0.00/0.04 YES 0.00/0.04 0.00/0.04 Problem 1: 0.00/0.04 0.00/0.04 (VAR x y) 0.00/0.04 (STRATEGY CONTEXTSENSITIVE 0.00/0.04 (f_1) 0.00/0.04 (g_1) 0.00/0.04 (a_0) 0.00/0.04 (i_0 1) 0.00/0.04 ) 0.00/0.04 (RULES 0.00/0.04 f_1(i_0(x),i_0(g_1(x))) -> a_0 0.00/0.04 f_1(x,i_0(x)) -> f_1(x,x) 0.00/0.04 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x))) 0.00/0.04 f_1(x,y) -> x 0.00/0.04 g_1(x) -> i_0(x) 0.00/0.04 ) 0.00/0.04 0.00/0.04 Problem 1: 0.00/0.04 0.00/0.04 Dependency Pairs Processor: 0.00/0.04 -> Pairs: 0.00/0.04 F_1(x,i_0(x)) -> F_1(x,x) 0.00/0.04 F_1(x,x) -> F_1(i_0(x),g_1(g_1(x))) 0.00/0.04 F_1(x,y) -> x 0.00/0.04 G_1(x) -> x 0.00/0.04 -> Rules: 0.00/0.04 f_1(i_0(x),i_0(g_1(x))) -> a_0 0.00/0.04 f_1(x,i_0(x)) -> f_1(x,x) 0.00/0.04 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x))) 0.00/0.04 f_1(x,y) -> x 0.00/0.04 g_1(x) -> i_0(x) 0.00/0.04 -> Unhiding Rules: 0.00/0.04 g_1(g_1(x)) -> G_1(g_1(x)) 0.00/0.04 i_0(x2) -> x2 0.00/0.04 0.00/0.04 Problem 1: 0.00/0.04 0.00/0.04 SCC Processor: 0.00/0.04 -> Pairs: 0.00/0.04 F_1(x,i_0(x)) -> F_1(x,x) 0.00/0.04 F_1(x,x) -> F_1(i_0(x),g_1(g_1(x))) 0.00/0.04 F_1(x,y) -> x 0.00/0.04 G_1(x) -> x 0.00/0.04 -> Rules: 0.00/0.04 f_1(i_0(x),i_0(g_1(x))) -> a_0 0.00/0.04 f_1(x,i_0(x)) -> f_1(x,x) 0.00/0.04 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x))) 0.00/0.04 f_1(x,y) -> x 0.00/0.04 g_1(x) -> i_0(x) 0.00/0.04 -> Unhiding rules: 0.00/0.04 g_1(g_1(x)) -> G_1(g_1(x)) 0.00/0.04 i_0(x2) -> x2 0.00/0.04 ->Strongly Connected Components: 0.00/0.04 ->->Cycle: 0.00/0.04 ->->-> Pairs: 0.00/0.04 G_1(x) -> x 0.00/0.04 ->->-> Rules: 0.00/0.04 f_1(i_0(x),i_0(g_1(x))) -> a_0 0.00/0.04 f_1(x,i_0(x)) -> f_1(x,x) 0.00/0.04 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x))) 0.00/0.04 f_1(x,y) -> x 0.00/0.04 g_1(x) -> i_0(x) 0.00/0.04 ->->-> Unhiding rules: 0.00/0.04 g_1(g_1(x)) -> G_1(g_1(x)) 0.00/0.04 i_0(x2) -> x2 0.00/0.04 0.00/0.04 Problem 1: 0.00/0.04 0.00/0.04 Reduction Pairs Processor: 0.00/0.04 -> Pairs: 0.00/0.04 G_1(x) -> x 0.00/0.04 -> Rules: 0.00/0.04 f_1(i_0(x),i_0(g_1(x))) -> a_0 0.00/0.04 f_1(x,i_0(x)) -> f_1(x,x) 0.00/0.04 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x))) 0.00/0.04 f_1(x,y) -> x 0.00/0.04 g_1(x) -> i_0(x) 0.00/0.04 -> Unhiding rules: 0.00/0.04 g_1(g_1(x)) -> G_1(g_1(x)) 0.00/0.04 i_0(x2) -> x2 0.00/0.04 -> Usable rules: 0.00/0.04 g_1(x) -> i_0(x) 0.00/0.04 ->Interpretation type: 0.00/0.04 Linear 0.00/0.04 ->Coefficients: 0.00/0.04 Natural Numbers 0.00/0.04 ->Dimension: 0.00/0.04 1 0.00/0.04 ->Bound: 0.00/0.04 2 0.00/0.04 ->Interpretation: 0.00/0.04 0.00/0.04 [g_1](X) = 2.X + 2 0.00/0.04 [i_0](X) = 2.X 0.00/0.04 [G_1](X) = 2.X + 2 0.00/0.04 0.00/0.04 Problem 1: 0.00/0.04 0.00/0.04 Basic Processor: 0.00/0.04 -> Pairs: 0.00/0.04 Empty 0.00/0.04 -> Rules: 0.00/0.04 f_1(i_0(x),i_0(g_1(x))) -> a_0 0.00/0.04 f_1(x,i_0(x)) -> f_1(x,x) 0.00/0.04 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x))) 0.00/0.04 f_1(x,y) -> x 0.00/0.04 g_1(x) -> i_0(x) 0.00/0.04 -> Unhiding rules: 0.00/0.04 g_1(g_1(x)) -> G_1(g_1(x)) 0.00/0.04 i_0(x2) -> x2 0.00/0.04 -> Result: 0.00/0.04 Set P is empty 0.00/0.04 0.00/0.04 The problem is finite. 0.00/0.04 EOF