0.00/0.20 YES 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 (VAR x y) 0.00/0.20 (THEORY 0.00/0.20 (AC f)) 0.00/0.20 (RULES 0.00/0.20 f(g(f(h(a),a)),a) -> f(h(a),f(a,a)) 0.00/0.20 f(g(h(a)),f(f(a,a),a)) -> f(g(f(h(a),a)),a) 0.00/0.20 f(h(a),a) -> f(h(a),b) 0.00/0.20 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.20 f(i(x,y),f(a,y)) -> f(g(i(x,y)),y) 0.00/0.20 ) 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 Reduction Order Processor: 0.00/0.20 -> Rules: 0.00/0.20 f(g(f(h(a),a)),a) -> f(h(a),f(a,a)) 0.00/0.20 f(g(h(a)),f(f(a,a),a)) -> f(g(f(h(a),a)),a) 0.00/0.20 f(h(a),a) -> f(h(a),b) 0.00/0.20 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.20 f(i(x,y),f(a,y)) -> f(g(i(x,y)),y) 0.00/0.20 ->Interpretation type: 0.00/0.20 Linear 0.00/0.20 ->Coefficients: 0.00/0.20 Natural Numbers 0.00/0.20 ->Dimension: 0.00/0.20 1 0.00/0.20 ->Bound: 0.00/0.20 2 0.00/0.20 ->Interpretation: 0.00/0.20 0.00/0.20 [f](X1,X2) = X1 + X2 0.00/0.20 [a] = 2 0.00/0.20 [b] = 2 0.00/0.20 [g](X) = X + 1 0.00/0.20 [h](X) = 2.X + 2 0.00/0.20 [i](X1,X2) = 2.X1 + X2 + 1 0.00/0.20 0.00/0.20 Problem 1: 0.00/0.20 0.00/0.20 Reduction Order Processor: 0.00/0.20 -> Rules: 0.00/0.20 f(g(h(a)),f(f(a,a),a)) -> f(g(f(h(a),a)),a) 0.00/0.20 f(h(a),a) -> f(h(a),b) 0.00/0.20 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.20 f(i(x,y),f(a,y)) -> f(g(i(x,y)),y) 0.00/0.20 ->Interpretation type: 0.00/0.20 Linear 0.00/0.20 ->Coefficients: 0.00/0.20 Natural Numbers 0.00/0.20 ->Dimension: 0.00/0.20 1 0.00/0.20 ->Bound: 0.00/0.20 2 0.00/0.20 ->Interpretation: 0.00/0.20 0.00/0.20 [f](X1,X2) = X1 + X2 + 2 0.00/0.20 [a] = 2 0.00/0.20 [b] = 0 0.00/0.20 [g](X) = X + 2 0.00/0.20 [h](X) = 2.X + 2 0.00/0.20 [i](X1,X2) = 2.X1 + X2 + 1 0.00/0.21 0.00/0.21 Problem 1: 0.00/0.21 0.00/0.21 Reduction Order Processor: 0.00/0.21 -> Rules: 0.00/0.21 f(h(a),a) -> f(h(a),b) 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 f(i(x,y),f(a,y)) -> f(g(i(x,y)),y) 0.00/0.21 ->Interpretation type: 0.00/0.21 Linear 0.00/0.21 ->Coefficients: 0.00/0.21 Natural Numbers 0.00/0.21 ->Dimension: 0.00/0.21 1 0.00/0.21 ->Bound: 0.00/0.21 2 0.00/0.21 ->Interpretation: 0.00/0.21 0.00/0.21 [f](X1,X2) = X1 + X2 + 2 0.00/0.21 [a] = 1 0.00/0.21 [b] = 0 0.00/0.21 [g](X) = X + 2 0.00/0.21 [h](X) = X + 2 0.00/0.21 [i](X1,X2) = X1 + 2.X2 0.00/0.21 0.00/0.21 Problem 1: 0.00/0.21 0.00/0.21 Reduction Order Processor: 0.00/0.21 -> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 f(i(x,y),f(a,y)) -> f(g(i(x,y)),y) 0.00/0.21 ->Interpretation type: 0.00/0.21 Linear 0.00/0.21 ->Coefficients: 0.00/0.21 Natural Numbers 0.00/0.21 ->Dimension: 0.00/0.21 1 0.00/0.21 ->Bound: 0.00/0.21 2 0.00/0.21 ->Interpretation: 0.00/0.21 0.00/0.21 [f](X1,X2) = X1 + X2 + 2 0.00/0.21 [a] = 1 0.00/0.21 [b] = 0 0.00/0.21 [g](X) = X + 2 0.00/0.21 [h](X) = X 0.00/0.21 [i](X1,X2) = X1 + X2 0.00/0.21 0.00/0.21 Problem 1: 0.00/0.21 0.00/0.21 Dependency Pairs Processor: 0.00/0.21 -> FAxioms: 0.00/0.21 F(f(x2,x3),x4) = F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) = F(x3,x2) 0.00/0.21 -> Pairs: 0.00/0.21 F(f(h(a),g(a)),x2) -> F(f(g(h(a)),a),x2) 0.00/0.21 F(f(h(a),g(a)),x2) -> F(g(h(a)),a) 0.00/0.21 F(h(a),g(a)) -> F(g(h(a)),a) 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(f(x2,x3),x4) -> F(x2,x3) 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 0.00/0.21 Problem 1: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> FAxioms: 0.00/0.21 F(f(x2,x3),x4) = F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) = F(x3,x2) 0.00/0.21 -> Pairs: 0.00/0.21 F(f(h(a),g(a)),x2) -> F(f(g(h(a)),a),x2) 0.00/0.21 F(f(h(a),g(a)),x2) -> F(g(h(a)),a) 0.00/0.21 F(h(a),g(a)) -> F(g(h(a)),a) 