0.00/0.09 YES 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 (VAR x x0 y z) 0.00/0.09 (STRATEGY CONTEXTSENSITIVE 0.00/0.09 (*top*_0 1) 0.00/0.09 (f_0 1 2) 0.00/0.09 (f_1) 0.00/0.09 (a_1) 0.00/0.09 (c_0) 0.00/0.09 ) 0.00/0.09 (RULES 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 ) 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 Dependency Pairs Processor: 0.00/0.09 -> Pairs: 0.00/0.09 *TOP*_0(a_1) -> *TOP*_0(f_0(a_1,a_1)) 0.00/0.09 *TOP*_0(a_1) -> F_0(a_1,a_1) 0.00/0.09 F_0(a_1,x0) -> F_1(f_0(a_1,a_1),x0) 0.00/0.09 F_0(x0,a_1) -> F_1(x0,f_0(a_1,a_1)) 0.00/0.09 F_1(x,f_0(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 -> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 -> Unhiding Rules: 0.00/0.09 Empty 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 *TOP*_0(a_1) -> *TOP*_0(f_0(a_1,a_1)) 0.00/0.09 *TOP*_0(a_1) -> F_0(a_1,a_1) 0.00/0.09 F_0(a_1,x0) -> F_1(f_0(a_1,a_1),x0) 0.00/0.09 F_0(x0,a_1) -> F_1(x0,f_0(a_1,a_1)) 0.00/0.09 F_1(x,f_0(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 -> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 -> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 F_1(x,f_0(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 ->->-> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 ->->-> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 *TOP*_0(a_1) -> *TOP*_0(f_0(a_1,a_1)) 0.00/0.09 ->->-> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 ->->-> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 0.00/0.09 0.00/0.09 The problem is decomposed in 2 subproblems. 0.00/0.09 0.00/0.09 Problem 1.1: 0.00/0.09 0.00/0.09 Reduction Pairs Processor: 0.00/0.09 -> Pairs: 0.00/0.09 F_1(x,f_0(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 -> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 -> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 -> Usable rules: 0.00/0.09 Empty 0.00/0.09 ->Interpretation type: 0.00/0.09 Linear 0.00/0.09 ->Coefficients: 0.00/0.09 Natural Numbers 0.00/0.09 ->Dimension: 0.00/0.09 1 0.00/0.09 ->Bound: 0.00/0.09 2 0.00/0.09 ->Interpretation: 0.00/0.09 0.00/0.09 [f_0](X1,X2) = X1 + 2.X2 + 2 0.00/0.09 [f_1](X1,X2) = X1 + 2.X2 + 2 0.00/0.09 [F_1](X1,X2) = X1 + 2.X2 0.00/0.09 0.00/0.09 Problem 1.1: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 -> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 -> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 ->->-> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 ->->-> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 0.00/0.09 Problem 1.1: 0.00/0.09 0.00/0.09 Reduction Pairs Processor: 0.00/0.09 -> Pairs: 0.00/0.09 F_1(x,f_0(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 -> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 -> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 -> Usable rules: 0.00/0.09 Empty 0.00/0.09 ->Interpretation type: 0.00/0.09 Linear 0.00/0.09 ->Coefficients: 0.00/0.09 Natural Numbers 0.00/0.09 ->Dimension: 0.00/0.09 1 0.00/0.09 ->Bound: 0.00/0.09 2 0.00/0.09 ->Interpretation: 0.00/0.09 0.00/0.09 [f_0](X1,X2) = X1 + 2.X2 + 2 0.00/0.09 [f_1](X1,X2) = X1 + X2 + 2 0.00/0.09 [F_1](X1,X2) = X1 + 2.X2 0.00/0.09 0.00/0.09 Problem 1.1: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 -> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 -> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 ->->-> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 ->->-> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 0.00/0.09 Problem 1.1: 0.00/0.09 0.00/0.09 Reduction Pairs Processor: 0.00/0.09 -> Pairs: 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_0(x,y),z) 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 -> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 -> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 -> Usable rules: 0.00/0.09 Empty 0.00/0.09 ->Interpretation type: 0.00/0.09 Linear 0.00/0.09 ->Coefficients: 0.00/0.09 Natural Numbers 0.00/0.09 ->Dimension: 0.00/0.09 1 0.00/0.09 ->Bound: 0.00/0.09 2 0.00/0.09 ->Interpretation: 0.00/0.09 0.00/0.09 [f_0](X1,X2) = 2.X2 + 2 0.00/0.09 [f_1](X1,X2) = X1 + 2.X2 + 2 0.00/0.09 [F_1](X1,X2) = X1 + 2.X2 0.00/0.09 0.00/0.09 Problem 1.1: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 -> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 -> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 ->->-> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 ->->-> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 0.00/0.09 Problem 1.1: 0.00/0.09 0.00/0.09 Reduction Pairs Processor: 0.00/0.09 -> Pairs: 0.00/0.09 F_1(x,f_1(y,z)) -> F_1(f_1(x,y),z) 0.00/0.09 -> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 -> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 -> Usable rules: 0.00/0.09 Empty 0.00/0.09 ->Interpretation type: 0.00/0.09 Linear 0.00/0.09 ->Coefficients: 0.00/0.09 Natural Numbers 0.00/0.09 ->Dimension: 0.00/0.09 1 0.00/0.09 ->Bound: 0.00/0.09 2 0.00/0.09 ->Interpretation: 0.00/0.09 0.00/0.09 [f_1](X1,X2) = X1 + X2 + 1 0.00/0.09 [F_1](X1,X2) = X1 + 2.X2 0.00/0.09 0.00/0.09 Problem 1.1: 0.00/0.09 0.00/0.09 Basic Processor: 0.00/0.09 -> Pairs: 0.00/0.09 Empty 0.00/0.09 -> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 -> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 -> Result: 0.00/0.09 Set P is empty 0.00/0.09 0.00/0.09 The problem is finite. 0.00/0.09 0.00/0.09 Problem 1.2: 0.00/0.09 0.00/0.09 Reduction Pairs Processor: 0.00/0.09 -> Pairs: 0.00/0.09 *TOP*_0(a_1) -> *TOP*_0(f_0(a_1,a_1)) 0.00/0.09 -> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 -> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 -> Usable rules: 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 ->Interpretation type: 0.00/0.09 Linear 0.00/0.09 ->Coefficients: 0.00/0.09 Natural Numbers 0.00/0.09 ->Dimension: 0.00/0.09 1 0.00/0.09 ->Bound: 0.00/0.09 2 0.00/0.09 ->Interpretation: 0.00/0.09 0.00/0.09 [f_0](X1,X2) = 1 0.00/0.09 [f_1](X1,X2) = 0 0.00/0.09 [a_1] = 2 0.00/0.09 [c_0] = 0 0.00/0.09 [*TOP*_0](X) = 2.X 0.00/0.09 0.00/0.09 Problem 1.2: 0.00/0.09 0.00/0.09 Basic Processor: 0.00/0.09 -> Pairs: 0.00/0.09 Empty 0.00/0.09 -> Rules: 0.00/0.09 *top*_0(a_1) -> *top*_0(f_0(a_1,a_1)) 0.00/0.09 f_0(a_1,x0) -> f_1(f_0(a_1,a_1),x0) 0.00/0.09 f_0(x0,a_1) -> f_1(x0,f_0(a_1,a_1)) 0.00/0.09 f_1(f_0(x,y),z) -> c_0 0.00/0.09 f_1(f_1(x,y),z) -> c_0 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_0(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_0(x,y),z) 0.00/0.09 f_1(x,f_1(y,z)) -> f_1(f_1(x,y),z) 0.00/0.09 -> Unhiding rules: 0.00/0.09 Empty 0.00/0.09 -> Result: 0.00/0.09 Set P is empty 0.00/0.09 0.00/0.09 The problem is finite. 0.00/0.09 EOF