*_0(g_1(x)) -> F_0(g_1(x)) 0.00/0.05 F_0(g_1(x)) -> F_1(f_0(g_1(x))) 0.00/0.05 G_1(x) -> F_1(g_1(x)) 0.00/0.05 -> Rules: 0.00/0.05 *top*_0(g_1(x)) -> *top*_0(f_0(g_1(x))) 0.00/0.05 f_0(g_1(x)) -> f_1(f_0(g_1(x))) 0.00/0.05 f_1(f_0(x)) -> b_0 0.00/0.05 f_1(f_1(x)) -> b_0 0.00/0.05 f_1(g_1(a_0)) -> a_0 0.00/0.05 g_1(x) -> f_1(g_1(x)) 0.00/0.05 -> Unhiding rules: 0.00/0.05 Empty 0.00/0.05 ->Strongly Connected Components: 0.00/0.05 ->->Cycle: 0.00/0.05 ->->-> Pairs: 0.00/0.05 *TOP*_0(g_1(x)) -> *TOP*_0(f_0(g_1(x))) 0.00/0.05 ->->-> Rules: 0.00/0.05 *top*_0(g_1(x)) -> *top*_0(f_0(g_1(x))) 0.00/0.05 f_0(g_1(x)) -> f_1(f_0(g_1(x))) 0.00/0.05 f_1(f_0(x)) -> b_0 0.00/0.05 f_1(f_1(x)) -> b_0 0.00/0.05 f_1(g_1(a_0)) -> a_0 0.00/0.05 g_1(x) -> f_1(g_1(x)) 0.00/0.05 ->->-> Unhiding rules: 0.00/0.05 Empty 0.00/0.05 0.00/0.05 Problem 1: 0.00/0.05 0.00/0.05 Reduction Pairs Processor: 0.00/0.05 -> Pairs: 0.00/0.05 *TOP*_0(g_1(x)) -> *TOP*_0(f_0(g_1(x))) 0.00/0.05 -> Rules: 0.00/0.05 *top*_0(g_1(x)) -> *top*_0(f_0(g_1(x))) 0.00/0.05 f_0(g_1(x)) -> f_1(f_0(g_1(x))) 0.00/0.05 f_1(f_0(x)) -> b_0 0.00/0.05 f_1(f_1(x)) -> b_0 0.00/0.05 f_1(g_1(a_0)) -> a_0 0.00/0.05 g_1(x) -> f_1(g_1(x)) 0.00/0.05 -> Unhiding rules: 0.00/0.05 Empty 0.00/0.05 -> Usable rules: 0.00/0.05 f_0(g_1(x)) -> f_1(f_0(g_1(x))) 0.00/0.05 f_1(f_0(x)) -> b_0 0.00/0.05 f_1(f_1(x)) -> b_0 0.00/0.05 f_1(g_1(a_0)) -> a_0 0.00/0.05 g_1(x) -> f_1(g_1(x)) 0.00/0.05 ->Interpretation type: 0.00/0.05 Linear 0.00/0.05 ->Coefficients: 0.00/0.05 Natural Numbers 0.00/0.05 ->Dimension: 0.00/0.05 1 0.00/0.05 ->Bound: 0.00/0.05 2 0.00/0.05 ->Interpretation: 0.00/0.05 0.00/0.05 [f_0](X) = 1 0.00/0.05 [f_1](X) = X 0.00/0.05 [g_1](X) = X + 2 0.00/0.05 [a_0] = 1 0.00/0.05 [b_0] = 0 0.00/0.05 [*TOP*_0](X) = 2.X 0.00/0.05 0.00/0.05 Problem 1: 0.00/0.05 0.00/0.05 Basic Processor: 0.00/0.05 -> Pairs: 0.00/0.05 Empty 0.00/0.05 -> Rules: 0.00/0.05 *top*_0(g_1(x)) -> *top*_0(f_0(g_1(x))) 0.00/0.05 f_0(g_1(x)) -> f_1(f_0(g_1(x))) 0.00/0.05 f_1(f_0(x)) -> b_0 0.00/0.05 f_1(f_1(x)) -> b_0 0.00/0.05 f_1(g_1(a_0)) -> a_0 0.00/0.05 g_1(x) -> f_1(g_1(x)) 0.00/0.05 -> Unhiding rules: 0.00/0.05 Empty 0.00/0.05 -> Result: 0.00/0.05 Set P is empty 0.00/0.05 0.00/0.05 The problem is finite. 0.00/0.05 EOF