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(f(x2,x3),x4) -> F(x2,x3) 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 ->->Cycle: 0.00/0.21 ->->-> Pairs: 0.00/0.21 F(f(h(a),g(a)),x2) -> F(f(g(h(a)),a),x2) 0.00/0.21 F(f(h(a),g(a)),x2) -> F(g(h(a)),a) 0.00/0.21 F(h(a),g(a)) -> F(g(h(a)),a) 0.00/0.21 -> FAxioms: 0.00/0.21 f(f(x2,x3),x4) -> f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) -> f(x3,x2) 0.00/0.21 F(f(x2,x3),x4) -> F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) -> F(x3,x2) 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 ->->-> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(f(x2,x3),x4) -> F(x2,x3) 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 0.00/0.21 Problem 1: 0.00/0.21 0.00/0.21 Reduction Pairs Processor: 0.00/0.21 -> FAxioms: 0.00/0.21 F(f(x2,x3),x4) = F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) = F(x3,x2) 0.00/0.21 -> Pairs: 0.00/0.21 F(f(h(a),g(a)),x2) -> F(f(g(h(a)),a),x2) 0.00/0.21 F(f(h(a),g(a)),x2) -> F(g(h(a)),a) 0.00/0.21 F(h(a),g(a)) -> F(g(h(a)),a) 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Usable Equations: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> Usable Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(f(x2,x3),x4) -> F(x2,x3) 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 ->Interpretation type: 0.00/0.21 Linear 0.00/0.21 ->Coefficients: 0.00/0.21 Natural Numbers 0.00/0.21 ->Dimension: 0.00/0.21 1 0.00/0.21 ->Bound: 0.00/0.21 2 0.00/0.21 ->Interpretation: 0.00/0.21 0.00/0.21 [f](X1,X2) = X1 + X2 0.00/0.21 [a] = 2 0.00/0.21 [b] = 0 0.00/0.21 [g](X) = 2.X + 1 0.00/0.21 [h](X) = 1 0.00/0.21 [i](X1,X2) = 0 0.00/0.21 [F](X1,X2) = 2.X1 + 2.X2 0.00/0.21 0.00/0.21 Problem 1: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> FAxioms: 0.00/0.21 F(f(x2,x3),x4) = F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) = F(x3,x2) 0.00/0.21 -> Pairs: 0.00/0.21 F(f(h(a),g(a)),x2) -> F(g(h(a)),a) 0.00/0.21 F(h(a),g(a)) -> F(g(h(a)),a) 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(f(x2,x3),x4) -> F(x2,x3) 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 ->->Cycle: 0.00/0.21 ->->-> Pairs: 0.00/0.21 F(f(h(a),g(a)),x2) -> F(g(h(a)),a) 0.00/0.21 F(h(a),g(a)) -> F(g(h(a)),a) 0.00/0.21 -> FAxioms: 0.00/0.21 f(f(x2,x3),x4) -> f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) -> f(x3,x2) 0.00/0.21 F(f(x2,x3),x4) -> F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) -> F(x3,x2) 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 ->->-> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(f(x2,x3),x4) -> F(x2,x3) 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 0.00/0.21 Problem 1: 0.00/0.21 0.00/0.21 Reduction Pairs Processor: 0.00/0.21 -> FAxioms: 0.00/0.21 F(f(x2,x3),x4) = F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) = F(x3,x2) 0.00/0.21 -> Pairs: 0.00/0.21 F(f(h(a),g(a)),x2) -> F(g(h(a)),a) 0.00/0.21 F(h(a),g(a)) -> F(g(h(a)),a) 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Usable Equations: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> Usable Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(f(x2,x3),x4) -> F(x2,x3) 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 ->Interpretation type: 0.00/0.21 Linear 0.00/0.21 ->Coefficients: 0.00/0.21 Natural Numbers 0.00/0.21 ->Dimension: 0.00/0.21 1 0.00/0.21 ->Bound: 0.00/0.21 2 0.00/0.21 ->Interpretation: 0.00/0.21 0.00/0.21 [f](X1,X2) = X1 + X2 + 2 0.00/0.21 [a] = 1 0.00/0.21 [b] = 0 0.00/0.21 [g](X) = X 0.00/0.21 [h](X) = X + 1 0.00/0.21 [i](X1,X2) = 0 0.00/0.21 [F](X1,X2) = 2.X1 + 2.X2 0.00/0.21 0.00/0.21 Problem 1: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> FAxioms: 0.00/0.21 F(f(x2,x3),x4) = F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) = F(x3,x2) 0.00/0.21 -> Pairs: 0.00/0.21 F(h(a),g(a)) -> F(g(h(a)),a) 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(f(x2,x3),x4) -> F(x2,x3) 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 ->->Cycle: 0.00/0.21 ->->-> Pairs: 0.00/0.21 F(h(a),g(a)) -> F(g(h(a)),a) 0.00/0.21 -> FAxioms: 0.00/0.21 f(f(x2,x3),x4) -> f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) -> f(x3,x2) 0.00/0.21 F(f(x2,x3),x4) -> F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) -> F(x3,x2) 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 ->->-> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(f(x2,x3),x4) -> F(x2,x3) 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 0.00/0.21 Problem 1: 0.00/0.21 0.00/0.21 Reduction Pairs Processor: 0.00/0.21 -> FAxioms: 0.00/0.21 F(f(x2,x3),x4) = F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) = F(x3,x2) 0.00/0.21 -> Pairs: 0.00/0.21 F(h(a),g(a)) -> F(g(h(a)),a) 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Usable Equations: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> Usable Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(f(x2,x3),x4) -> F(x2,x3) 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 ->Interpretation type: 0.00/0.21 Linear 0.00/0.21 ->Coefficients: 0.00/0.21 Natural Numbers 0.00/0.21 ->Dimension: 0.00/0.21 1 0.00/0.21 ->Bound: 0.00/0.21 2 0.00/0.21 ->Interpretation: 0.00/0.21 0.00/0.21 [f](X1,X2) = X1 + X2 + 1 0.00/0.21 [a] = 1 0.00/0.21 [b] = 0 0.00/0.21 [g](X) = X + 2 0.00/0.21 [h](X) = X + 1 0.00/0.21 [i](X1,X2) = 0 0.00/0.21 [F](X1,X2) = X1 + X2 0.00/0.21 0.00/0.21 Problem 1: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> FAxioms: 0.00/0.21 F(f(x2,x3),x4) = F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) = F(x3,x2) 0.00/0.21 -> Pairs: 0.00/0.21 F(h(a),g(a)) -> F(g(h(a)),a) 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 ->->Cycle: 0.00/0.21 ->->-> Pairs: 0.00/0.21 F(h(a),g(a)) -> F(g(h(a)),a) 0.00/0.21 -> FAxioms: 0.00/0.21 f(f(x2,x3),x4) -> f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) -> f(x3,x2) 0.00/0.21 F(f(x2,x3),x4) -> F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) -> F(x3,x2) 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 ->->-> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 0.00/0.21 Problem 1: 0.00/0.21 0.00/0.21 Reduction Pairs Processor: 0.00/0.21 -> FAxioms: 0.00/0.21 F(f(x2,x3),x4) = F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) = F(x3,x2) 0.00/0.21 -> Pairs: 0.00/0.21 F(h(a),g(a)) -> F(g(h(a)),a) 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Usable Equations: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> Usable Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 ->Interpretation type: 0.00/0.21 Linear 0.00/0.21 ->Coefficients: 0.00/0.21 Natural Numbers 0.00/0.21 ->Dimension: 0.00/0.21 1 0.00/0.21 ->Bound: 0.00/0.21 2 0.00/0.21 ->Interpretation: 0.00/0.21 0.00/0.21 [f](X1,X2) = X1 + X2 0.00/0.21 [a] = 2 0.00/0.21 [b] = 0 0.00/0.21 [g](X) = 2.X 0.00/0.21 [h](X) = 1 0.00/0.21 [i](X1,X2) = 0 0.00/0.21 [F](X1,X2) = 2.X1 + 2.X2 0.00/0.21 0.00/0.21 Problem 1: 0.00/0.21 0.00/0.21 SCC Processor: 0.00/0.21 -> FAxioms: 0.00/0.21 F(f(x2,x3),x4) = F(x2,f(x3,x4)) 0.00/0.21 F(x2,x3) = F(x3,x2) 0.00/0.21 -> Pairs: 0.00/0.21 Empty 0.00/0.21 -> EAxioms: 0.00/0.21 f(f(x2,x3),x4) = f(x2,f(x3,x4)) 0.00/0.21 f(x2,x3) = f(x3,x2) 0.00/0.21 -> Rules: 0.00/0.21 f(h(a),g(a)) -> f(g(h(a)),a) 0.00/0.21 -> SRules: 0.00/0.21 F(x2,f(x3,x4)) -> F(x3,x4) 0.00/0.21 ->Strongly Connected Components: 0.00/0.21 There is no strongly connected component 0.00/0.21 0.00/0.21 The problem is finite. 0.00/0.21 EOF